Activities of SPP2026
On this site you find all conferences, workshops and seminars that were (financially and organisationally) supported by the DFG priority programme „Geometry at Infinity“.
- all projects
- 01Hitchin components for orbifolds
- 02Asymptotic geometry of sofic groups and manifolds
- 03Geometric operators on a class of manifolds with bounded geometry
- 04Secondary invariants for foliations
- 05Index theory on Lorentzian manifolds
- 06Spectral Analysis of Sub-Riemannian Structures
- 07Asymptotic geometry of moduli spaces of curves
- 08Parabolics and invariants
- 09Diffeomorphisms and the topology of positive scalar curvature
- 10Duality and the coarse assembly map
- 11Topological and equivariant rigidity in the presence of lower curvature bounds
- 12Anosov representations and Margulis spacetimes
- 13Analysis on spaces with fibred cusps
- 14Boundaries of acylindrically hyperbolic groups and applications
- 15Spaces and Moduli Spaces of Riemannian Metrics with Curvature Bounds on compact and non-compact Manifolds
- 16Minimizer of the Willmore energy with prescribed rectangular conformal class
- 17Existence, regularity and uniqueness results of geometric variational problems
- 18Analytic L2-invariants of non-positively curved spaces
- 19Boundaries, Greens formulae and harmonic functions for graphs and Dirichlet spaces
- 20Compactifications and Local-to-Global Structure for Bruhat-Tits Buildings
- 21Stability and instability of Einstein manifolds with prescribed asymptotic geometry
- 22Willmore functional and Lagrangian surfaces
- 23Spectral geometry, index theory and geometric flows on singular spaces
- 24Minimal surfaces in metric spaces
- 25The Willmore energy of degenerating surfaces and singularities of geometric flows
- 26Projective surfaces, Segre structures and the Hitchin component for PSL(n,R)
- 27Invariants and boundaries of spaces
- 28Rigidity, deformations and limits of maximal representations
- 29Curvature flows without singularities
- 30Nonlinear evolution equations on singular manifolds
- 31Solutions to Ricci flow whose scalar curvature is bounded in Lp.
- 32Asymptotic geometry of the Higgs bundle moduli space
- 33Gerbes in renormalization and quantization of infinite-dimensional moduli spaces
- 34Asymptotic geometry of sofic groups and manifolds II
- 35Geometric operators on singular domains
- 36Cohomogeneity, curvature, cohomology
- 37Boundary value problems and index theory on Riemannian and Lorentzian manifolds
- 38Geometry of surface homeomorphism groups
- 39Geometric invariants of discrete and locally compact groups
- 40Construction of Riemannian manifolds with scalar curvature constraints and applications to general relativity
- 41Geometrically defined asymptotic coordinates in general relativity
- 42Spin obstructions to metrics of positive scalar curvature on nonspin manifolds
- 43Singular Riemannian foliations and collapse
- 44Actions of mapping class groups and their subgroups
- 45Macroscopic invariants of manifolds
- 46Ricci flows for non-smooth spaces, monotonic quantities, and rigidity
- 47Self-adjointness of Laplace and Dirac operators on Lorentzian manifolds foliated by noncompact hypersurfaces
- 48Profinite and RFRS groups
- 49Analysis on spaces with fibred cusps II
- 50Probabilistic and spectral properties of weighted Riemannian manifolds with Kato bounded Bakry-Emery-Ricci curvature
- 51The geometry of locally symmetric manifolds via natural maps
- 52Spaces and Moduli Spaces of Riemannian Metrics with Curvature Bounds on compact and non-compact Manifolds II
- 53Gauge-theoretic methods in the geometry of G2-manifolds
- 54Cohomology of symmetric spaces as seen from infinity
- 55New hyperkähler spaces from the the self-duality equations
- 56Large genus limit of energy minimizing compact minimal surfaces in the 3-sphere
- 57Existence, regularity and uniqueness results of geometric variational problems II
- 58Profinite perspectives on l2-cohomology
- 59Laplacians, metrics and boundaries of simplicial complexes and Dirichlet spaces
- 60Property (T)
- 61At infinity of symmetric spaces
- 62A unified approach to Euclidean buildings and symmetric spaces of noncompact type
- 63Uniqueness in mean curvature flow
- 64Spectral geometry, index theory and geometric flows on singular spaces II
- 65Resonances for non-compact locally symmetric spaces
- 66Minimal surfaces in metric spaces II
- 67Asymptotics of singularities and deformations
- 68Minimal Lagrangian connections and related structures
- 69Wall-crossing and hyperkähler geometry of moduli spaces
- 70Spectral theory with non-unitary twists
- 71Rigidity, deformations and limits of maximal representations II
- 72Limits of invariants of translation surfaces
- 73Geometric Chern characters in p-adic equivariant K-theory
- 74Rigidity, stability and deformations in nearly parallel G2-geometry
- 75Solutions to Ricci flow whose scalar curvature is bounded in L^p II
- 76Singularities of the Lagrangian mean curvature flow
- 77Asymptotic geometry of the Higgs bundle moduli space II
- 78Duality and the coarse assembly map II
- 79Alexandrov geometry in the light of symmetry and topology
- 80Nonlocal boundary problems: Index theory and semiclassical asymptotics
15/01/2020 | Seminar
Wave equations and Fourier integral operators on models of an expanding universe
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
01/04/2019 | Conference
SPP Conference "Geometry at Infinity"
This is the first of two international conferences representing the full scope of research activites within the priority programme Geometry at Infinity. Besides a number of plenary lectures there will be parallel sessions for contributed talks.
