Archiv

01.12.2022, 16:00  –  Raum 1.10 Forschungsseminar Differentialgeometrie

Inversion of Radon transform and applications to microlocal regularity

Rubens Longhi (UP)

We aim at extending the classical notion of smooth wavefront set employing the Radon transform in order to capture different degrees of lack of $$\mathcal{F}$$-regularity of a...

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10.11.2022, 16:00  –  Raum 1.10 Forschungsseminar Differentialgeometrie

Seeley's 'Complex Powers of an Elliptic operator'

Alberto Richtsfeld (UP)

In this talk, I will review Seeley's groundbreaking paper 'Complex Powers of an Elliptic Operator'. In this paper, he defines complex powers of an elliptic, classical pseudo-differential operator...

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27.10.2022, 16:00  –  Raum 1.10 Forschungsseminar Differentialgeometrie

Index of Dirac operator on a globally hyperbolic spacetime with timelike boundary

Onirban Islam (UP)

The Atiyah-Singer index theorem is one of the monumental results in Mathematics of the last century. Various extensions of this theorem in the context of Riemannian geometry are available but a...

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20.10.2022, 16:15  –  Raum 1.10 Forschungsseminar Differentialgeometrie

A generalization of the microlocal regularity theorem

Rubens Longhi (UP)

The theorem of microlocal elliptic regularity is useful to determine the singularities of the solution of linear partial differential equations on manifolds. It states that if $$P$$ is a linear...

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28.07.2022, 16:15  –  Raum 0.14 Forschungsseminar Differentialgeometrie

Local index theory for Lorentzian manifolds

Christian Bär

We prove a local version of the index theorem for Dirac-type operators on globally hyperbolic Lorentzian manifolds with Cauchy boundary. In case the Cauchy hypersurface is compact, we do not assume...

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Christian Bär

07.07.2022, 16:00  –  2.09.0.14 Forschungsseminar Differentialgeometrie

Order-preserving isomorphisms of algebras of pseudo-differential operators

Alessandro Contini (Leibniz University Hanover)

In 1971 Egorov proved his famous Theorem, stating that conjugating a pseudo-differential operator with an invertible Fourier Integral Operator produces a new $$\Psi$$DO with the same principal symbol....

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23.06.2022, 16:00  –  Raum 0.14 Forschungsseminar Differentialgeometrie

A Gutzwiller Trace formula for Dirac Operators on a Stationary Spacetime

Onirban Islam

A Duistermaat-Guillemin-Gutzwiller trace formula for a Dirac-type operator D on a globally hyperbolic spatially compact standard stationary spacetime $$(M,g,Z)$$ is achieved by generalising the recent...

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16.06.2022, 16:00  –  Raum 0.14 Forschungsseminar Differentialgeometrie

On the spectrum of the Rarita-Schwinger operator on the Berger Spheres

Peter Grabs (UP)

We look at what might be involved in determining the above.

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19.05.2022, 16:00-17:30  –  2.09.0.14 Forschungsseminar Differentialgeometrie

Non-local boundary conditions for the Dirac operator on spacetimes with timelike boundary

Penelope Gehring

Non-local boundary conditions - for example the Atiyah-Patodi-Singer (APS) conditions -  for Dirac operators on Riemannian manifolds are rather well-understood, while not much is known for such...

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12.05.2022, 16:15-17:45  –  2.09.0.14 Forschungsseminar Differentialgeometrie

Feynman propagators for Wave-type and Dirac-type operators

Onirban Islam

It is a classic result that any normally hyperbolic operator on a globally hyperbolic spacetime admits unique advanced and retarded propagators. With the advent of quantum field theory, a new type of...

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03.03.2022, 16:15  –  2.09.0.12 Forschungsseminar Differentialgeometrie

Why study random Schrödinger operators?

Mehran Seyedhosseini

I will first talk about the relationship between the spectral theory of Schrödinger operators and the dynamical properties of physical systems. I will then motivate the study of the spectral...

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17.02.2022, 16:15  –  Online via zoom Seminar Geometrie

Gromov’s cube conjecture II

Artem Nepechiy

Zoom link available at this moodle.

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14.02.2022, 16:15  –  Raum 0.12 Forschungsseminar Differentialgeometrie

Die Pfaff'sche

Dominik Ulrich

Die Determinante ist eine wichtige Kenngröße quadratischer Matrizen und jeder, der auch nur ein Semester Mathematik studiert hat, hat bereits von ihr gehört. Aber wussten sie zum Beispiel, dass die...

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07.02.2022, 16:15  –  Raum 0.12. Forschungsseminar Differentialgeometrie

Heat expansion and eta invariant for certain non-selfadjoint elliptic operators

Alberto Richtsfeld

In this talk, I will present a slightly generalized version of the Atiyah-Patodi-Singer Index Theorem for Differential Operators with normal adapted boundary operators. This will lead to a version of...

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03.02.2022, 16:15  –  Online via zoom Seminar Geometrie

Gromov’s cube conjecture I

Bernhard Hanke

Zoom link available at this moodle.

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31.01.2022, 16:15  –  2.09.0.12 Forschungsseminar Differentialgeometrie

Wave front sets of different regularity

Rubens Longhi

The usual notion of wavefront set identifies the directions along which a distribution $$u$$ fails to be smooth. We present an equivalent definition that makes use of the Radon transform and which is...

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27.01.2022, 16:15  –  Online via zoom Seminar Geometrie

The band width estimates

Georg Frenck

Zoom link available at this moodle.

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24.01.2022, 16:15  –  Raum 0.12 Forschungsseminar Differentialgeometrie

Die Klassifikation der Kreuzprodukte

Vanessa Hahn (UP)

Die Definition des Kreuzproduktes auf $$\mathbb{R}^3$$ ist uns bekannt. Nun stellen wir uns die Frage, in welchen Dimensionen wir ein solches noch definieren können und welche Eigenschaften dieses...

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17.01.2022, 16:15  –  Online via zoom Forschungsseminar Differentialgeometrie

Møller operators for Dirac fields with MIT boundary conditions

Nicolò Drago (Trento)

Classical and quantum field theories are based on the study of the space of solutions to certain differential operators $$D$$ (e.g. the Dirac operator) on globally hyperbolic spacetimes $$(M,g)$$ -...

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Rubens Longhi

10.01.2022, 16:15  –  2.09.0.12 Forschungsseminar Differentialgeometrie

Hyperelastic material models II

Claudia Grabs

Besides physical assumptions that need to be made on the energy density function of an hyperelastic material, there are several requirements that arise from the mathematical perspective. In order to...

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03.01.2022, 16:15  –  Online via Zoom Forschungsseminar Differentialgeometrie

The stringor representation of the string group

Matthias Ludewig (Regensburg)

We construct a representation for the string group String(d), realized as a strict 2-group, where by “representation” we mean a continuous strict homomorphism into the strict automorphism 2-group of a...

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13.12.2021, 16:15  –  Online via zoom Forschungsseminar Differentialgeometrie

Global hyperbolicity in general relativity and in less regular theories

Ettore Minguzzi (Florence)

I discuss the properties of global hyperbolicity in general relativity and how its definition should be modified under low regularity assumptions.

Zoom access data are available at this moodle.

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09.12.2021, 16:15  –  Raum 2.9.0.12 Seminar Geometrie

Spectral estimates for Callias operators

Alberto Richtsfeld

25.11.2021, 16:15  –  Raum 2.9.0.12 Seminar Geometrie

Index theory for relative Dirac bundles

Jonas Rungenhagen

22.11.2021, 16:15  –  Raum 2.9.0.12 Forschungsseminar Differentialgeometrie

Christian Bär

The Faddeev-LeVerrier algorithm is an algorithm for the computation of the characteristic polynomial of a square matrix. It is slower than Gauss elimination but in contrast to the former it is...

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Penelope Gehring

15.11.2021, 16:15  –  2.09.0.12 Forschungsseminar Differentialgeometrie

Boundary value problems for Dirac Operators on graphs

Alberto Richtsfeld

In this talk, I will present the results of my master’s thesis concerning the index and the spectrum of Dirac operators on metric digraphs, which are subject to general boundary conditions. Relying on...

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11.11.2021, 16:15  –  Online via Zoom Seminar Geometrie

The classical Dirac operator

Helge Frerichs

Zoom link available at this moodle.

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08.11.2021, 16:15  –  2.09.0.12 Forschungsseminar Differentialgeometrie

Hyperelastic material models

Claudia Grabs

An elastic material, for that the stress tensor field of a certain deformation can be derived as gradient tensor field from a scalar potential function (called strain energy density function) is...

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Marten Steuer

01.11.2021, 16:15  –  2.09.0.12 Forschungsseminar Differentialgeometrie

Cauchy problems of the Dirac-Operator on spacetimes with timelike boundary

Penelope Gehring

Global boundary conditions for elliptic first order differential operators on Riemannian manifolds are rather well understood. Bär-Strohmaier introduced APS-conditions for the Lorentzian...

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Rubens Longhi

17.06.2021, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

Analyticity of quasinormal modes in the Kerr and Kerr-de Sitter spacetimes

Quasinormal modes are fundamental in the study of wave equations on black hole spacetimes. In this talk, I will explain why the quasinormal modes in the Kerr and Kerr-de Sitter spacetimes are real...

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03.06.2021, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

An index theorem on asymptotically static spacetimes with compact Cauchy surface

Michał Wrochna (Cergy Paris Université)

A theorem due to Bär and Strohmaier (Amer. J. Math., 141 (5)) says that the Dirac operator on a Lorentzian manifold with compact Cauchy surface is Fredholm if Atiyah-Patodi-Singer boundary conditions...

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27.05.2021, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

A link between the 2D and 3D elastic moduli for isotropic homogeneous elastic materials

Claudia Grabs (UP)

There are many elastic moduli for isotropic elastic materials, such as the bulk modulus and the Youngs modulus, but they all are related to two basic material parameters, namely the Lamé parameters,...

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20.05.2021, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

Scalar and mean curvature comparison via the Dirac operator

Rudolf Zeidler (Universität Münster)

In recent years, Gromov proposed studying the geometry of positive scalar curvature (psc) via various metric inequalities vaguely reminiscent of classical comparison geometry. For instance, let...

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29.04.2021, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

Weyl laws for regular realizations of elliptic operators

Magnus Goffeng (Lund University)

Using a Bär-Ballmann type machinery, one can describe all realizations of elliptic operators on manifolds with boundary. Classically, boundary value problems are phrased in terms of imposing a...

