Oskar Riedler
A well known result of Sebastian Goette and Uwe Semmelmann states that a spin map \(M\to N\) to a space of non-negative curvature operator is a Riemannian submersion, provided the map satisfies...
mehr erfahrenRudolf Zeidler
We will first revisit Witten’s spinorial proof of the Riemannian positive mass theorem. Then we discuss a recent alternative proof using a scalar- and mean curvature comparison principle. The latter...
mehr erfahrenBernhard Hanke (Augsburg)
Spaces of Riemannian metrics of positive scalar curvature on closed smooth manifolds have been studied intensively for many years. Typically, these spaces, if non-empty, are topologically highly...
mehr erfahrenSimone Cecchini (Texas A&M)
Using index theory for twisted Dirac operators on Lipschitz bundles over non-compact manifolds, I will present Llarull-type comparison results in the setting of low-regularity scalar curvature...
mehr erfahrenJohannes Ebert (Münster)
It is well-known that 4-dimensional smooth topology offers many exotic phenomena, typically detected by means of gauge theory, and it is also well-known
that these exoticities are very unstable when...
Matthias Lesch (Bonn)
Heat and resolvent expansions are a fundamental tool in spectral geometry and index theory. In the noncommutative world (á la Connes) such expansions exhibit fundamentally new structures. I will...
mehr erfahrenYujie Wu (Stanford)
Firstly, we apply the method of generalized soap bubbles (µ-bubbles) to study manifolds with positive scalar curvature; we prove a rigidity result for free boundary minimal hypersurfaces in a...
mehr erfahrenLyko Matti (Greifswald)
Analytic K-homology is a homology theory whose cycles are elliptic operators, and as such is a useful tool around which to organize index calculations on compact manifolds. On non-compact manifolds...
mehr erfahrenOskar Riedler
Harmonic morphisms between Riemannian manifolds can be defined as those maps preserving Laplace’s equation. They form an interesting class of maps and are intimately connected to minimal submanifolds.
... mehr erfahrenThomas Tony
Llarull proved in the late '90s that the round n-sphere is area-extremal, meaning that one cannot simultaneously increase both its scalar curvature and its metric. Goette and Semmelmann generalized...
mehr erfahrenUwe Semmelmann (Stuttgart)
A well-known conjecture of LeBrun and Salamon states that quaternion Kähler manifolds of positive scalar curvature should be symmetric. This conjecture is still widely open. But even under the much...
mehr erfahrenHans-Joachim Hein (Münster)
We will describe an example of a degeneration of degree 6 algebraic surfaces in \(\mathbb{CP}^3\) with an isolated triple point singularity on its central fiber. Then we will show how the unique...
mehr erfahrenIhsane Malass
We investigate the existence of gaussian bounds for heat kernel constructed by the parametrix methods of E.E.Levi and the single / double layer potential on a manifold with boundary, and its...
mehr erfahrenPeter Grabs
We investigate the Rarita-Schwinger operator using methods previously applied in the Dirac case. The structure of the underlying manifold \(\mathcal{S}^3 \cong \mathrm{SU}(2)\) as a Lie group implies...
mehr erfahrenLennart Ronge (UP)
This is a work-in-progress description on an unfinished approach to proving a Lorentzian version of the equivariant index theorem, which assigns an index to a Dirac operator in the presence of a group...
mehr erfahrenLennart Ronge
Given a Dirac type operator on a manifold with boundary and a group action that preserves all relevant structures, one can define a generalized index for any group element. Analogous to the APS index...
mehr erfahrenChristoph Böhm (Münster)
Let \(M^n\) be a smooth, compact manifold and let \(N\) denote the set of Riemannian metrics on \(M^n\) with a fixed smooth volume density \(\mu\) of volume 1. For any \(g_0 \in N\) , we show that...
mehr erfahrenBernd Ammann (Regensburg)
The classical Atiyah-Singer theorem tells us: if \(M\) is a closed spin manifold, carrying a metric \(g\) of non-negative scalar curvature, then either the Dirac operator is invertible or \((M,g)\)...
mehr erfahrenOnirban Islam
For differential operators preserved by the action of a Lie group G, the notion of index generalises to the G-index. A prototype of this situation arises for spin-Dirac operators on a compact...