Start: Monday, 01/04/2019 09:00 am
End: Friday, 05/04/2019 12:00 am
Related project(s):
01Hitchin components for orbifolds02Asymptotic geometry of sofic groups and manifolds03Geometric operators on a class of manifolds with bounded geometry04Secondary invariants for foliations05Index theory on Lorentzian manifolds06Spectral Analysis of Sub-Riemannian Structures07Asymptotic geometry of moduli spaces of curves08Parabolics and invariants09Diffeomorphisms and the topology of positive scalar curvature10Duality and the coarse assembly map11Topological and equivariant rigidity in the presence of lower curvature bounds12Anosov representations and Margulis spacetimes13Analysis on spaces with fibred cusps14Boundaries of acylindrically hyperbolic groups and applications15Spaces and Moduli Spaces of Riemannian Metrics with Curvature Bounds on compact and non-compact Manifolds16Minimizer of the Willmore energy with prescribed rectangular conformal class17Existence, regularity and uniqueness results of geometric variational problems18Analytic L2-invariants of non-positively curved spaces19Boundaries, Greens formulae and harmonic functions for graphs and Dirichlet spaces20Compactifications and Local-to-Global Structure for Bruhat-Tits Buildings21Stability and instability of Einstein manifolds with prescribed asymptotic geometry22Willmore functional and Lagrangian surfaces23Spectral geometry, index theory and geometric flows on singular spaces24Minimal surfaces in metric spaces25The Willmore energy of degenerating surfaces and singularities of geometric flows26Projective surfaces, Segre structures and the Hitchin component for PSL(n,R)27Invariants and boundaries of spaces28Rigidity, deformations and limits of maximal representations29Curvature flows without singularities30Nonlinear evolution equations on singular manifolds31Solutions to Ricci flow whose scalar curvature is bounded in Lp.32Asymptotic geometry of the Higgs bundle moduli space33Gerbes in renormalization and quantization of infinite-dimensional moduli spaces
04/02/2019 | Workshop, Conference
AUSTRALIAN-GERMAN WORKSHOP ON DIFFERENTIAL GEOMETRY IN THE LARGE
In the first week of the program, we plan an international conference to highlight recent advances in global Riemannian and metric geometry, topology, and geometric analysis to foster communication between experts and early career researchers from Australia and abroad and identify directions to set the stage for future advances.
In the second week, we plan to hold the first Australian-German workshop on differential geometry with Australian and German geometers who participated in the conference, focussing on new problems and potential directions of future research that came up in the first week.
Organisers: Owen Dearricott ( University of Melbourne), Diarmuid Crowley (University of Melbourne), Thomas Leistner (University of Adelaide), Yuri Nikolayevsky (LaTrobe University), Wilderich Tuschmann (Karlsruhe Institute of Technology).
Start: Monday, 04/02/2019 12:00 am
End: Friday, 15/02/2019 05:05 pm
Related project(s):
01Hitchin components for orbifolds02Asymptotic geometry of sofic groups and manifolds03Geometric operators on a class of manifolds with bounded geometry04Secondary invariants for foliations05Index theory on Lorentzian manifolds06Spectral Analysis of Sub-Riemannian Structures07Asymptotic geometry of moduli spaces of curves08Parabolics and invariants09Diffeomorphisms and the topology of positive scalar curvature10Duality and the coarse assembly map11Topological and equivariant rigidity in the presence of lower curvature bounds12Anosov representations and Margulis spacetimes13Analysis on spaces with fibred cusps14Boundaries of acylindrically hyperbolic groups and applications15Spaces and Moduli Spaces of Riemannian Metrics with Curvature Bounds on compact and non-compact Manifolds16Minimizer of the Willmore energy with prescribed rectangular conformal class17Existence, regularity and uniqueness results of geometric variational problems18Analytic L2-invariants of non-positively curved spaces19Boundaries, Greens formulae and harmonic functions for graphs and Dirichlet spaces20Compactifications and Local-to-Global Structure for Bruhat-Tits Buildings21Stability and instability of Einstein manifolds with prescribed asymptotic geometry22Willmore functional and Lagrangian surfaces23Spectral geometry, index theory and geometric flows on singular spaces24Minimal surfaces in metric spaces25The Willmore energy of degenerating surfaces and singularities of geometric flows26Projective surfaces, Segre structures and the Hitchin component for PSL(n,R)27Invariants and boundaries of spaces28Rigidity, deformations and limits of maximal representations29Curvature flows without singularities30Nonlinear evolution equations on singular manifolds31Solutions to Ricci flow whose scalar curvature is bounded in Lp.32Asymptotic geometry of the Higgs bundle moduli space33Gerbes in renormalization and quantization of infinite-dimensional moduli spaces
03/09/2018 | Workshop
Ricci flow, mean curvature flow and related singular flows
This 4-day workshop is addressed to graduate students and researchers in geometric analysis and differential geometry. It will mainly focus on geometric flows on smooth and singular manifolds and related topics such as Ricci solitons.
Start: Monday, 03/09/2018 01:30 pm
End: Thursday, 06/09/2018 01:30 pm
Related project(s):
21Stability and instability of Einstein manifolds with prescribed asymptotic geometry23Spectral geometry, index theory and geometric flows on singular spaces29Curvature flows without singularities31Solutions to Ricci flow whose scalar curvature is bounded in Lp.
05/02/2018 | Seminar
Winter School "Geometric Evolution Equations"
In this winter school we plan to bring together the working groups of the projects because of their related research topics. Everyone who is interested in the projects is welcome.
Start: Monday, 05/02/2018 10:00 am
End: Friday, 09/02/2018 12:00 pm
Related project(s):
21Stability and instability of Einstein manifolds with prescribed asymptotic geometry23Spectral geometry, index theory and geometric flows on singular spaces29Curvature flows without singularities31Solutions to Ricci flow whose scalar curvature is bounded in Lp.