Activities

The Women in Mathematical Physics Workshop at BIRS will have multiple research groups. One of them is on the topic of "Mathematical relativity: static Lorentzian length spaces" and fits into the framework of this SPP. It is led by Carla Cederbaum (Eberhard-Karls-Universität Tübingen, Germany) and Melanie Graf (University of Washington, US).

Applications for the workshop are open until Dec 20, 2019. For more information,

see sites.google.com/site/womathphys/.

Start: Sunday, 20/09/2020 09:00 am
End: Friday, 25/09/2020 04:00 pm
Related project(s):
05Index theory on Lorentzian manifolds

The unifying background of the meeting will be rigid differential-geometric structures, such as conformal and projective structures. This refers both to structures locally modelled on homogeneous spaces and to their curved analogues. One topic will be applications of Cartan connections to locally homogeneous structures, their moduli spaces, and compactifications. A related topic will be conformal compactifications such as Poincare-Einstein manifolds, and analogues for other ambient geometries. Another topic will be group actions preserving such structures and their rigidity.

Start: Monday, 20/07/2020 01:30 pm
End: Friday, 24/07/2020 12:00 pm
Related project(s):
01Hitchin components for orbifolds07Asymptotic geometry of moduli spaces of curves12Anosov representations and Margulis spacetimes26Projective surfaces, Segre structures and the Hitchin component for PSL(n,R)28Rigidity, deformations and limits of maximal representations32Asymptotic geometry of the Higgs bundle moduli space

Isoperimetric comparisons may be used to uncover new properties of curved spaces, and to estimate eigenvalues of operators of physical significance. Isoperimetric estimates have an ancient history, comparing the area and perimeter of regions. Only recently have the complex geometric situations seen in nature begun to be understood. These include excitation energies in quantum mechanics, and the geometry of soap bubbles. The field brings together the theory of PDE, differential geometry and non-smooth metric geometry and has continued to produce novel and exciting

mathematics since antiquity.

This program will gather together experts in such isoperimetric inequalities to progress this challenging, yet recently quite fruitful area. In particular it will facilitate communication between researchers working on different aspects of the field that may not yet be communicating with each other. For example, those researchers with expertise in PDE aspects may not be up to date on the latest results in RCD spaces and vice-versa.

Start: Monday, 13/07/2020 12:00 am
End: Friday, 24/07/2020 12:00 am
Related project(s):
22Willmore functional and Lagrangian surfaces

The conference will be held in honor of Karsten Grove.

The conference "Differential geometry and geometric analysis" will take place June 29 to July 3, 2020 in Florence, Italy.

Several major themes have been selected for the conference, including:

- Analysis in metric spaces, Geometric group theory, Geometric measure theory,

- Geometric theory of PDE's, Group actions on Riemannian manifolds, Manifolds of positive and nonpositive curvature,

- Metrics with special holonomy, Minimal manifolds and Min-Max Theory, Ricci Flow.

Start: Monday, 29/06/2020 09:00 am
End: Friday, 03/07/2020 06:00 pm
Related project(s):
15Spaces and Moduli Spaces of Riemannian Metrics with Curvature Bounds on compact and non-compact Manifolds

Arithmetic groups provide a fruitful link between various areas, such as geometry, topology, representation theory and number theory. Methods from geometry and topology hinge on the fact that arithmetic groups are lattices in Lie groups, whereas the theory of automorphic forms establishes a connection to representation theory and number theory. This interplay is especially intriguing in the setting of hyperbolic 3-manifolds. Indeed, many conjectures in 3-manifold theory tend to be much more accessible for hyperbolic 3-manifolds whose fundamental groups are arithmetic, and conversely, such manifolds provide the simplest set-up in which some of the most exciting new phenomena in the Langlands program can be studied. This conference will bring together researchers with various backgrounds around links between number theory and 3-manifolds. Central topics of the conference are the cohomology of arithmetic groups, the relation between torsion and L2-torsion, profinite invariants of 3-manifolds, and number theoretic ramifications.