mehr erfahrenChristian Bär (UP)
I will explain an eigenvalue estimate for Dirac operators in terms of the hyperspherical radius of the underlying manifold. When combined with other known eigenvalue estimates this has a number of...
mehr erfahrenFlorian Hanisch
The spectral shift function is an object from scattering theory. It was invented to describe/compute traces of certain operators and generalizes the notion of spectral flow. It is moreover closely...
mehr erfahrenChristoph Stephan
I will give an introduction to the Lean 4 proof assistant, focusing on basics of interactive theorem proving, dependend type theory and its applications in mathematics. The talk will be suitable for...
mehr erfahrenAndrea Mondino (Oxford)
Optimal transport tools have been extremely powerful to study Ricci curvature, in particular Ricci lower bounds in the non-smooth setting of metric measure spaces (which can be been as a non-smooth...
mehr erfahrenChristian Bär (UP)
Let \(M\) be an n-dimensional closed Riemannian spin manifold. A fill-in of \(M\) is a compact (n+1)-dimensional Riemannian spin manifold \(X\) whose boundary is \(M\). If \(X\) has nonnegative scalar...
mehr erfahrenOnirban Islam
I shall introduce the Chazarain method to construct retarded and advanced Green operators for a Dirac operator on a globally hyperbolic spacetime with timelike boundary.
mehr erfahrenAlberto Richtsfeld (UP)
In this talk I will report on my progress in computing the transgression forms for characteristic classes. First, I will compute the transgression form of characteristic classes of power sum symmetric...
mehr erfahrenChristian Bär (UP)
If M is a spacelike hypersurface of a Lorentzian manifold, then M inherits an induced Riemannian metric g and a second fundamental form q. The triple (M,g,q) is then called the induced initial data...
mehr erfahrenLennart Ronge (UP)
Vorbereitung auf das Blockseminar "Geometrie" nach dem Inverted-Classroom-Prinzip.
Indexsatz, Chern-Klassen, Pontrjagin-Klassen (3.4 - 4.3.7 im Skript)
Christian Bär (UP)
Vorbereitung auf das Blockseminar "Geometrie" nach dem Inverted-Classroom-Prinzip.
2.4-2.5.11, 2.5.17-18, Thm 5.1.1 im Skript
mehr erfahrenChristian Bär (UP)
Vorbereitung auf das Blockseminar "Geometrie" nach dem Inverted-Classroom-Prinzip.
Clifford-Algebren, Spingruppe, Spinoren (2.1-2.3 im Skript)
Lennart Ronge (UP)
Given a Dirac operator on a Lorentzian manifold with timelike boundary, its Fredholm index (and whether it is Fredholm at all) heavily depends on the boundary conditions that one imposes on the...
mehr erfahrenRebecca Roero
Presentation of an innovative way to compute the eta invariants for the Dirac operator of the Berger spheres. We can use the Atyiah-Patodi-Singer theorem for the index of the classical Dirac operator...
mehr erfahrenRudolf Zeidler (Münster)
We will present variants of the spacetime positive mass theorem in the spin setting: Firstly, its conclusion \(E \geq|P|\) holds for a single asymptotically flat (AF) end in a spin initial data set...
mehr erfahrenLashi Bandara
In this talk, I will discuss the Hodge theorem in the context of rough metrics (locally bounded measurable coefficient metrics). This is work in progress with Georges Habib (Beirut).
mehr erfahrenJonathan Glöckle (Regensburg)
Initial data sets are pairs of a Riemannian metric and a symmetric 2-tensor on a manifold \(M\). They arise in General Relativity as induced Riemannian metric and induced second fundamental form,...
mehr erfahrenIhsane Malass
Ray and Singer proved that on a closed manifold the analytic torsion is independent of the choice of Riemannian metric and on a compact manifold with boundary under relative / absolute boundary...
mehr erfahrenClaudia Grabs
The solution of a boundary value problem for static deformations of hyperelastic membranes depends on some constant material parameters describing the elastic properties of the material. These can be...
mehr erfahrenOnirban Islam
Loosely speaking, if two (pseudo)differential operators differ only by smoothing operators then they are called microlocal conjugate to each other. It is a classic result by Duistermaat and Hörmander...