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22.04.2021, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

Graphical decompositions for higher order boundary value problems

Lashi Bandara (UP)

The graphical decomposition for elliptic boundary conditions, obtained by Bär-Ballmann, is an important characterisation of such boundary conditions.
It allows for deformations of these boundary...

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15.04.2021, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

Eigenvalue estimates involving Bessel functions

Georges Habib (Lebanese University Beirut)

Given a compact Riemannian manifold $$(M^n ,g)$$ with smooth boundary $$\partial M$$, we give an estimate for the quotient $$\frac{\int_{\partial M} f dv_g}{\int_M f dv_g}$$ in terms of the Bessel...

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25.03.2021, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

Positive scalar curvature on manifolds with odd order abelian fundamental groups

Bernhard Hanke (Augsburg)

We introduce Riemannian metrics of positive scalar curvature on manifolds with Baas-Sullivan singularities, prove a corresponding homology invariance principle and discuss admissible products. Using...

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18.03.2021, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

Index theorems on non-closed manifolds

Mehran Seyedhosseini (UP)

I will talk about an index theorem of Roe for open manifolds and some of its geometric applications. Along the way, we will encounter localised analytic indices of Connes and Moscovici. I will then...

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11.03.2021, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

Linear wave equations on the Schwarzschild black hole spacetime

Ariane Beier (UP)

The radial part of the scalar wave equation (SWE) on the Schwarzschild spacetime can be interpreted and analysed as a Sturm-Liouville problem. Considering a topological quantum number or fields of...

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11.02.2021, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

About the irreducible Representations of SU(3)

Jonas Rungenhagen (UP)

In this talk, I want to go over some representation theoretical background to introduce the irreducible representations of the special unitary group SU(3). This is motivated by the calculation of the...

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04.02.2021, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

Relative Traces in Obstacle Scattering

Florian Hanisch (UP)

In obstacle scattering, one is interested in properties of the Laplacian
∆ on the complement of a compact set O ("the obstacles") in Euclidean
space. It may be compared with the free Laplacian ∆₀  and...

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28.01.2021, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

Center of mass in general relativity

Alejandro Peñuela Diaz (UP)

We will see different approaches to the problem of defining a center of mass of a system in general relativity, specifically in the setting of the initial value formulation of general relativity. We...

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21.01.2021, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

Splitting of the Jacobi operator for extremal submanifolds with higher codimension

Claudia Grabs (UP)

We consider a Riemannian manifold with an embedded submanifold, which is extremal for some energy functional. For these embeddings, we compare the Jacobi operators corresponding to the different...

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14.01.2021, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

First order differential operators on spacetimes with timelike boundary

Penelope Gehring (UP)

Boundary value problems for elliptic first order differential operators on Riemannian manifolds are rather well understood. Recently, Bär-Strohmaier introduced APS-conditions for the Dirac operator on...

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07.01.2021, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

Geometric Inverse Problems in Gauge Theory

Chen Xi (Cambridge, UK)

The fundamental interactions of elementary particles are described by the Euler-Lagrange equations in the Standard Model of particle physics. The Yang-Mills equation addresses the electroweak and...

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17.12.2020, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

L^p-stability and positive scalar curvature rigidity of Ricci-flat ALE manifolds

Klaus Kröncke (Tübingen)

We prove stability of integrable ALE manifolds with a parallel spinor under Ricci flow, given an initial metric which is close in $$L^p\cap L^{\infty}$$, for any $$p \in (1, n)$$, where n is the...

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10.12.2020, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

Long-time estimates for heat flows on ALE manifolds

We consider the heat equation associated to Schrödinger operators acting on vector bundles on asymptotically locally Euclidean (ALE) manifolds. Assuming that the Schrödinger operator can be written as...

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03.12.2020, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

Boundary Value Problems for the Lorentzian Dirac operator

Sebastian Hannes (UP)

I'm going to briefly explain the main problems and results of my thesis and then focus on discussing some examples to show how these results apply, where they they can be extended, and also where they...

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26.11.2020, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

Functorial construction of functional spaces on vector bundles

Rubens Longhi (UP)

A suitable category of vector bundles will be introduced, in which every object is obtained as a limit of trivial vector bundles. Then, a functorial definition for general functional spaces will be...

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29.10.2020, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

On the Cauchy problem for symmetric hyperbolic systems on globally hyperbolic manifolds with timelike boundary

Simone Murro

The well-posedness of the Cauchy problem for symmetric hyperbolic systems on a Lorentzian manifold is a classical problem that has been thoroughly studied in many contexts. Particularly, if the...

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16.07.2020, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

A relative Cheeger-Gromov rho-invariant and the space of positive scalar curvature metrics on manifolds with boundary

Mehran Seyedhosseini

Secondary invariants associated to positive scalar curvature metrics on closed spin manifolds have been used to study the space of such metrics on a fixed manifold. I will first talk about a result of...

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09.07.2020, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

A long neck principle for Riemannian spin manifolds with positive scalar curvature

Simone Cecchini (Göttingen)

We develop index theory on compact Riemannian spin manifolds with boundary in the case when the topological information is encoded by bundles which are supported away from the boundary. As a first...

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02.07.2020, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

Spectral theory on stationary spacetimes

Alexander Strohmaier (Leeds)

For compact Riemannian manifolds the Gutzwiller-Duistermaat-Guillemin trace formula is one of the standard tools to show Weyl laws, investigate questions of quantum chaos, and prove inverse spectral...

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25.06.2020, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

Self-adjoint codimension 2 boundary conditions for Dirac operators

Bernd Ammann (Regensburg)

Let N be an oriented compact submanifold of codimension 2 in an oriented complete Riemannian manifold M. We assume that M\N is spin and carries a unitary line bundle L. We study the self-adjoint...

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18.06.2020, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

The KO-valued spectral flow for skew-adjoint Fredholm operators

Matthias Lesch (Bonn)

We give a comprehensive treatment of a ‘Clifford module flow’ along paths in the skew-adjoint Fredholm operators on a real Hilbert space that takes values in KO(R) via the Clifford index of...

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11.06.2020, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

On the evolution of hypersurfaces along their inverse spacetime mean curvature

Markus Wolff (Tübingen)

We introduce a new inverse curvature flow on asymptotically flat Initial Data sets (M,g,K). In General Relativity, such a triple (M,g,K) arises naturally as a spacelike hypersurface of a Lorentzian...

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04.06.2020, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

Functional spaces on manifolds and vector bundles

Rubens Longhi

I will construct the space of distributional sections of general vector bundles and give a general definition for local and compactly supported functional spaces.

Access data at: https://moodle2.uni-p...

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28.05.2020, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

Minimal surfaces, periodic tangling and wrinkly skin

Myfanwy Evans

This talk will introduce the use of geometric ideas in the characterisation and analysis of biophysical systems. Triply-periodic minimal surfaces and their occurrences in nature will provide the...

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14.05.2020, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

Manifolds with many Rarita-Schwinger fields

Christian Bär

The Rarita-Schwinger operator is the twisted Dirac operator restricted to 3/2-spinors. Rarita-Schwinger fields are solutions of this operator which are in addition divergence-free. This is an...

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30.04.2020, 16:15  –  Online-Seminar Forschungsseminar Differentialgeometrie

Scalar positive immersions

Bernhard Hanke (Augsburg)

As shown by Gromov-Lawson and Stolz the only obstruction to the existence of positive scalar curvature metrics on closed simply connected manifolds in dimensions at least five appears on spin...

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23.04.2020, 16:15  –  Online Seminar Forschungsseminar Differentialgeometrie

Horizons in general relativity

Moncrief and Isenberg conjectured in 1983 that any compact Cauchy horizon in a smooth vacuum spacetime is a smooth Killing horizon. We present a proof of this conjecture, under the assumption that the...

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Lashi Bandara

06.02.2020, 14:15  –  Haus 9, Raum 1.10 Seminar Geometrie

Josephine Bommer

Aigner, Ziegler: Das BUCH der Beweise, Kapitel 27

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04.02.2020, 16:15  –  Haus 9, Raum 1.10 Forschungsseminar Differentialgeometrie

Geometry of minimal elastic energy surfaces with SageManifolds

Claudia Grabs

We show how to compute minimal elastic energy surfaces for rotationally symmetric deformations of annulus shaped reference configurations. The computations are done with the SageManifolds extension of...

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Sylvie Paycha

30.01.2020, 14:15  –  Haus 9, Raum 1.10 Seminar Geometrie

Das endliche Kakeya-Problem

Benjamin Baron

Aigner, Ziegler: Das BUCH der Beweise, Kapitel 35

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28.01.2020, 16:15  –  Haus 9, Raum 1.10 Forschungsseminar Differentialgeometrie

Representations of Compact Lie Groups

Jonas Rungenhagen

In this talk, I want to give an overview about the representation theory of compact Lie groups as it has various applications.

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Christian Bär

23.01.2020, 14:15  –  Haus 9, Raum 1.10 Seminar Geometrie

Zerlegung von Rechtecken

Aigner, Ziegler: Das BUCH der Beweise, Kapitel 29

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21.01.2020, 16:15  –  Haus 9, Raum 1.10 Forschungsseminar Differentialgeometrie

Edge-following topological states

Recently, physicists have been able to create “topological states” localised on the boundary of a 2D system, which have rather crazy properties: they fill up spectral gaps in the boundary-less 2D...

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Christian Bär

16.01.2020, 14:15  –  Haus 9, Raum 1.10 Seminar Geometrie

Die Borsuk-Vermutung

Martin Botushev

Aigner, Ziegler: Das BUCH der Beweise, Kapitel 18

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14.01.2020, 16:15  –  Haus 9, Raum 1.10 Forschungsseminar Differentialgeometrie

Construction of asymptotically hyperbolic electrically charged manifolds

Penelope Gehring

Mantoulidis and Schoen constructed smooth asymptotically flat manifolds of dimension 3 with prescribed horizon boundary, whose mass can be made arbitrarily close to the optimal value in the Riemannian...

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Markus Klein

09.01.2020, 14:15  –  Haus 9, Raum 1.10 Seminar Geometrie

Stumpfe Winkel

Josephin Kühne

Aigner, Ziegler: Das BUCH der Beweise, Kapitel 17

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07.01.2020, 16:15  –  Raum 1.10 Forschungsseminar Differentialgeometrie

Geometric and obstacle scattering at low energy

Alden Waters (Groningen)

We consider the problem of obstacle scattering for the Helmholtz equation with the p-form Laplace Beltrami operator. On manifolds which are asymptotically Euclidean we show resolvent expansions, and...

