aktuelle Professuren

Das Institut für Mathematik. Wer wir sind.

Das Institut für Mathematik gehört zu den acht Instituten der Mathematisch-Naturwissenschaftlichen Fakultät. Die Fakultät ist dabei die größte der Universität Potsdam. Derzeit gibt es 13 Professuren am Institut für Mathematik in Potsdam. Die Arbeitsgruppen vertreten ein breites Spektrum der mathematischen Lehre und aktueller mathematischer Forschungsrichtungen.

Folgende Professuren gibt es im Institut:
Algebra und Zahlentheorie | Prof. Dr. Gräter
Analysis | Prof. Dr. Paycha & apl. Prof. Dr. Tarkhanov
Angewandte Mathematik | Prof. Dr. Holschneider
Didaktik der Mathematik | Prof. Dr. Kortenkamp
Erdmagnetfeld | Prof. Dr. Stolle
Geometrie | Prof. Dr. Bär & apl. Prof. Dr. Andersson
Graphentheorie | Prof. Dr. Keller
Mathematische Modellierung und Systembiologie | Prof. Dr. Huisinga
Mathematische Physik | Prof. Dr. Klein
Mathematische Statistik | Prof. Dr. Blanchard & apl. Prof. Dr. Liero
Numerische Mathematik | Prof. Dr. Reich & apl. Prof. Dr. Böckmann
Partielle Differentialgleichungen | Prof. Dr. Metzger
Wahrscheinlichkeitstheorie | Prof. Dr. Roelly
Emeriti und Ehemalige

Forschungsverbünde

Mehrere Arbeitsgruppen des Instituts für Mathematik sind unter anderem an folgenden Forschungsverbünden beteiligt:

SFB 1294 "Data Assimilation"
Der Sonderforschungsbereich 1294 "Data Assimilation" wird seit 2017 von der Deutschen Forschungsgemeinschaft (DFG) gefördert. Beteiligt sind folgende Institutionen: Universität Potsdam, Humboldt-Universität zu Berlin, GFZ Potsdam, TU Berlin und WIAS-Institut Berlin. Leitung am Institut für Mathematik der Universität Potsdam.

 

SPP 2026 "Geometry at Infinity"
Das Schwerpunktprogramm 2026 "Geometry at Infinity" wird seit 2017 von der Deutschen Forschungsgemeinschaft (DFG) gefördert. Beteiligt sind Wissenschaftler und Wissenschaftlerinnen aus mehr als 20 Instituten in Deutschland und der Schweiz. Leitung an den Instituten für Mathematik der Universität Augsburg und der Universität Potsdam.

neue Publikationen

2018 | Error estimates for spectral convergence of the graph Laplacian on random geometric graphs towards the Laplace--Beltrami operator | Nicolas Garcia Trillos, Moritz Gerlach, Matthias Hein, Dejan Slepcev

Error estimates for spectral convergence of the graph Laplacian on random geometric graphs towards the Laplace--Beltrami operator

Autoren: Nicolas Garcia Trillos, Moritz Gerlach, Matthias Hein, Dejan Slepcev (2018)


2018 | Focal Points at Infinity for Short-Range Scattering Trajectories | Horst Hohberger, Markus Klein
Zeitschrift: J. Shanghai Jia Tong Univ. (Sci.) Seiten: 1-12 Band: 23(1)

Focal Points at Infinity for Short-Range Scattering Trajectories

Autoren: Horst Hohberger, Markus Klein (2018)

Classical scattering trajectories are known to form a Lagrangian manifold in euclidean phase space, which allows the classification of local focal points for sufficiently small dimensions. For the case of a short-range potential, we show that the natural description of focal points at infinity is a Lagrangian manifold in the cotangent bundle of the sphere and establish the relationship between focal points at infinity and the projection singularities of the manifold.

Zeitschrift:
J. Shanghai Jia Tong Univ. (Sci.)
Seiten:
1-12
Band:
23(1)

2018 | On the asymptotic behavior of static perfect fluids | Lars Andersson, Annegret Y. Burtscher

On the asymptotic behavior of static perfect fluids

Autoren: Lars Andersson, Annegret Y. Burtscher (2018)

Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether solutions have finite extent (stars with a vacuum exterior) or infinite extent. In the latter case, the matter extends globally with the density approaching zero at infinity. The asymptotic behavior largely depends on the equation of state of the fluid and is still poorly understood. While a few such unbounded solutions are known to be asymptotically flat with finite ADM mass, the vast majority are not. We provide a full geometric description of the asymptotic behavior of static spherically symmetric perfect fluid solutions with linear and polytropic-type equations of state. In order to capture the asymptotic behavior we introduce a notion of scaled quasi-asymptotic flatness, which encodes a form of asymptotic conicality. In particular, these spacetimes are asymptotically simple.