mehr erfahrenOnirban Islam (UP)
Loosely speaking, if two (pseudo)differential operators differ only by smoothing operators then they are called microlocal conjugate to each other. It is a classic result by Duistermaat and Hörmander...
mehr erfahrenChristoph Stephan
The talk commences with an exploration of the fundamental mechanisms of modern electronic exchanges and their statistical properties, setting the groundwork for understanding price formation in crypto...
mehr erfahrenChristian Bär (UP)
The holographic index theorem relates the index of a Dirac-type operator on a compact manifold with boundary subject to certain local boundary conditions to the index of an induced operator on the...
mehr erfahrenLennart Ronge (UP)
Hadamard coefficients are a Lorentzian equivalent to the Riemannian heat kernel coefficients. They encode information about the geometry of the underlying Lorentzian manifold (e.g. the scalar...
mehr erfahrenBernd Ammann (Regensburg)
A geodesic \(c : \mathbf{R}\to M\) is called minimal if a lift to the universal covering globally minimizes distance. On the 2-dimensional torus with an arbitrary Riemannian metric there are...
mehr erfahrenChristian Bär (UP)
We give a simple proof of the tameness of the Fréchet space of smooth sections of a vector bundle over a compact manifold.
mehr erfahrenRubens Longhi
Connections on Fréchet vector bundles and Fréchet Lie groups. [I.4.5-I.4.6]
mehr erfahrenChristian Bär (UP)
I'll give a concise introduction to jet bundles of vector bundles. They allow to treat (higher) derivatives of sections in a coordinate invariant way without the need to introduce connections....
mehr erfahrenFlorian Hanisch
Fréchet manifolds and vector bundles. [I.4.1-I.4.4]
mehr erfahrenChristian Bär
Higher derivatives in Fréchet spaces. [I.3.5-I.3.6]
mehr erfahrenChristoph Stephan
Differentiation in Fréchet spaces [I.3.1-I.3.4]
mehr erfahrenChristian Bär
In a series of lectures we introduce some basics for the block seminar on the Nash-Moser inverse function theorem. We start with the definition of and examples for Fréchet spaces and discuss Fréchet-s...
mehr erfahrenAlberto Richtsfeld (UP)
The APS theorem is the extension of the Atiyah-Singer index theorem to manifolds with boundary. While the Atiyah-Singer index theorem holds for all elliptic differential operators, the APS theorem in...
mehr erfahrenOnirban Islam
The Dirac operator on a globally hyperbolic spacetime admits unique retarded and advanced fundamental solutions. They are well-known to be Lagrangian distributions. Recently, Bär and Gehring...
mehr erfahrenPeter Grabs
We look at \(S^3\) as a Lie Group and its representations, spin structure and Rarita-Schwinger operator. (In preparation to one day compute the Rarita-Schwinger spectrum using representation...
mehr erfahrenClaudia Grabs (UP)
Following chapter 10 in the book "Theoretical Elasticity" of A.E. Green and W. Zerna from 1968, we present basic equations for elastic shells. Since the three-dimensional equations for an elastic...
mehr erfahrenRubens 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...
mehr erfahrenAlberto 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...
mehr erfahrenOnirban 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...
mehr erfahrenRubens 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...
mehr erfahrenChristian 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...
mehr erfahrenChristian Bär
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....
mehr erfahrenOnirban 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...
mehr erfahrenPeter Grabs (UP)
We look at what might be involved in determining the above.
mehr erfahrenPenelope 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...
mehr erfahrenOnirban 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...
mehr erfahrenMehran 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...
mehr erfahrenArtem Nepechiy
Zoom link available at this moodle.
mehr erfahrenDominik 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...
mehr erfahrenAlberto 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...
mehr erfahrenBernhard Hanke
Zoom link available at this moodle.
mehr erfahrenRubens 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...
mehr erfahrenGeorg Frenck
Zoom link available at this moodle.
mehr erfahrenVanessa 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...
mehr erfahrenNicolò 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 \((M,g)\) -...
mehr erfahrenClaudia 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...
mehr erfahrenMatthias 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...
mehr erfahrenEttore 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.
mehr erfahrenAlberto Richtsfeld
Jonas Rungenhagen
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...
mehr erfahrenAlberto 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...
mehr erfahrenHelge Frerichs
Zoom link available at this moodle.
mehr erfahrenClaudia 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...
mehr erfahrenMarten Steuer
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...
mehr erfahrenRubens Longhi
Oliver Lindblad Petersen (Stanford)
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...
mehr erfahrenMichał 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...
mehr erfahrenClaudia 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,...
mehr erfahrenRudolf 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...
mehr erfahrenMagnus 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...
mehr erfahrenLashi 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...