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Lukas Minogue

19.12.2019, 14:15  –  Haus 9, Raum 1.10 Seminar Geometrie

Simplexe, die einander berühren

Noreen Fischer

Aigner, Ziegler: Das BUCH der Beweise, Kapitel 16

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17.12.2019, 16:15  –  Haus 9, Raum 1.10 Forschungsseminar Differentialgeometrie

Boundary value problems for the Lorentzian Dirac operator

Sebastian Hannes

We consider the Dirac operator on a globally hyperbolic spacetime with compact, spacelike Cauchy hypersurfaces. In this setting the Dirac operator is known to be Fredholm and have a smooth solution...

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Markus Klein

12.12.2019, 14:15  –  Haus 9, Raum 1.10 Seminar Geometrie

Der Starrheitssatz von Cauchy

Luise Fritsche

Aigner, Ziegler: Das BUCH der Beweise, Kapitel 14

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10.12.2019, 16:15  –  Haus 9, Raum 1.10 Forschungsseminar Differentialgeometrie

Wavefront set of a distribution

Wai Tung Poon

On the presentation of my scientific project, I am going to show some properties about microlocal analysis. Firstly, I will define some basic notions about the distribution and Fourier transform of a...

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Andreas Hermann

05.12.2019, 14:15  –  Haus 9, Raum 1.10 Seminar Geometrie

Drei Anwendungen der Euler'schen Polyederformel

Mara Martin

Aigner, Ziegler: Das BUCH der Beweise, Kapitel 13

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03.12.2019, 16:15  –  Haus 9, Raum 1.10 Forschungsseminar Differentialgeometrie

Maxwell's Equations on Globally Hyperbolic Spacetimes with Timelike Boundary

Rubens Longhi

We study Maxwell's equation as a theory for smooth k-forms on globally hyperbolic spacetimes with timelike boundary as defined by Aké, Flores and Sanchez. In particular we start by investigating on...

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Andreas Braunß

28.11.2019, 14:15  –  Haus 9, Raum 1.10 Seminar Geometrie

Hilberts drittes Problem: Zerlegung von Polyedern

Hanna Jürß

Aigner, Ziegler: Das BUCH der Beweise, Kapitel 10

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26.11.2019, 16:15  –  Haus 9, Raum 1.10 Forschungsseminar Differentialgeometrie

A Functional Analytic Index Theorem

Lennart Ronge (Bonn)

Considering a family of self-adjoint Fredholm operators A(t), the equality ind(D_APS)=sf(A) will be shown under certain conditions. Here, sf(A) denotes the spectral flow of the family A, D_APS is the...

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Lashi Bandara

21.11.2019, 14:15  –  Haus 9, Raum 1.10 Seminar Geometrie

Cayleys Formel für die Anzahl der Bäume

Maximilian Tieze

Aigner, Ziegler: Das BUCH der Beweise, Kapitel 33

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21.11.2019, 10:00  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Ricci flow from Algebraic Quantum Field Theory III

Claudio Dappiaggi (Pavia)

We discuss the freedom in the construction of Wick polynomials for a non linear Sigma model and we introduce the associated renormalization group flow, proving that it coincides with the Ricci flow.

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20.11.2019, 16:30  –  Haus 9, Raum 0.12 Forschungsseminar Differentialgeometrie

Ricci flow from Algebraic Quantum Field Theory II

Claudio Dappiaggi (Pavia)

We apply the algebraic approach to construct the algebra of observables associated to non linear Sigma models. In particular we discuss the notion of Wick polynomials and their realization in terms of...

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19.11.2019, 16:15  –  Haus 9, Raum 1.10 Forschungsseminar Differentialgeometrie

Ricci flow from Algebraic Quantum Field Theory I

Claudio Dappiaggi (Pavia)

The goal of the these lectures is to give a rigorous derivation of Ricci flow starting from non linear Sigma models, within the framework of algebraic quantum field theory. In the first talk we...

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Siegfried Beckus

14.11.2019, 14:15  –  Haus 9, Raum 1.10 Seminar Geometrie

Gitterwege und Determinanten

Artem Istranin

Aigner, Ziegler: Das BUCH der Beweise, Kapitel 32

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Elke Rosenberger

07.11.2019, 14:15  –  Haus 9, Raum 1.10 Seminar Geometrie

Wenige Steigungen

René Hintze

Aigner, Ziegler: Das BUCH der Beweise, Kapitel 12

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05.11.2019, 16:15  –  Raum 1.10 Forschungsseminar Differentialgeometrie

Vector Bundles and Characteristic Classes in SageManifolds

Michael Jung

SageMath ("System for Algebra and Geometry Experimentation") is an open source computer algebra system based on Python. It uses various libraries written in R, Fortran, Maxima etc. to realize an...

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29.10.2019, **16:00**  –  Raum 1.10 Forschungsseminar Differentialgeometrie

Unique continuation for wave equations and applications in general relativity

In a recent paper, Ionescu and Klainerman showed that Killing vector fields on Lorentzian manifolds can be extended using only unique continuation statements for wave equations. Before their work,...

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24.10.2019, 14:15  –  Haus 9, Raum 1.10 Seminar Geometrie

Geraden in der Ebene und Zerlegung von Graphen

Andrea Hübner

Aigner, Ziegler: Das BUCH der Beweise, Kapitel 11

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22.10.2019, 16:15  –  Raum 1.10 Forschungsseminar Differentialgeometrie

On the number of closed geodesics

It is an open question whether any Riemannian metric on a compact manifold has infinitely many geometrically distinct closed geodesics. We first revisit results for generic metrics in the case of...

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15.10.2019, 16:15  –  Raum 1.10 Forschungsseminar Differentialgeometrie

The Twist of the Free Fermion

In this talk we study the free fermion in the framework of functional field theory. It turns out that the theory is twisted due to the chiral anomaly of the free fermion. We give a detailed...

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18.07.2019, 16:15  –  Haus 9, Raum 0.12 Forschungsseminar Differentialgeometrie

Elliptic boundary conditions in linearized elastostatics

Claudia Grabs

We consider boundary value problems in linearized elastostatics for isotropic materials. It is known that Dirichlet boundary conditions are strongly elliptic boundary conditions in the sense of...

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15.07.2019, 16:00  –  Raum 2.22 Forschungsseminar Differentialgeometrie

Around the Relative Index

Mehran Seyedhosseini (Göttingen)

Peter Grabs

20.06.2019, 16:15  –  Haus 9, Raum 0.12 Forschungsseminar Differentialgeometrie

Boundary value problems for the Dirac operator on Riemannian and Lorentzian manifolds

Christian Bär

Boundary value problems for the Dirac operator on a Riemannian manifolds are rather well understood. In particular, one has a general description of admissible boundary conditions. The Lorentzian case...

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16.05.2019, 16:15  –  Haus 9, Raum 0.12 Forschungsseminar Differentialgeometrie

Total squared curvature of surfaces in Riemannian manifolds

Ernst Kuwert (Albert-Ludwigs-Universität Freiburg)

We discuss the problem of minimizing the total squared curvature of compact surfaces in closed Riemannian manifolds. In particular, we present an area bound in terms of the curvature for many...

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02.05.2019, 16:15  –  Haus 9, Raum 0.12 Forschungsseminar Differentialgeometrie

Hadamard states for bosonic quantum field theory on globally hyperbolic spacetimes

Max Lewandowski

The semiclassical model of quantum field theory on curved spacetimes is considered as an intermediate step in the direction of some quantum theory of gravitation, which however already yields...

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25.04.2019, 16:15  –  Haus 9, Raum 0.12 Forschungsseminar Differentialgeometrie

The Yamabe problem on Lorentzian manifolds

Viktoria Rothe

Let M be a spatially compact globally hyperbolic Lorentzian manifold of dimension 4. We will examine under which conditions the Yamabe equation on M has a positive solution for all times in a given...

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28.03.2019, 14:15  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Attractors of the Einstein-Klein-Gordon system

Zoe Wyatt (University of Edinburgh)

A key question in general relativity is whether solutions to the Einstein equations, viewed as an initial value problem, are stable to small perturbations of the initial data. For example, previous...

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28.03.2019, 15:30  –  Albert-Einstein-Institut, Raum 0.01 Seminar Geometry and Physics

Structure from turbulence, or why you might want to care about plasma physics even if you are not a plasma physicist

Ilya Y. Dodin (Princeton University)

Turbulence has always been a tough subject to study. Interestingly though, typical turbulence equations are similar in form to those that govern nondegenerate quantum plasmas, which are easier to...

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11.03.2019, 15:15  –  Haus 9, Raum 1.10 Forschungsseminar Differentialgeometrie

Wave equations on the Schwarzschild spacetime

Ariane Beier

The scalar wave equation on Schwarzschild spacetime allows physical relevant generalizations incorperating a topological quantum number and fields of higher spin. This talk focusses on the derivation...

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28.02.2019, **15:15**  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Feynman integrals with the Green kernel

Pavel Hajek (Universität Augsburg)

For a closed oriented Riemannian manifold M, we consider integrals associated to trivalent ribbon graphs decorated with harmonic forms at exterior vertices and the Green kernel G(x,y) at interior...

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26.02.2019, **15:15**  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Complements of 2-tori in closed smooth simply connected 4-manifolds that admit a complete finite volume hyperbolic structure

Hemanth Saratchandran (Universität Augsburg)

The study of hyperbolic knot complements has a long history leading to many exciting results in the field of 3-manifold topology. In this talk, I will present a 4-dimensional analogue of this study....

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Andreas Hermann

04.02.2019, 11:00  –  Albert-Einstein-Institut, Raum 0.01 Seminar Geometry and Physics

Stability and instability issues for Vlasov-like equations in gravitational kinetic theory

Mohammed Lemou (IRMAR Rennes, France)

I will start by giving a short overview of the history around stability and instability issues in gravitational systems driven by kinetic equations. Conservations properties and families of...

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Andreas Hermann

31.01.2019, 16:15  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Infinite dimensionality of kernels of Neumann Laplacians induced by first-order elliptic operators

Lashi Bandara

We consider first-order elliptic differential operators on a compact manifold with boundary. We show that the kernel of the maximal extension, which coincides with the kernel of its associated Neumann...

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31.01.2019, 11:00  –  Albert-Einstein-Institut, Raum 0.01 Seminar Geometry and Physics

Classical and Quantum impulsive Scattering

Herbert Balasin (TU Wien)

Using the framework of Colombeau's generalized functions, I will discuss the motion of both the classical as well as the quantum motion of a particle in an impulsive background.

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Lashi Bandara

24.01.2019, 16:15  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Cauchy problem for the Dirac operator on globally hyperbolic manifolds with timelike boundary

We consider the Dirac operator on globally hyperbolic manifolds with timelike boundary and ask for well-posedness of the Cauchy initial-boundary value problem coupled to MIT-boundary conditions. This...