2018 | Conditioned point processes with application to Lévy bridges | Giovanni Conforti, Tetiana Kosenkova, Sylvie Roelly

Conditioned point processes with application to Lévy bridges

Autoren: Giovanni Conforti, Tetiana Kosenkova, Sylvie Roelly (2018)

Our first result concerns a characterisation by means of  a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalised version of Mecke's formula.  En passant, it also allows to gain quantitative results about stochastic domination for Poisson point processes under linear constraints.
Since bridges of a pure jump Lévy process in R^d with a height h can be interpreted as a Poisson point process on space-time conditioned by pinning its first moment to h, our approach allows us to characterize bridges of Lévy processes by means of a functional equation.
The latter result has two direct applications:
first we obtain a constructive and simple way to sample Lévy bridge dynamics; second it allows to estimate the number of jumps for such bridges. We finally show that our method remains valid for linearly perturbed Lévy processes like periodic Ornstein-Uhlenbeck processes driven by Lévy noise.


2018 | Packungen aus Kreisscheiben | Charlotte Dombrowsky, Myriam Fradon, Sylvie Roelly

Packungen aus Kreisscheiben

Autoren: Charlotte Dombrowsky, Myriam Fradon, Sylvie Roelly (2018)

Wir beschäftigen uns mit Konfigurationen von gleichgroßen Kreisscheiben in einer Ebene, die sich nicht überlappen. Wir sind insbesondere daran interessiert, die Konfiguration(en) zu finden, die eine minimale quadratische Energie besitzen.
In der Tat, ist die genaue Geometrie der optimalen Konfiguration(en) nur für sehr kleine Systeme schon bekannt. Wir schlagen hier eine  wahrscheinlichkeitstheoretische Methode vor, die  effizient für Systeme jeder Größe ist.


2018 | Empilements de disques ou comment une approche probabiliste peut compléter une analyse géométrique ... | Charlotte Dombrowsky, Myriam Fradon, Sylvie Roelly
Zeitschrift: Quadrature Band: 107

Empilements de disques ou comment une approche probabiliste peut compléter une analyse géométrique ...

Autoren: Charlotte Dombrowsky, Myriam Fradon, Sylvie Roelly (2018)

Zeitschrift:
Quadrature
Band:
107

2018 | Hidden symmetries and decay for the Vlasov equation on the Kerr spacetime | Lars Andersson, Pieter Blue, Jeremie Joudioux
Zeitschrift: Comm. PDE Verlag: Taylor & Francis

Hidden symmetries and decay for the Vlasov equation on the Kerr spacetime

Autoren: Lars Andersson, Pieter Blue, Jeremie Joudioux (2018)

This paper proves the existence of a bounded energy and integrated energy decay for solutions of the massless Vlasov equation in the exterior of a very slowly rotating Kerr spacetime. This combines methods previously developed to prove similar results for the wave equation on the exterior of a very slowly rotating Kerr spacetime with recent work applying the vector-field method to the relativistic Vlasov equation.

Zeitschrift:
Comm. PDE
Verlag:
Taylor & Francis

2018 | Geometry of black hole spacetimes | Lars Andersson, Thomas Bäckdahl, Pieter Blue
Reihe: London Mathematical Society Lecture Note Series Verlag: Cambridge University Press Buchtitel: T. Daudé, D. Häfner, J.-P. Nicolas (eds.): Asymptotic Analysis in General Relativity Seiten: 9-85 Band: 443

Geometry of black hole spacetimes

Autoren: Lars Andersson, Thomas Bäckdahl, Pieter Blue (2018)

These notes, based on lectures given at the summer school on Asymptotic Analysis in General Relativity, collect material on the Einstein equations, the geometry of black hole spacetimes, and the analysis of fields on black hole backgrounds. The Kerr model of a rotating black hole in vacuum is expected to be unique and stable. The problem of proving these fundamental facts provides the background for the material presented in these notes.
Among the many topics which are relevant for the uniqueness and stability problems are the theory of fields on black hole spacetimes, in particular for gravitational perturbations of the Kerr black hole, and more generally, the study of nonlinear field equations in the presence of trapping. The study of these questions requires tools from several different fields, including Lorentzian geometry, hyperbolic differential equations and spin geometry, which are all relevant to the black hole stability problem.

Reihe:
London Mathematical Society Lecture Note Series
Verlag:
Cambridge University Press
Buchtitel:
T. Daudé, D. Häfner, J.-P. Nicolas (eds.): Asymptotic Analysis in General Relativity
Seiten:
9-85
Band:
443

2017 | On a Semigroup of n-ary Operations | Susanti, Y., Koppitz, J.
Zeitschrift: Far East Journal of Mathematical Sciences (FJMS) Band: 102 no.4

On a Semigroup of n-ary Operations

Autoren: Susanti, Y., Koppitz, J. (2017)

Zeitschrift:
Far East Journal of Mathematical Sciences (FJMS)
Band:
102 no.4

2017 | Regular Semigroups of Partial Transformations Preserving a Fence | Lohapan, L., Koppitz, J.
Zeitschrift: Novi Sad Journal of Mathematics (NSJOM) Band: 47 no. 2

Regular Semigroups of Partial Transformations Preserving a Fence

Autoren: Lohapan, L., Koppitz, J. (2017)

Zeitschrift:
Novi Sad Journal of Mathematics (NSJOM)
Band:
47 no. 2