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...
mehr erfahrenBernhard 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...
mehr erfahrenMehran 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...
mehr erfahrenAriane 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...
mehr erfahrenJonas 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...
mehr erfahrenFlorian 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...
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...
mehr erfahrenClaudia 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...
mehr erfahrenPenelope 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...
mehr erfahrenChen 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...
mehr erfahrenKlaus 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...
mehr erfahrenOliver Lindblad Petersen (Stanford)
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...
mehr erfahrenSebastian 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...
mehr erfahrenRubens 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...
mehr erfahrenSimone 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...
mehr erfahrenMehran 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...
mehr erfahrenSimone 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...
mehr erfahrenAlexander 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...
mehr erfahrenBernd 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...
mehr erfahrenMatthias 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...
mehr erfahrenMarkus 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...
mehr erfahrenRubens 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...
mehr erfahrenMyfanwy 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...
mehr erfahrenChristian 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...
mehr erfahrenBernhard 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...
mehr erfahrenOliver Lindblad Petersen (Stanford)
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...
mehr erfahrenLashi Bandara
Josephine Bommer
Aigner, Ziegler: Das BUCH der Beweise, Kapitel 27
mehr erfahrenClaudia 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...
mehr erfahrenSylvie Paycha
Benjamin Baron
Aigner, Ziegler: Das BUCH der Beweise, Kapitel 35
mehr erfahrenJonas Rungenhagen
In this talk, I want to give an overview about the representation theory of compact Lie groups as it has various applications.
mehr erfahrenChristian Bär
Nazli Mammadova
Aigner, Ziegler: Das BUCH der Beweise, Kapitel 29
mehr erfahrenMatthias Ludewig (Adelaide)
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...
mehr erfahrenChristian Bär
Martin Botushev
Aigner, Ziegler: Das BUCH der Beweise, Kapitel 18
mehr erfahrenPenelope 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...
mehr erfahrenMarkus Klein
Josephin Kühne
Aigner, Ziegler: Das BUCH der Beweise, Kapitel 17
mehr erfahrenAlden 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...
mehr erfahrenLukas Minogue
Noreen Fischer
Aigner, Ziegler: Das BUCH der Beweise, Kapitel 16
mehr erfahrenSebastian 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...
mehr erfahrenMarkus Klein
Luise Fritsche
Aigner, Ziegler: Das BUCH der Beweise, Kapitel 14
mehr erfahrenWai 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...
mehr erfahrenAndreas Hermann
Mara Martin
Aigner, Ziegler: Das BUCH der Beweise, Kapitel 13
mehr erfahrenRubens 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...
mehr erfahrenAndreas Braunß
Hanna Jürß
Aigner, Ziegler: Das BUCH der Beweise, Kapitel 10
mehr erfahrenLennart 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...
mehr erfahrenLashi Bandara
Maximilian Tieze
Aigner, Ziegler: Das BUCH der Beweise, Kapitel 33
mehr erfahrenClaudio 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.
mehr erfahrenClaudio 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...
mehr erfahrenClaudio 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...
mehr erfahrenSiegfried Beckus
Artem Istranin
Aigner, Ziegler: Das BUCH der Beweise, Kapitel 32
mehr erfahrenElke Rosenberger
René Hintze
Aigner, Ziegler: Das BUCH der Beweise, Kapitel 12
mehr erfahrenMichael 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...
mehr erfahrenOliver Lindblad Petersen (Uni Hamburg)
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,...
mehr erfahrenAndrea Hübner
Aigner, Ziegler: Das BUCH der Beweise, Kapitel 11
mehr erfahrenHans-Bert Rademacher (Uni Leipzig)
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...
mehr erfahrenSaskia Roos
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...
mehr erfahrenClaudia 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...
mehr erfahrenMehran Seyedhosseini (Göttingen)
Peter Grabs
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...
mehr erfahrenErnst 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...
mehr erfahrenMax 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...
mehr erfahrenViktoria 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...