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Lashi Bandara

17.01.2019, 16:15  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Asymptotically hyperbolic extensions of Riemannian manifolds

Penelope Gehring (Tübingen)

Mantoulidis and Schoen constructed smooth asymptotically flat initial data sets of dimension 3 with prescribed horizon boundary, whose mass can be made arbitrary close to the optimal value in the...

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17.01.2019, 11:00  –  Albert-Einstein-Institut, Raum 1.63 Seminar Geometry and Physics

An elementary introduction to MHD equations

Huali Zhang (AEI)

Magnetohydrodynamics (MHD) is the study of the dynamics and magnetic properties of electrically conducting fluids. In this talk, we will give a brief derivation of MHD equations, and also introduce...

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Michael Jung

10.01.2019, 16:15  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Causal variational principles and energy estimates for linearized fields

Felix Finster (Regensburg)

After a brief general introduction to causal fermion systems and causal variational principles, the concept of linearized fields is introduced. Formulating the Cauchy problem locally in so-called...

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10.01.2019, 11:00  –  Albert-Einstein-Institut, Raum 1.63 Seminar Geometry and Physics

Asymptotically flat vacuum asymptotics: Things that remain to be done

Helmut Friedrich (AEI)

In the last 30 years an enormous amount of work has been done on the existence and global structure of asymptotically flat solutions to Einstein's field equations. Many of these contributions are in...

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Claudia Grabs

Sebastian Hannes

13.12.2018, 16:15  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Spacetime diffeomorphisms as matter fields

Dmitri Vassiliev (UCL London)

We work on a 4-manifold equipped with Lorentzian metric g and consider a volume-preserving diffeomorphism which is the unknown quantity of our mathematical model. The diffeomorphism defines a...

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13.12.2018, 11:00  –  Albert-Einstein-Institut, Raum 0.01 Seminar Geometry and Physics

The Berry Phase: Introduction and Examples

Lukas Böke (AEI - ETH)

The Berry phase was introduced by Michael Berry in the 80s, and a little later an elegant description in terms of holonomy was observed by Barry Simon. We introduce the Berry phase and the Berry-Simon...

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Andreas Hermann

06.12.2018, 16:15  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Wave equations with initial data on compact Cauchy horizons

I will present a new existence and uniqueness result for wave equations with initial data on compact Cauchy horizons. As an application, we prove that any vacuum spacetime containing a compact...

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Peter Grabs

29.11.2018, 11:00  –  Albert-Einstein-Institut, Raum 0.01 Seminar Geometry and Physics

Jeff Winicour (University of Pittsburgh)

I will review results about linear and nonlinear radiation memory for electromagnetic and gravitational fields and present some new results for the collision of black holes.

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29.11.2018, 16:15  –  Raum 0.14 Forschungsseminar Differentialgeometrie

Counter-intuitive existence and approximation results

Christian Bär

We will discuss a general approximation theorem which allows to solve overdetermined partial differential relations on an open dense subset of the domain. Let K be a real number. Applications will...

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22.11.2018, 11:00  –  Albert-Einstein-Institut, Raum 0.01 Seminar Geometry and Physics

Introduction to the Wigner transform

Jérémie Joudioux (AEI)

The Wigner transform was introduced at the beginning of the 30s to understand quantum corrections to classical statistical mechanics. It has then been used in optics to perform analysis in phase space...

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22.11.2018, 16:15  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

First-order elliptic boundary value problems for manifolds with non-compact boundary

Lashi Bandara

In this talk, I'll have a yarn about ongoing work on the question of BVPs for elliptic first-order BVPs where the boundary is non-compact, whenever the adapted operator on the boundary is essentially...

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Sebastian Hannes

15.11.2018, 11:00  –  Albert-Einstein-Institut, Raum 0.01 Seminar Geometry and Physics

Helicity and spin in Maxwell theory and linearized gravity

Sajad Aghapour (Sharif University of Technology, Tehran, and AEI)

The classical definitions of helicity, spin and orbital angular momenta of the electromagnetic field in free space have been improved in recent years in theoretical optics, stimulated by experiments...

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Michael Jung

08.11.2018, 16:15  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Positivity of scalar Hadamard-bisolutions for the wave equation on globally hyperbolic Lorentzian manifolds

Max Lewandowski

Let W be a scalar Hadamard-bisolution for the wave equation on a globally hyperbolic Lorentzian manifold M, then positivity W[φ,φ]≥0 only affects the symmetric part Ws of W, which is essentially...

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08.11.2018, 11:00  –  Albert-Einstein-Institut, Raum 0.01 Seminar Geometry and Physics

Using the geometric optics approach to connect the Dirac equation to the linearised MPD equations

Lukas Böke (AEI)

We present a correspondence, established in papers by R. Rüdiger and J. Audretsch, between quantum mechanical equations of motion and classical equations of spinning massive particles in a...

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Claudia Grabs

01.11.2018, 11:00  –  Albert-Einstein-Institut, Raum 0.01 Seminar Geometry and Physics

Conservation laws for spinning fields

Noether's theorem states that for a Lagrangian field theory, symmetries of the action gives rise to conserved currents and charges. The most well-known symmetries are those which arise from Killing...

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01.11.2018, 16:15  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

The stability of Minkowski space as a solution to the Einstein-Vlasov system

Jérémie Joudioux (Radboud University and AEI)

We discuss in this talk the proof of the stability of Minkowski space as a solution to the Einstein-Vlasov system. This proof is based on the construction of appropriate commutators with the...

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Peter Grabs

13.09.2018, 16:15  –  Haus 9, Raum 2.22 Forschungsseminar Differentialgeometrie

Eigenvalue asymptotic for weighted Laplacians on rough Riemannian manifolds with boundary

Medet Nursultanov

We investigate an asymptotic of the eigenvalues of the of the indefinite-weighted Laplace equation, $\Delta u = \lambda P u$, on the Riemannian manifold equipped with a rough metric. Namely, for the...

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19.07.2018, 16:15  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

The kernel of the Rarita-Schwinger operator on Riemannian spin manifolds

Uwe Semmelmann (Stuttgart)

The Rarita-Schwinger operator is a twisted Dirac operator. It has several  interesting applications in physics and differential geometry. In my talk I will introduce this operator, give some of its...

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16.07.2018, 16:00  –  Haus 9, Raum 0.14 Oberseminar Analysis, Geometrie, Physik

How close are two Lévy(-type) processes?

Tania Kosenkova

Lévy(-type) processes arise naturally as models of a (state dependent) jump behaviour in a wide variety of situations in natural sciences and finance. The topic of this talk is induced by the need to...

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12.07.2018, 16:15  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

The Yamabe problem on Lorentzian manifolds

Viktoria Rothe

In this talk we will consider the Yamabe equation on 4-dimensional globally hyperbolic Lorentzian manifolds. We will discuss some different approaches how one could get a positive global solution to...

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Markus Klein

TBA

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05.07.2018, 16:15  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Linearized elastic shell theory

Claudia Grabs

The total elastic energy is an extrinsic geometric functional for an embedding of some body manifold into an ambient space. We want to compute the first and second variation of this extrinsic...

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Elke Rosenberger

TBA

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Youness Boutaib

TBA

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14.06.2018, 16:15  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Outermost apparent horizons with non-trivial topology

Mattias Dahl

It is a well known fact that outermost apparent horizons must allow metrics of positive scalar curvature. It is conceivable that this is also the only restriction on a bounding manifold to be an...

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04.06.2018, 16:00  –  Haus 9, Raum 0.14 Oberseminar Analysis, Geometrie, Physik

Finite- and infinite-dimensional random dynamics and their equilibrium states

Sylvie Roelly

We first consider random diffusions with geometrical constraints and the problem of their convergence towards stationary states. Then we extend the framework to infinitely many interacting diffusions....

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31.05.2018, 16:15 Forschungsseminar Differentialgeometrie

First-order elliptic boundary value problems beyond self-adjoint induced boundary operators

Lashi Bandara

The Bär-Ballmann framework is a comprehensive framework for considering elliptic boundary value problems for first-order elliptic operators on manifolds with compact and smooth boundary, provided...

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Sylvie Paycha

TBA

mehr erfahren

17.05.2018, 16:15  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Boundary Value Problems for the Lorentzian Dirac Operator

Sebastian Hannes (Potsdam)

We will discuss some progress and some failures in the treatment of (Pseudo-)local boundary conditions for the Lorentzian Dirac operator on a globally hyperbolic spacetime.

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14.05.2018, 16:00  –  Haus 9, Raum 0.14 Oberseminar Analysis, Geometrie, Physik

Improving Hardy's inequality

Matthias Keller

About 100 years ago Hardy proved his famous inequality. Since then such inequalities have been proven in various contexts. We address the question of not only proving a sharp constant but also the...

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07.05.2018, 16:00  –  Haus 9, Raum 0.14 Oberseminar Analysis, Geometrie, Physik

How to plant a bubble tree

Alexander Friedrich

TBA

mehr erfahren

03.05.2018, 16:15  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Gromov’s weak flexibility lemma

Bernhard Hanke (Augsburg)

Jet bundles and partial differential relations allow a coordinate free characterisation of many topological and geometric structures, including immersions and submersions, symplectic and contact...

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Jan Metzger

TBA

mehr erfahren

26.04.2018, 16:15  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

The Atiyah-Patodi-Singer index on manifolds with non-compact boundary

Maxim Braverman (Northeastern Univ., Boston, USA)

We study the index of the APS boundary value problem for a strongly Callias-type operator D on a complete Riemannian manifold M. We use this index to define the relative eta-invariant of two strongly...

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23.04.2018, 16:00  –  Haus 9, Raum 0.14 Oberseminar Analysis, Geometrie, Physik

The Positive Mass Conjecture for closed Riemannian manifolds

Andreas Hermann

The Positive Mass Conjecture for asymptotically flat Riemannian manifolds is a famous problem in geometric analysis which has been open for a long time and seems to have been solved in recent work by...

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19.04.2018, 16:15  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Symmetry of the Hadamard coefficients for a formally self-adjoint, normally hyperbolic operator on a globally hyperbolic Lorentzian manifold

Max Lewandowski

In the case of the Klein-Gordon field on Minkowski space a certain linear combination of the 4 standard fundamental solutions (advanced, retarded, Feynman and anti-Feynman propagator) yields a...

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16.04.2018, 16:00  –  Haus 9, Raum 0.14 Oberseminar Analysis, Geometrie, Physik

Index theory on spacetimes

Christian Bär

We will give a survey on recent developments in index theory on spacetimes and discuss open problems.