Start: Monday, 23/03/2020 11:00 am
End: Friday, 27/03/2020 01:00 pm
Related project(s):
18Analytic L2-invariants of non-positively curved spaces

The topic of the workshop is Rational Homotopy Theory and applications in Geometry. The aim is to bring together researchers from different areas with a common interest in rational methods. There will be an introductory talk in the beginning and ample time for discussions and questions.

Start: Wednesday, 18/03/2020 04:00 pm
End: Friday, 20/03/2020 12:00 pm
Related project(s):
15Spaces and Moduli Spaces of Riemannian Metrics with Curvature Bounds on compact and non-compact Manifolds

www.uni-giessen.de/mathematik-airportseminar

The thematic focus of the conference series is on geometric, analytic and ergodic theoretical aspects of groups and their actions, but the conferences aim to explore also related areas of mathematics from representation theory and harmonic analysis over differential and metric geometry to topology, algebraic geometry and model theory, as well as to set a spotlight on newly emerging areas.

Start: Monday, 16/03/2020 02:00 pm
End: Tuesday, 17/03/2020 05:00 pm

This is the second meeting in a series of seminars on Geometric Analysis jointly organized by the Universities of Freiburg, Heidelberg, Stuttgart and Tübingen. It is intended to be a regular meeting of researchers from the South-West with an interest in the fields of geometry and analysis.

Start: Friday, 24/01/2020 01:00 pm
End: Friday, 24/01/2020 06:00 pm
Related project(s):
03Geometric operators on a class of manifolds with bounded geometry32Asymptotic geometry of the Higgs bundle moduli space

Mathematical general relativity is based on the theory of wave equations on curved spaces. In fact, even the gravitational field itself satisfies a non-linear wave equation, known as Einstein’s equation. Einstein’s equation is, in general, very difficult to solve and one therefore studies the wave equations on special models of the universe. The most simple model is the Minkowski space, which is the model of the universe in special relativity. This model is, however, not “expanding” and therefore not a good model for our universe (which is known to expand). The second most simple model for the universe is the so-called de Sitter space, which is believed to be a more accurate, since it is expanding. Fortunately, it is much easier to predict (estimate) solutions to wave equations on de Sitter space, than on Minkowski space. Moreover, there are natural generalizations of the de Sitter space including models for black holes. One of the most remarkable recent results in mathematical general relativity is the proof that such blackhole models are stable, by work of Hintz and Vasy [HV18].

In this winter school, we study wave equations on de Sitter space and the generalizations, including black holes. Though the proof of stability, mentioned above, lies beyond the scope of this winter school, the topics we will discuss are the natural first steps in this direction. We mainly will focus on a paper by Vasy [Vas10], where linear wave equations on asymptotically de Sitter spaces (generalizing de Sitter space) are studied in detail. Many of the non-technical ideas and basic structures in [HV18 ]are already present in [Vas10]. Vasy uses a microlocal analysis point of view,which gives a modern treatment of a classical problem. The methods include the construction and analysis of so-called Fourier integral operators (generalizing pseudo-differential operators), which will be studied in detail. From the time when the paper [Vas10] was published, a sequence of papers including [Vas13], [MSBV14], and [HV15], was published, building up for the final stability result in [HV18]. Even though most of the focus will be on [Vas10], the winter school will include a brief overview of all these papers and in particular an outline of the approach towards [HV18].

Start: Wednesday, 15/01/2020 01:30 am
End: Friday, 17/01/2020 05:00 pm
Related project(s):
21Stability and instability of Einstein manifolds with prescribed asymptotic geometry

This is the sixth instance of the Bavarian Geometry & Topology Meeting, which brings together researchers from Bavaria with international experts.

Start: Thursday, 05/12/2019 10:00 am
End: Friday, 06/12/2019 05:00 pm
Related project(s):
15Spaces and Moduli Spaces of Riemannian Metrics with Curvature Bounds on compact and non-compact Manifolds