mehr erfahrenZoe 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...
mehr erfahrenIlya 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...
mehr erfahrenAriane 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...
mehr erfahrenPavel 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...
mehr erfahrenHemanth 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....
mehr erfahrenAndreas Hermann
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...
mehr erfahrenAndreas Hermann
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...
mehr erfahrenHerbert 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.
mehr erfahrenLashi Bandara
Nadine Große (Freiburg)
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...
mehr erfahrenLashi Bandara
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...
mehr erfahrenHuali 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...
mehr erfahrenMichael Jung
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...
mehr erfahrenHelmut 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...
mehr erfahrenClaudia Grabs
Sebastian Hannes
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...
mehr erfahrenLukas 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...
mehr erfahrenAndreas Hermann
Oliver Lindblad Petersen (Hamburg)
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...
mehr erfahrenPeter Grabs
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.
mehr erfahrenChristian 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...
mehr erfahrenSaskia Roos
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...
mehr erfahrenLashi 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...
mehr erfahrenSebastian Hannes
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...
mehr erfahrenMichael Jung
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...
mehr erfahrenLukas 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...
mehr erfahrenClaudia Grabs
Lars Andersson
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...
mehr erfahrenJérémie 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...
mehr erfahrenPeter Grabs
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...
mehr erfahrenUwe 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...
mehr erfahrenTania 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...
mehr erfahrenViktoria 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...
mehr erfahrenMarkus Klein
TBA
mehr erfahrenClaudia 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...
mehr erfahrenElke Rosenberger
TBA
mehr erfahrenYouness Boutaib
TBA
mehr erfahrenMattias 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...
mehr erfahrenSylvie 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....
mehr erfahrenLashi 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...
mehr erfahrenSylvie Paycha
TBA
mehr erfahrenSebastian 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.
mehr erfahrenMatthias 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...
mehr erfahrenAlexander Friedrich
TBA
mehr erfahrenBernhard 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...
mehr erfahrenJan Metzger
TBA
mehr erfahrenMaxim 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...
mehr erfahrenAndreas 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...
mehr erfahrenMax 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...
mehr erfahrenChristian Bär
We will give a survey on recent developments in index theory on spacetimes and discuss open problems.
mehr erfahrenChristopher 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...
mehr erfahrenFlorian Hanisch
[1, Ch. 7F]
mehr erfahrenVolker 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...
mehr erfahrenChandrashekar Devchand
This semester we will study the first chapters of the book "Harmonic Maps, Conservation Laws and Moving Frames" by Frédéric Hélein.
mehr erfahrenClaudia Grabs
[1, Ch. 7C]
mehr erfahrenJan Metzger
This semester we will study the first chapters of the book "Harmonic Maps, Conservation Laws and Moving Frames" by Frédéric Hélein.
mehr erfahrenChristian Bär
[1, Ch. 7B, incl. proof of Thm. 7.19], see also [2, p. 176]
mehr erfahrenKlaus 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...
mehr erfahrenSylvie Paycha / Florian Hanisch
This semester we will study the first chapters of the book "Harmonic Maps, Conservation Laws and Moving Frames" by Frédéric Hélein.
mehr erfahrenSebastian Hannes
[3, 3.65-3.68]
mehr erfahrenViktoria 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...
mehr erfahrenMarkus Klein
This semester we will study the first chapters of the book "Harmonic Maps, Conservation Laws and Moving Frames" by Frédéric Hélein.
mehr erfahrenVít 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...
mehr erfahrenAndreas Hermann
[3, 3.58-3.64]
mehr erfahrenAlexander Friedrich
This semester we will study the first chapters of the book "Harmonic Maps, Conservation Laws and Moving Frames" by Frédéric Hélein.
mehr erfahrenAndreas Hermann
[3, 3.58-3.64]
mehr erfahrenMax 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...
mehr erfahrenJan Metzger
This semester we will study the first chapters of the book "Harmonic Maps, Conservation Laws and Moving Frames" by Frédéric Hélein.
mehr erfahrenAndreas Hermann
[3, 3.44-3.57]
mehr erfahrenClaudia 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...
mehr erfahrenSara Azzali
This semester we will study the first chapters of the book "Harmonic Maps, Conservation Laws and Moving Frames" by Frédéric Hélein.