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12.04.2018, 16:15  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

A nonlocal generalization of Green hyperbolic operators

Christopher Fewster (York, England)

I describe how Bär's theory of Green hyperbolic partial differential operators can be generalized to nonlocal operators, where the nonlocality is confined to a compact spacetime region. Operators of...

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Florian Hanisch

[1, Ch. 7F]

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08.02.2018, 16:15  –  Haus 9, Raum 1.10 Forschungsseminar Differentialgeometrie

The supersymmetric nonlinear sigma model as a geometric variational problem: A status report

Volker Branding (Universität Wien)

We will discuss the functional of the supersymmetric nonlinear sigma model as a geometric variational problem. Its critical points couple the harmonic map equation to spinor fields, these became known...

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05.02.2018, 16.00  –  Haus 9, Raum 0.14 Oberseminar Analysis, Geometrie, Physik

Harmonic Maps with Values in Lie Groups

Chandrashekar Devchand

This semester we will study the first chapters of the book "Harmonic Maps, Conservation Laws and Moving Frames" by Frédéric Hélein.

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Claudia Grabs

[1, Ch. 7C]

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29.01.2018, 16.00  –  Haus 9, Raum 0.14 Oberseminar Analysis, Geometrie, Physik

Regularity of Weakly Stationary Maps with Values in the Sphere

Jan Metzger

This semester we will study the first chapters of the book "Harmonic Maps, Conservation Laws and Moving Frames" by Frédéric Hélein.

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25.01.2018, 14:15  –  Haus 9, Raum 1.10 Seminar Geometrie

Lie groups and homogeneous spaces: Riemannian homogeneous spaces

Christian Bär

[1, Ch. 7B, incl. proof of Thm. 7.19], see also [2, p. 176]

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25.01.2018, 16:15  –  Haus 9, Raum 1.10 Forschungsseminar Differentialgeometrie

Global existence of wave maps and some generalizations on expanding spacetimes

Klaus Kröncke (Hamburg)

We prove the global existence of wave maps with small initial data on globally hyperbolic manifolds of arbitrary dimension which satisfy a suitable growth condition. In addition, we also prove a...

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22.01.2018, 16.00  –  Haus 9, Raum 0.14 Oberseminar Analysis, Geometrie, Physik

Lorentz Spaces / Wente Inequality refined

Sylvie Paycha / Florian Hanisch

This semester we will study the first chapters of the book "Harmonic Maps, Conservation Laws and Moving Frames" by Frédéric Hélein.

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Sebastian Hannes

[3, 3.65-3.68]

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18.01.2018, 16:15  –  Haus 9, Raum 1.10 Forschungsseminar Differentialgeometrie

The Yamabe problem on Lorentzian manifolds

Viktoria Rothe

We will consider the Yamabe Problem on globally hyperbolic spatially compact Lorentzian manifolds (M,g) of dimension 4: Given a Lorentzian metric g on M, find a metric conformal to g with constant...

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15.01.2018, 16.00  –  Haus 9, Raum 0.14 Oberseminar Analysis, Geometrie, Physik

Hardy Spaces

Markus Klein

This semester we will study the first chapters of the book "Harmonic Maps, Conservation Laws and Moving Frames" by Frédéric Hélein.

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11.01.2018, 16:15  –  Haus 9, Raum 1.10 Forschungsseminar Differentialgeometrie

Invariant differential operators

Vít Tuček (Prag)

It is well known that Laplace and Dirac operators on $\mathbb{R}^{p, q}$ admit strictly larger Lie algebra of symmetries than just the orthogonal ones, namely they are invariant with respect to...

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Andreas Hermann

[3, 3.58-3.64]

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08.01.2018, 16.00  –  Haus 9, Raum 0.14 Oberseminar Analysis, Geometrie, Physik

Wente Inequality

Alexander Friedrich

This semester we will study the first chapters of the book "Harmonic Maps, Conservation Laws and Moving Frames" by Frédéric Hélein.

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Andreas Hermann

[3, 3.58-3.64]

mehr erfahren

04.01.2018, 16:00  –  Haus 9, Raum 1.10 Forschungsseminar Differentialgeometrie

Symmetry of the Hadamard coefficients for a formally self-adjoint, normally hyperbolic operator on a globally hyperbolic Lorentzian manifold

Max Lewandowski

We will start with the case of operators with analytic coefficients and show that the Hadamard series in some point converges in some open neighborhood of that point. In that neighborhood the symmetry...

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18.12.2017, 16.00  –  Haus 9, Raum 0.14 Oberseminar Analysis, Geometrie, Physik

Weak Compactness and Regularity of Harmonic Maps with Values in the Sphere

Jan Metzger

This semester we will study the first chapters of the book "Harmonic Maps, Conservation Laws and Moving Frames" by Frédéric Hélein.

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Andreas Hermann

[3, 3.44-3.57]

mehr erfahren

14.12.2017, 16:15  –  Haus 9, Raum 1.10 Forschungsseminar Differentialgeometrie

Minimal elastic energy surfaces

Claudia Grabs

Starting with a relaxed elastic shell, any deformation yields certrain stresses inside the material. In the static case, equilibrium configurations for a given deformation of the boundary are obtained...

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11.12.2017, 16.00  –  Haus 9, Raum 0.14 Oberseminar Analysis, Geometrie, Physik

Harmonic Maps with Values in Lie Groups 2

Sara Azzali

This semester we will study the first chapters of the book "Harmonic Maps, Conservation Laws and Moving Frames" by Frédéric Hélein.

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Philipp Bartmann

[3, 3.38-3.43]

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07.12.2017, 16:15  –  Haus 9, Raum 1.10 Forschungsseminar Differentialgeometrie

Boundary Value Problems for the Lorentzian Dirac Operator

Sebastian Hannes

On a globally hyperbolic spacetime the Lorentzian Dirac Operator under APS boundary conditions is Fredholm and its kernel consists of smooth spinors. We will discuss a certain class of boundary...

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04.12.2017, 16.00  –  Haus 9, Raum 0.14 Oberseminar Analysis, Geometrie, Physik

Harmonic Maps with Values in Lie Groups 1

Florian Hanisch

This semester we will study the first chapters of the book "Harmonic Maps, Conservation Laws and Moving Frames" by Frédéric Hélein.

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Viktoria Rothe

[3, 3.29-3.37]

mehr erfahren

30.11.2017, 16:15  –  Haus 9, Raum 1.10 Forschungsseminar Differentialgeometrie

The local version of the Lorentzian index theorem

Christian Bär

The Atiyah-Singer index theorem for Dirac operators D on compact Riemannian spin n-manifolds can be proved using the heat kernels of D*D and of DD*.  Namely, one easily sees that

<tex>\mathrm{ind}(D)...

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27.11.2017, 16.00  –  Haus 9, Raum 0.14 Oberseminar Analysis, Geometrie, Physik

Sphere-Valued Maps and the Bäcklund Transformation

Alexander Friedrich

This semester we will study the first chapters of the book "Harmonic Maps, Conservation Laws and Moving Frames" by Frédéric Hélein.

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Claudia Grabs

[3, 3.22-3.28]

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16.11.2017, 16:15  –  Raum 1.10 Forschungsseminar Differentialgeometrie

Margarita Kraus (Mainz)

A local expansion of a distributional bisolution of the Klein Gordon equation is proposed. This expansion is given by sequences of functions, which satisfy certain transport equations. These equations...

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Florian Hanisch

[3, 3.17-3.21]

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13.11.2017, 16.00  –  Haus 9, Raum 0.14 Oberseminar Analysis, Geometrie, Physik

Sobolev Spaces and the Variational Approach

Elke Rosenberger

This semester we will study the first chapters of the book "Harmonic Maps, Conservation Laws and Moving Frames" by Frédéric Hélein.

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06.11.2017, 16.00  –  Haus 9, Raum 0.14 Oberseminar Analysis, Geometrie, Physik

Conservation Laws for Harmonic Maps 2

Philip Thonke

This semester we will study the first chapters of the book "Harmonic Maps, Conservation Laws and Moving Frames" by Frédéric Hélein.

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Max Lewandowski

[3, 3.13-3.16]

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02.11.2017, 16:15  –  Haus 9, Raum 1.10 Forschungsseminar Differentialgeometrie

Supersymmetric Path Integrals (I)

Florian Hanisch

Integration over the space of superpaths, associated to a Riemannian manifold, plays an important role in the path integral approach to the Atiyah-Singer index theorem. This is indeed equivalent to...

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26.10.2017, 16:15  –  Raum 1.10 Forschungsseminar Differentialgeometrie

Constructing temporal functions and isometric embeddings of Lorentzian manifolds

Olaf Müller (HU Berlin)

In the last years, several new methods for the construction of temporal functions with specified geometric properties on a given spacetime have been developed. In this talk, a selection of them is ...

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Sebastian Hannes

[3, 3.1-3.12]

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19.10.2017, 16:15  –  Raum 1.10 Forschungsseminar Differentialgeometrie

Dirac eigenvalues under codimension one collaps

After giving a characterization of a collaps of codimension one we study the behavior of Dirac eigenvalues in that situation. We show that there are converging eigenvalues if and only if there is an...

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20.07.2017, 16:15 Uhr  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Solutions to the linearized Einstein constraint equations

Any closed Riemannian manifold which has vanishing scalar curvature is a solution to the relativistic vacuum constraint equations. Examples include the flat torus and certain Berger spheres. If the...

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13.07.2017, 16:15 Uhr  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Linear wave equations with initial data on compact Cauchy horizons

When studying wave equations in a region of a curved spacetime, one usually assumes that the region satisfies certain causality conditions. Expressed in mathematical terms, one assumes that the region...

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06.07.2017, 14:15 Uhr  –  Haus 9, Raum 0.14 Seminar Geometry and Physics

A General Definition of Conserved Quantities in General Relativity

In this talk I will review a paper by Zoupas and Wald which summarizes the proposal for a general definition of "conserved quantities" in General Relativity and other theories of gravity developed by...

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22.06.2017, 16:15  –  Raum 0.14 Forschungsseminar Differentialgeometrie

Heat kernel estimates for general boundary problems

Alexander Strohmaier

The heat kernel in a domain with Dirichlet boundary conditions satisfies so-called “not feeling the boundary estimates”. These reflect the locality of the heat expansion and can for example be derived...

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22.06.2017, 14:15 Uhr  –  Haus 9, Raum 0.14 Seminar Geometry and Physics

Introduction to conformal Killing forms

Andreas Hermann

Conformal Killing p-forms are a generalization of conformal Killing vector fields on semi-Riemannian manifolds. In this talk we review some known properties of conformal Killing p-forms. We describe...