mehr erfahrenPhilipp Bartmann
[3, 3.38-3.43]
mehr erfahrenSebastian 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...
mehr erfahrenFlorian Hanisch
This semester we will study the first chapters of the book "Harmonic Maps, Conservation Laws and Moving Frames" by Frédéric Hélein.
mehr erfahrenViktoria Rothe
[3, 3.29-3.37]
mehr erfahrenChristian 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)...
mehr erfahrenAlexander Friedrich
This semester we will study the first chapters of the book "Harmonic Maps, Conservation Laws and Moving Frames" by Frédéric Hélein.
mehr erfahrenClaudia Grabs
[3, 3.22-3.28]
mehr erfahrenMargarita 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...
mehr erfahrenFlorian Hanisch
[3, 3.17-3.21]
mehr erfahrenElke Rosenberger
This semester we will study the first chapters of the book "Harmonic Maps, Conservation Laws and Moving Frames" by Frédéric Hélein.
mehr erfahrenPhilip Thonke
This semester we will study the first chapters of the book "Harmonic Maps, Conservation Laws and Moving Frames" by Frédéric Hélein.
mehr erfahrenMax Lewandowski
[3, 3.13-3.16]
mehr erfahrenFlorian 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...
mehr erfahrenOlaf 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 ...
mehr erfahrenSebastian Hannes
[3, 3.1-3.12]
mehr erfahrenSaskia Roos (Bonn)
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...
mehr erfahrenOliver Lindblad Petersen
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...
mehr erfahrenOliver Lindblad Petersen
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...
mehr erfahrenSajad Aghapour (IPM, Teheran)
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...
mehr erfahrenAlexander 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...
mehr erfahrenAndreas 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...
mehr erfahrenIgor 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...
mehr erfahrenLars Andersson
I will discuss how Hertz potentials can be used to construct conservation laws for massless fields including Maxwell and linearized gravity.
mehr erfahrenChristian Bär
Ich werde erklären, wie sich der Fredholm-Index eines äquivarianten elliptischen Operators über einem homogenen Raum darstellungstheoretisch berechnen lässt.
mehr erfahrenCedric 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 erfahrenMax 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 erfahrenMax Lewandowski
Dirac-Operator auf riemannschen Mannigfaltigkeiten, Elliptizität, wesentliche Selbstadjungiertheit, Diskretheit des Spektrums
mehr erfahrenAndreas Hermann
Hauptfaserbündel, assoziierte Vektorbündel, Spinorbündel, Clifford-Multiplikation und Zusammenhang auf dem Spinor-Bündel
Sebastian Hannes
Clifford-Algebren, Clifford-Multiplikation, Pin-Gruppe, Spin-Gruppe, Spinor-Darstellung, invariantes inneres Produkt
mehr erfahrenMattias 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...
mehr erfahrenMax 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...
mehr erfahrenLars Andersson
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...
mehr erfahrenLashi 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 erfahrenOliver Lindblad Petersen
Der Fall positiver Eulerzahl
[CK, S. 148-156]
mehr erfahrenChristian 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 erfahrenJonas Rungenhagen
Harnack-Ungleichung
[CK, S. 143-148]
mehr erfahrenDaniel 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...
mehr erfahrenOlof 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...
mehr erfahrenSara Azzali
Guillemin-Sternberg, Chapter IV, §3
mehr erfahrenSebastian Hannes
Abschätzungen für die Krümmung und ihre Ableitung
[CK, S. 137u.-143]
mehr erfahrenLashi 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 erfahrenSara Azzali
Guillemin-Sternberg, Chapter IV, §3
mehr erfahren
Alexander Friedrich
Flächenentropie
[CK, S. 133-137]
mehr erfahrenSebastian 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 erfahrenChristian Bär
Vorbereitung und Strategie im Fall positiver Eulerzahl
[CK, S. 128-132]
mehr erfahrenAndreas 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...
mehr erfahrenClaudia Grabs
Ricci-Solitonen
[CK, S. 112, 116-119], [CLT]
mehr erfahrenAndreas Hermann
Konvergenz im Fall Eulerzahl = 0
[CK, S. 123u.-128]
mehr erfahrenBatu 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...
mehr erfahrenIgor 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...
mehr erfahrenOliver Lindblad Petersen
Konvergenz im Fall negativer Eulerzahl
[CK, S. 120-123]
mehr erfahrenLars Andersson
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...