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14.06.2017, 15:30 Uhr  –  Albert Einstein Institute, Room 0.01 Seminar Geometry and Physics

Applications of PDE compatibility complexes in relativity

Igor Khavkine

I will discuss the Killing operator (K_{ab}[v] = \nabla_a v_b + \nabla_b v_a) on a (pseudo-)Riemannian manifold as an overdetermined PDE and its (formal) compatibility complex. It has been observed...

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08.06.2017, 14:15 Uhr  –  Haus 9, Raum 0.14 Seminar Geometry and Physics

Potentials and conservation laws

I will discuss how Hertz potentials can be used to construct conservation laws for massless fields including Maxwell and linearized gravity.

mehr erfahren

08.06.2017, 16:15  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Ein Indexsatz für homogene Räume

Christian Bär

Ich werde erklären, wie sich der Fredholm-Index eines äquivarianten elliptischen Operators über einem homogenen Raum darstellungstheoretisch berechnen lässt.

mehr erfahren

01.06.2017, 14:15 Uhr  –  Haus 9, Raum 0.14 Seminar Geometry and Physics

Electromagnetic duality in linearized gravity

Cedric Troessaert

I will review how, in the Hamiltonian formalism, one use a double potential formalism to obtain a manifestly duality invariant description of linearized gravity.

mehr erfahren

01.06.2017, 16:15 Uhr  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Foundations on elliptic operators on compact manifolds

Max Lewandowski

After establishing some important basics about pseudo differential operators we will construct a parametrix for elliptic operators on compact manifolds, which allows several conclusions, e.g. elliptic...

mehr erfahren

18.05.2017, 16:15 Uhr  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Einführung in die Spin-Geometrie: Analytische Grundlagen

Max Lewandowski

Dirac-Operator auf riemannschen Mannigfaltigkeiten, Elliptizität, wesentliche Selbstadjungiertheit, Diskretheit des Spektrums

mehr erfahren

11.05.2017, 16:15 Uhr  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Einführung in die Spin-Geometrie: Geometrische Grundlagen

Andreas Hermann

Hauptfaserbündel, assoziierte Vektorbündel, Spinorbündel, Clifford-Multiplikation und Zusammenhang auf dem Spinor-Bündel

mehr erfahren

04.05.2017, 16:15 Uhr  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Einführung in die Spin-Geometrie: Algebraische Grundlagen

Sebastian Hannes

Clifford-Algebren, Clifford-Multiplikation, Pin-Gruppe, Spin-Gruppe, Spinor-Darstellung, invariantes inneres Produkt

mehr erfahren

26.04.2017, 10:15-11:45  –  Haus 9, Raum 2.22 Forschungsseminar Differentialgeometrie

Mass-like invariants for asymptotically hyperbolic metrics

Mattias Dahl

Asymptotically Euclidean and asymptotically hyperbolic manifolds have mass invariants computed at infinity. These invariants have the interpretation as the total mass of the manifold as a slice of...

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20.04.2017, 16:15 Uhr  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

The Cauchy-Problem for fundamental solutions of formally self-adjoint wave operators on globally hyperbolic Lorentzian manifolds

Max Lewandowski

We start by discussing under which circumstances a fundamental solution can be restricted to a spacelike Cauchy hypersurface so that the corresponding Cauchy problem is well-posed which will demand...

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20.04.2017, 14:15 Uhr  –  Haus 9, Raum 0.14 Seminar Geometry and Physics

Symmetries and hidden symmetries of Maxwell theory

Maxwell's theory of electromagnetism is a relativistic field theory on Minkowski space, and is symmetric under the 10-dimensional Poincare group of isometries of Minkowski space. However, it admits...

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23.03.2017, 16:00-17:30  –  Raum 1.10 Forschungsseminar Differentialgeometrie

Geometric singularities and a flow tangential to the Ricci flow

Lashi Bandara

In 2012, Gigli and Mantegazza introduced a new geometric flow via heat kernels. They demonstrated that this flow is tangential to the Ricci flow in a suitable weak sense for smooth, compact Riemannian...

mehr erfahren

09.02.2017, 14:15 Uhr  –  Haus 9, Raum 0.14 Seminar Geometrie

Ricci-Fluss auf Flächen: Der Fall positiver Eulerzahl

Der Fall positiver Eulerzahl

[CK, S. 148-156]

mehr erfahren

09.02.2017, 16:15 Uhr  –  Haus 9, Raum 0.12 Forschungsseminar Differentialgeometrie

The curl operator on odd-dimensional manifolds

Christian Bär

We study the spectral properties of curl, a linear differential operator of first order acting on differential forms of appropriate degree on an odd-dimensional closed oriented Riemannian manifold. In...

mehr erfahren

02.02.2017, 14:15 Uhr  –  Haus 9, Raum 0.14 Seminar Geometrie

Ricci-Fluss auf Flächen: Harnack-Ungleichung

Jonas Rungenhagen

Harnack-Ungleichung

[CK, S. 143-148]

mehr erfahren

02.02.2017, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.12 Forschungsseminar Differentialgeometrie

Konforme Geodäten im Cartankalkül

Daniel Platt

Ein Cartan-Zusammenhang ist eine 1-Form, die dieselben Invarianzeigenschaften wie ein Hauptfaserbündel-Zusammenhang hat und zusätzlich einen absoluten Parallelismus (in eine geeignete Lie-Algebra) in...

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31.01.2017, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.14 Seminar Geometry and Physics

Introduction to Supergravity

Olof Ahlén

Supersymmetry has been a very active research area in both elementary particle physics as well as models for quantum gravity. In this talk, I will outline the motivation for analyzing supersymmetric...

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30.01.2017, 16:00 Uhr  –  Haus 9, Raum 0.14 Oberseminar Analysis, Geometrie, Physik

Geometric asymptotics: Cross index and Maslov class

Sara Azzali

Guillemin-Sternberg, Chapter IV, §3

mehr erfahren

26.01.2017, 14:15 Uhr  –  Haus 9, Raum 0.14 Seminar Geometrie

Ricci-Fluss auf Flächen: Abschätzungen für die Krümmung und ihre Ableitung

Sebastian Hannes

Abschätzungen für die Krümmung und ihre Ableitung

[CK, S. 137u.-143]

mehr erfahren

26.01.2017, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.12 Forschungsseminar Differentialgeometrie

Spectral flow and the Riesz stability of the Atiyah-Singer Dirac operator under bounded perturbations of local boundary conditions

Lashi Bandara

We study the Atiyah-Singer Dirac operator on smooth Riemannian Spin manifolds with smooth compact boundary. Under lower bounds on injectivity radius and bounds on the Ricci curvature and its first...

mehr erfahren

23.01.2017, 16:00 Uhr  –  Haus 9, Raum 0.14 Oberseminar Analysis, Geometrie, Physik

Geometric asymptotics: Cross index and Maslov class

Sara Azzali

Guillemin-Sternberg, Chapter IV, §3

mehr erfahren

19.01.2017, 14:15 Uhr  –  Haus 9, Raum 0.14 Seminar Geometrie

Ricci-Fluss auf Flächen: Flächenentropie

Alexander Friedrich

Flächenentropie

[CK, S. 133-137]

mehr erfahren

19.01.2017, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.12 Forschungsseminar Differentialgeometrie

Index of the Dirac Operator on Lorentzian Spacetime

Sebastian Hannes

We will prove Fredholm property of the Dirac operator on a globally hyperbolic spacetime under generalized APS boundary conditions and their deformations. Then we can derive relative index formulas...

mehr erfahren

12.01.2017, 14:15 Uhr  –  Haus 9, Raum 0.14 Seminar Geometrie

Ricci-Fluss auf Flächen: Vorbereitung und Strategie im Fall positiver Eulerzahl

Christian Bär

Vorbereitung und Strategie im Fall positiver Eulerzahl

[CK, S. 128-132]

mehr erfahren

12.01.2017, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.12 Forschungsseminar Differentialgeometrie

First variation of the mass of a closed Riemannian manifold

Andreas Hermann

Let (M,g) be a closed Riemannian manifold such that all eigenvalues of the conformal Laplace operator L_g are strictly positive and such that g is flat on an open neighborhood of a point p. The...

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05.01.2017, 14:15 Uhr  –  Haus 9, Raum 0.14 Seminar Geometrie

Ricci-Fluss auf Flächen: Ricci-Solitonen

Claudia Grabs

Ricci-Solitonen

[CK, S. 112, 116-119], [CLT]

mehr erfahren

15.12.2016, 14:15 Uhr  –  Haus 9, Raum 0.14 Seminar Geometrie

Ricci-Fluss auf Flächen: Konvergenz im Fall Eulerzahl = 0

Andreas Hermann

Konvergenz im Fall Eulerzahl = 0

[CK, S. 123u.-128]

mehr erfahren

15.12.2016, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.12 Forschungsseminar Differentialgeometrie

The geometry of semiclassical limits on regular Dirichlet spaces

Batu Güneysu

In this talk, I will first explain how one can reformulate the known semiclassical limit results for the heat trace of Schrödinger operators on Riemannian manifolds and infinite weighted graphs in a...

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13.12.2016, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.14 Seminar Geometry and Physics

Higher conserved currents

Igor Khavkine

A conserved current for a PDE in $n$-variables can be thought of as a field dependent $(n-1)$-form that is closed on solutions. A similar definition can also be made in other form degrees. A field...

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08.12.2016, 14:15 Uhr  –  Haus 9, Raum 0.14 Seminar Geometrie

Ricci-Fluss auf Flächen: Konvergenz im Fall negativer Eulerzahl

Konvergenz im Fall negativer Eulerzahl

[CK, S. 120-123]

mehr erfahren

29.11.2016, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.14 Seminar Geometry and Physics

Action principles and conserved currents, continued

I will introduce the notions of Noether current and Noether charge for a Lagrangian field theory.

References:
Lee and Wald, Local symmetries and constraints, JMP 1990
Iyer and Wald, Some properties of...

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24.11.2016, 14:15 Uhr  –  Haus 9, Raum 0.14 Seminar Geometrie

Ricci-Fluss auf Flächen: Krümmungspotential und Krümmungsschranken

Andreas Hermann

Krümmungspotential und Krümmungsschranken

[CK, S. 112 (ab (5.8))-115]

fortgesetzt am 1.12.2016

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22.11.2016, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.14 Seminar Geometry and Physics

A short introduction to the basics of the Noether theorem and its application

Michael Jung

I will start with an infinitesimal symmetry transformation as a diffeomorphism and derive the Noether-current. The setting is a compact domain in the flat space and just with one scalar field and one...

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17.11.2016, 14:15 Uhr  –  Haus 9, Raum 0.14 Seminar Geometrie

Ricci-Fluss auf Flächen: Krümmungsevolution

Viktoria Rothe

Krümmungsevolution

[CK, S. 109u.-111]

mehr erfahren

17.11.2016, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.12 Forschungsseminar Differentialgeometrie

Zeta Functions and Mass of Conformal Differential Operators

Matthias Ludewig

I will explain the relation between the Green’s function of a Laplace type operator and its zeta function. In particular, we will see that the constant term in the asymptotic expansion (which is often...

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15.11.2016, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.14 Seminar Geometry and Physics

Action principles and conserved currents

I will introduce, and give examples of, the notions of symplectic potential current, symplectic current, and Noether current for a Lagrangian field theory with local symmetries.
References:
Lee and...

mehr erfahren

10.11.2016, 14:15 Uhr  –  Haus 9, Raum 0.14 Seminar Geometrie

Ricci-Fluss auf Flächen: Konforme Änderung der Metrik

Max Lewandowski

Konforme Änderung der Metrik

[CK, S. 107-109]

mehr erfahren

Sebastian Hannes

Maximumprinzip

[CK S. 93-96]

mehr erfahren

03.11.2016, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.12 Forschungsseminar Differentialgeometrie

On the construction of the Green operators and of the ground state for a massive scalar field theory in AdS

Claudio Dappiaggi

We consider a real, massive scalar field on the Poincaré domain of the (d+1)-dimensional AdS spacetime. Since the background is not globally hyperbolic, first we determine all admissible boundary...

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01.11.2016, 16:15 Uhr  –  Haus 9, Raum 0.14 Seminar Geometry and Physics

Lagrangian and Hamiltonian field theory

Florian Hanisch

We will briefly review some basic ideas of the Lagrangian and the Hamiltonian approach to classical field theory, including some examples. We will keep the talk at an elementary level (sometimes with...

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27.10.2016, 14:15 Uhr  –  Haus 9, Raum 0.14 Seminar Geometrie

Ricci-Fluss auf Flächen: Einführung

Christian Bär

Einführung und Vergabe der Vorträge

[B], [CK, S. 105]

mehr erfahren

27.10.2016, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.12 Forschungsseminar Differentialgeometrie

The Cauchy problem for the linearised Einstein equation

In this talk we discuss the well-posedness of the Cauchy problem for the linearised Einstein vacuum equation on arbitrary globally hyperbolic vacuum spacetimes. The solution space of the linearised...

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19.10.2016, 10:15 Uhr  –  Campus Golm, Haus 9, Raum 2.22 Forschungsseminar Differentialgeometrie

An analogue of the Coleman-Mandula theorem for QFT in curved spacetimes

Chris Fewster

The Coleman--Mandula (CM) theorem states that the Poincaré and internal symmetries of a Minkowski spacetime quantum field theory cannot combine nontrivially in an extended symmetry group. In this talk...

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18.10.2016, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.14 Seminar Geometry and Physics

Supersymmetry and the Duistermaat-Heckmann-formula in finite dimensions

Florian Hanisch

The first session of the seminar will consist of 2 parts:

1) Discussion of the program for the semester.

2) Talk by F. Hanisch: Supersymmetry and the Duistermaat-Heckmann-formula in finite...

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14.07.2016, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Boundary value problems for Dirac operators

Sebastian Hannes

The talk deals with boundary value problems for dirac type operators on a complete Riemannian manifold with compact boundary. After a short introduction to Dirac operators on Riemanian manifolds,...

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30.06.2016, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Dirac operators on foliations

Ken Richardson

Given a foliation on a closed Riemannian manifold, the transversal Dirac operator is a Dirac operator that differentiates only in the directions normal to the foliation and is thereby transversally...

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30.06.2016, 14:15 Uhr  –  Campus Golm, Haus 9, Raum 0.14 Seminar Geometry and Physics

Supersymmetry and the Atiyah-Singer Index Theorem

Matthias Ludewig, Florian Hanisch

The seminar will have two parts,

Matthias Ludewig: Finite dimensional approximation of path integrals (continuation).

Florian Hanisch: Supersymmetry and the Duistermaat-Heckman formula.

Witten's...

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29.06.2016, 14:15 Uhr  –  Campus Golm, Haus 9, Raum 2.22 Forschungsseminar Differentialgeometrie

Gamma-structures on symmetric spaces

Bernhard Hanke

Gamma-structures are weak forms of multiplications on closed oriented manifolds. As shown by Hopf the rational cohomology algebras of manifolds admitting Gamma-structures are free over odd degree...

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Florian Hanisch

[Shioya 3.2]

mehr erfahren

23.06.2016, 14:15 Uhr  –  Campus Golm, Haus 9, Raum 0.14 Seminar Geometry and Physics

Discretisation of path integrals

Matthias Ludewig

We will describe different ways of discretising path integrals and compare different metrics on the (discrete) path space. Moreover, we will discuss different boundary conditions for path (fixed...

mehr erfahren

Florian Hanisch

[Shioya, 3.1]

mehr erfahren

13.06.2016, 16:00 Uhr  –  Raum 2.09.0.14 Oberseminar Analysis, Geometrie, Physik

Spectrum of the Laplacian

Matthias Ludewig

[Shioya 2.6]
Eigenvalue estimates in terms of separation distance

mehr erfahren

09.06.2016, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

The scalar wave equation with(out) topological charge on Schwarzschild and Reissner-Nordström black hole spacetimes

Ariane Beier

The aim of this talk is to present the results of the analysis of the separated solutions of the scalar wave equation with and without topological charge on Schwarzschild and Reissner-Nordström black...

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09.06.2016, 14:15 Uhr  –  Campus Golm, Haus 9, Raum 0.14 Seminar Geometry and Physics

Supersymmetry and the Atiyah-Singer Index Theorem

Florian Hanisch

This talk will focus on supergeodesics.

Witten's heuristic proof of the index theorem using supergeometry is well known but still not fully mathematically understood. We present the approaches to the...

mehr erfahren

02.06.2016, 14:15 Uhr  –  Campus Golm, Haus 9, Raum 0.14 Seminar Geometry and Physics

Supersymmetry and the Atiyah-Singer Index Theorem: Finite dimensional approximation

This talk will focus on finite dimensional approximations of path integrals.

Witten's heuristic proof of the index theorem using supergeometry is well known but still not fully mathematically...

mehr erfahren

30.05.2016, 16:00 Uhr  –  Raum 2.09.0.14 Oberseminar Analysis, Geometrie, Physik

Manifolds with positive Ricci curvature

Phillip Thonke

[Shioya 2.5]
Bounds for observable diameter, more examples of Levy families

mehr erfahren

26.05.2016, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

On the positive mass conjecture for closed Riemannian manifolds

Andreas Hermann

Let (M,g) be a closed Riemannian manifold such that all eigenvalues of the conformal Laplace operator L_g of g are strictly positive and such that g is flat on an open neighborhood of a point p. The...

mehr erfahren

23.05.2016, 16:00 Uhr  –  Raum 2.09.0.14 Oberseminar Analysis, Geometrie, Physik

Separation distance

Sara Azzali

[Shioya 2.4 plus Thm 2.31 without proof and Lemma 2.32 with proof]
Relation between separation distance and observable diameter, Levy-Gromov isoperimetric inequality

mehr erfahren

19.05.2016, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Semilinear wave equations and the Yamabe problem on Lorentzian manifolds

Viktoria Rothe

In this talk we will consider the Cauchy problem for semilinear wave equations on globally hyperbolic Lorentzian manifolds. We will examine under which conditions we obtain time-global solutions for...

mehr erfahren

19.05.2016, 14:15 Uhr  –  Campus Golm, Haus 9, Raum 0.14 Seminar Geometry and Physics

Supersymmetry and the Atiyah-Singer Index Theorem

Florian Hanisch, Matthias Ludewig

This is a continuation of the seminar on April 21 and 28.
Witten's heuristic proof of the index theorem using supergeometry is well known but still not fully mathematically understood. We present the...

mehr erfahren

12.05.2016, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Isotropic hyperelastic shells – Geometry, Physics, Examples

Claudia Grabs

We consider two-dimensional shells made of isotropic and hyperelastic material. First, the basic equations of elasticity are recalled, with special emphasis on the constitutive laws. Subsequently we...

mehr erfahren

09.05.2016, 16:00 Uhr  –  Raum 2.09.0.14 Oberseminar Analysis, Geometrie, Physik

mm-spaces and Levy families

Elke Rosenberger

[Shioya 2.2-2.3]
Lipschitz order, observable diameter

mehr erfahren

02.05.2016, 16:00 Uhr  –  Raum 2.09.0.14 Oberseminar Analysis, Geometrie, Physik

Levy's isoperimetric inequality

Tania Kosenkova

[Shioya 2.1]
Maxwell-Boltzmann distribution law, normal law a la Levy

mehr erfahren

28.04.2016, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

The Cauchy problem of the linearised Einstein equations

In this talk, we consider the Cauchy problem of the linearised Einstein equation on smooth globally hyperbolic spacetimes, satisfying the non-linear Einstein equation. Given smooth or distributional...

mehr erfahren

28.04.2016, 14:15 Uhr  –  Campus Golm, Haus 9, Raum 0.14 Seminar Geometry and Physics

Supersymmetry and the Atiyah-Singer Index Theorem

Matthias Ludewig, Florian Hanisch

This is a continuation of the seminar on April 21.
Witten's heuristic proof of the index theorem using supergeometry is well known but still not fully mathematically understood. We present the...

mehr erfahren

25.04.2016, 16:00 Uhr  –  Raum 2.09.0.14 Oberseminar Analysis, Geometrie, Physik

Transport plans and convergence in measure

Tania Kosenkova

[Shioya Def 1.20-Lemma 1.27]
(Sub-)transport plan, Ky-Fan metric

mehr erfahren

21.04.2016, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Generalised Hyperbolicity for Singular Spacetimes

Yafet Sanchez Sanchez

A desirable property of any spacetime is that the evolution of any physical field is locally well-defined. For smooth spacetimes this is guaranteed by standard local well-posedness results. Moreover,...