Andreas Hermann
Krümmungspotential und Krümmungsschranken
[CK, S. 112 (ab (5.8))-115]
fortgesetzt am 1.12.2016
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...
mehr erfahrenViktoria Rothe
Krümmungsevolution
[CK, S. 109u.-111]
mehr erfahrenMatthias 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...
mehr erfahrenLars Andersson
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...
Max Lewandowski
Konforme Änderung der Metrik
[CK, S. 107-109]
mehr erfahrenSebastian Hannes
Maximumprinzip
[CK S. 93-96]
mehr erfahrenClaudio 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...
mehr erfahrenFlorian 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...
mehr erfahrenChristian Bär
Einführung und Vergabe der Vorträge
[B], [CK, S. 105]
mehr erfahren
Oliver Lindblad Petersen
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...
mehr erfahrenChris 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...
mehr erfahrenFlorian 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...
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,...
mehr erfahrenKen 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...
mehr erfahrenMatthias 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...
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...
mehr erfahrenFlorian Hanisch
[Shioya 3.2]
mehr erfahrenMatthias 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 erfahrenFlorian Hanisch
[Shioya, 3.1]
mehr erfahrenMatthias Ludewig
[Shioya 2.6]
Eigenvalue estimates in terms of separation distance
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...
mehr erfahrenFlorian 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 erfahrenLars Andersson
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 erfahrenPhillip Thonke
[Shioya 2.5]
Bounds for observable diameter, more examples of Levy families
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 erfahrenSara 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
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 erfahrenFlorian 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...
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 erfahrenElke Rosenberger
[Shioya 2.2-2.3]
Lipschitz order, observable diameter
Tania Kosenkova
[Shioya 2.1]
Maxwell-Boltzmann distribution law, normal law a la Levy
Oliver Lindblad Petersen
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 erfahrenMatthias 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...
Tania Kosenkova
[Shioya Def 1.20-Lemma 1.27]
(Sub-)transport plan, Ky-Fan metric
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,...
mehr erfahrenMatthias 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 erfahrenMoritz Gerlach
[Shioya, chapter 1.2 up to Thm 1.19 and additional references]
weak and vague convergence, Prohorov distance
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 ...
mehr erfahrenChristoph 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...
mehr erfahrenMartin 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)...
mehr erfahrenChristian 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...
mehr erfahrenMatthias Ludewig
[GB, 13-26]
mehr erfahrenChristoph Stephan
Eine Grundlage der mathematischen Modellierung des Standardmodells der Elementarteilchenphysik bilden Hauptfaserbündel und zu ihnen assoziierte Vektorbündel. Um die experimentell beobachteten...
mehr erfahrenOliver Lindblad Petersen
[GB, 1-13]
mehr erfahrenChristian 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 erfahrenClaudia Grabs
[F, 165-171]
mehr erfahrenChristian Becker
[F, 141-154]
mehr erfahrenMax 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 erfahrenChristoph Stephan
[F, 113-132]
mehr erfahrenOliver Lindblad Petersen
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...
mehr erfahrenMatthias 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 erfahrenFlorian Hanisch
[F, 113-132]
mehr erfahrenMatthias Keller
Ariane Beier
[F, 80-111]
mehr erfahrenAlexander 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...
mehr erfahrenMax Lewandowski
[F, 80-111]
mehr erfahrenAndreas Hermann, Florian Hanisch
[F, 63-73], [F, 73-77]
mehr erfahrenAriane Beier
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...
mehr erfahrenClaudia Grabs
Elementare Arithmetik und Strings auf der Kommandozeile und im Notebookinterface. [F, 41-63]
mehr erfahrenMarco 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...
mehr erfahrenChristian Bär
Installation und Überblick
mehr erfahrenChristian 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...
mehr erfahrenKen 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...
mehr erfahrenOliver Lindblad Petersen
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...
mehr erfahrenGeorges 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...
mehr erfahrenSara 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...
mehr erfahrenOlaf 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...
mehr erfahrenChristian 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...
mehr erfahrenAndreas 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...
mehr erfahrenFlorian 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...
mehr erfahrenChristian 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...
mehr erfahrenMichal 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...
mehr erfahrenIgor 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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