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21.04.2016, 14:15 Uhr  –  Campus Golm, Haus 9, Raum 0.14 Seminar Geometry and Physics

Supersymmetry and the Atiyah-Singer Index Theorem

Matthias Ludewig, Florian Hanisch

Witten's heuristic proof of the index theorem using supergeometry is well known but still not fully mathematically understood. We present the approaches to the subject by Witten, Atiyah and Lott (and...

mehr erfahren

18.04.2016, 16:00 Uhr  –  Raum 2.09.0.14 Oberseminar Analysis, Geometrie, Physik

Convergence of measures

Moritz Gerlach

[Shioya, chapter 1.2 up to Thm 1.19 and additional references]
weak and vague convergence, Prohorov distance

mehr erfahren

14.04.2016, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Construction of solutions of wave equations on global hyperbolic Lorentzian manifolds via Hadamard expansion

Max Lewandowski

I will start again with solutions of d'Alembert's equation on n-dimensional Minkowski space fulfilling Wightman's Axioms as a prototype with regard to general wave equations on global hyperbolic ...

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04.02.2016, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 1.11 Forschungsseminar Differentialgeometrie

Symmetriebrechung und der Higgsmechanismus II

Christoph Stephan

Nach einer kurzen Wiederholung der geometrischen Grundlagen des Higgs-Mechanismus diskutiere ich die Eigenschaften der Massenmatrix und die möglichen physikalischen Freiheitsgrade.

Die Anzahl der...

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28.01.2016, 15:00 Uhr  –  Campus Golm, Haus 9, Raum 0.12 Forschungsseminar Differentialgeometrie

Suborbifolds

Martin Weilandt

Inspired by work of Borzellino and Brunsden, we generalize the notion of a submanifold identifying a natural and sufficiently general condition which guarantees that a subset of an (effective)...

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21.01.2016, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 1.11 Forschungsseminar Differentialgeometrie

Präsentation und Kooperation mit Touchscreens

Christian Becker, Florian Hanisch, Christoph Stephan

Wir stellen die neuen Touchscreens des Instituts vor und erklären, wie man sie für Präsentationen und Kooperationen verwenden kann. Für Kooperationen bietet sich dabei Adobe Connect an, welches allen...

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Matthias Ludewig

[GB, 13-26]

mehr erfahren

14.01.2016, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 1.11 Forschungsseminar Differentialgeometrie

Symmetriebrechung und der Higgsmechanismus

Christoph Stephan

Eine Grundlage der mathematischen Modellierung des Standardmodells der Elementarteilchenphysik bilden Hauptfaserbündel und zu ihnen assoziierte Vektorbündel. Um die experimentell beobachteten...

mehr erfahren

[GB, 1-13]

mehr erfahren

07.01.2016, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 1.11 Forschungsseminar Differentialgeometrie

Visualisierung von Lösungen der Wärme- und Wellengleichung mittels SAGE

Christian Bär

Mit Hilfe der Computeralgebra-Software SAGE berechnen und visualisieren wir Lösungen der Wärmeleitungsgleichung und der Wellengleichung auf flachen 2-dimensionalen Tori. Nach einer kurzen...

mehr erfahren

Claudia Grabs

[F, 165-171]

mehr erfahren

Christian Becker

[F, 141-154]

mehr erfahren

10.12.2015, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 1.11 Forschungsseminar Differentialgeometrie

A new approach to physical solutions of scalar wave equations on globally hyperbolic Lorentzian manifolds

Max Lewandowski

After Radzikowski's celebrated equivalence theorem in the 1990's microlocal analysis and especially the wave front set of solutions of wave equations on globally hyperbolic Lorentzian manifolds...

mehr erfahren

03.12.2015, 12:15 Uhr  –  Haus 9, Raum 0.12 Seminar Geometrie

Einführung in Sage: Lineare Algebra II

Christoph Stephan

[F, 113-132]

mehr erfahren

03.12.2015, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 1.11 Forschungsseminar Differentialgeometrie

The Hamiltonian formulation of general relativity and the space of initial data

We recall the Hamiltonian formulation of Einstein's vacuum equation and explain the exact meaning of the lapse function and the shift vector. In this form, Einstein's equation can be seen as a flow on...

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26.11.2015, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 1.11 Forschungsseminar Differentialgeometrie

Path Integrals, Zeta-Determinants and the Gelfand-Yaglom Theorem

Matthias Ludewig

It is "well-known" in quantum field theories that the values of certain path integrals are given by associated zeta-determinants "up to a multiplicative constant". What is usually meant is that one...

mehr erfahren

Florian Hanisch

[F, 113-132]

mehr erfahren

Matthias Keller

Ariane Beier

[F, 80-111]

mehr erfahren

12.11.2015, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 1.11 Forschungsseminar Differentialgeometrie

Spectral functions of Dirac operators

Alexander Strohmaier

I will review some known general expansions of microlocal spectral counting functions of Dirac and Laplace operators. In special cases these relate directly to heat kernel coefficients. I will then...

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Max Lewandowski

[F, 80-111]

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05.11.2015, 12:15 Uhr  –  Haus 9, Raum 0.12 Seminar Geometrie

Einführung in Sage: Ausdrücke und Funktionen, Objekte

Andreas Hermann, Florian Hanisch

[F, 63-73], [F, 73-77]

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Ariane Beier

29.10.2015, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 1.11 Forschungsseminar Differentialgeometrie

Asymptotic Expansion of Path integrals

Matthias Ludewig

Given a parameter-dependent integral of the form $\int_M e^{-\phi(x)/2t} a(x) dx$ on a Riemannian manifold, it has an asymptotic expansion for small times, which can be calculated using the Laplace...

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29.10.2015, 12:15 Uhr  –  Haus 9, Raum 0.12 Seminar Geometrie

Einführung in Sage: Los geht's

Claudia Grabs

Elementare Arithmetik und Strings auf der Kommandozeile und im Notebookinterface. [F, 41-63]

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22.10.2015, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 1.10 Forschungsseminar Differentialgeometrie

Locally covariant QFT and the gauge puzzle

Marco Benini

Using the simple example of a free scalar field, I will illustrate the axiomatic formulation of locally covariant quantum field theory (LCQFT). With this framework in mind, the case of certain Abelian...

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22.10.2015, 12:15 Uhr  –  Haus 9, Raum 0.12 Seminar Geometrie

Sage: Installation und Überblick

Christian Bär

Installation und Überblick

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15.10.2015, 16:15  –  Campus Golm, Haus 9, Raum 1.10 Forschungsseminar Differentialgeometrie

Differential cohomology with compact support

Christian Becker

In this talk we introduce differential cohomology with compact support. There are several different models for differential cohomology. We use the model of differential characters which is originally...

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23.07.2015, 16:15 Uhr  –  Neues Palais, Haus 9, Raum 2.06 Forschungsseminar Differentialgeometrie

Eta and Zeta Functions and Us

Ken Richardson

Eta and zeta functions of geometric operators will be defined, and some elementary properties and relationsships will be described. Applications to classical and more recent work will be presented...

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02.07.2015, 16:15 Uhr  –  Neues Palais, Haus 9, Raum 2.06 Forschungsseminar Differentialgeometrie

Wellposedness of the Cauchy problem of the linearized Einstein-Klein-Gordon equations

We prove existence of a global solution to the linearized Einstein-Klein-Gordon equations, given initial data satisfying the linearized constraint equations. This solution is never unique, as one...

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25.06.2015, 16:15 Uhr  –  Neues Palais, Haus 9, Raum 2.06 Forschungsseminar Differentialgeometrie

Rigidity Results for manifolds with foliated boundary

Georges Habib (Lebanese University)

In this talk, we consider a compact Riemannian manifold whose boundary is endowed with a Riemannian flow. Under a suitable curvature assumption depending on the O'Neill tensor of the flow, we prove...

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18.06.2015, 16:15 Uhr  –  Haus 9, Raum 2.06 Forschungsseminar Differentialgeometrie

Flat bundles and K-theory with R/Z coefficients

Sara Azzali

With a flat unitary vector bundle E_a over a closed manifold M one can associate a class a in the K-theory of M with R/Z-coefficients. This class encodes the fact that a flat bundle admits a multiple...

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04.06.2015, 16:15 Uhr  –  Neues Palais, Haus 9, Raum 2.06 Forschungsseminar Differentialgeometrie

Conformal extendibility and Einstein-Maxwell-Dirac Theory

Olaf Müller (Universität Regensburg)

In this talk, we first present the concept of conformal extendibility and its importance in the analysis of the Maxwell-Dirac equations. Then we revise the restrictions conformal extendibility has on...

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28.05.2015, 16.15 Uhr  –  Raum 1.09.2.06 Forschungsseminar Differentialgeometrie

An index theorem for Lorentzian manifolds

Christian Bär

We prove an index theorem for the Dirac operator on compact

Lorentzian manifolds with spacelike boundary. Unlike in the

Riemannian situation, the Dirac operator is not elliptic. But

it turns out...

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04.05.2015, 16.00 Uhr  –  Raum 1.08.0.50 Oberseminar Analysis, Geometrie, Physik

The spectrum of the Dirac operator for generic metrics

Andreas Hermann (Potsdam)

Let $M$ be a closed spin manifold of dimension $n\geq 2$. For every Riemannian metric on $M$ we define the spinor bundle on $M$, a complex vector bundle whose sections are called spinors. We also...

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30.04.2015, 16.15 Uhr  –  Haus 9, Raum 2.06 Forschungsseminar Differentialgeometrie

Hyperbolic PDE 1

Florian Hanisch (Potsdam)

We will review the existence and uniqueness results for linear, symmetric hyperbolic systems of PDEs based on energy estimates. We will mostly follow the book by C.D. Sogge, "Lectures on Non-Linear...

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27.04.2015, 16:00 Uhr  –  Raum 1.08.0.50 Oberseminar Analysis, Geometrie, Physik

String structures and connections

Christian Becker (Potsdam)

Let $X$ be a compact Riemannian $n$-manifold, with $n \geq 3$.

The bundle of orthonormal frames is a principal $O_n$-bundle.

Several geometric structures on $X$ can be described in terms of lifts of...

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23.04.2015, 16:15 Uhr  –  Hörsaal 1.09.2.06 Forschungsseminar Differentialgeometrie

Forschungsseminar Differentialgeometrie: "Asymptotic and convergent expansions of heat traces"

Michal Eckstein

Asymptotic expansions of heat traces have multifarious applications both in pure mathematics (e.g. index theorems) as well as in mathematical physics (e.g. QFT). Drawing from the theory of general...

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02.04.2015, 14.15 Uhr  –  Haus 8, Raum 0.53 Forschungsseminar Differentialgeometrie

Forschungsseminar Differentialgeometrie: "Supergeometry in classical field theory"

Igor Khavkine

Ordinary (bosonic) classical field theory consists of "field" bundle on a spacetime manifold, a variational PDE on the field sections, its space of solutions (the "phase space", an infinite...

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