| Date | Speaker | Title |
| January 22 | Mikhail Skopenkov Higher School of Economics, Moscow and King Abdullah University, Saudi Arabia |
TBA |
| November 20 | Juliette Bruce Dartmouth College |
Cohomology of Locally Symmetric Varieties |
| November 13 | Irving Day UT Austin |
TBA |
| November 6 | Ivan Dynnikov Moscow State University and Steklov Mathematical Institute, Moscow |
TBA |
| September 25 | Eric Ling University of Copenhagen |
Singularities, topology, and rigidity in cosmological spacetimes satisfying the null energy conditions |
January 22, 2026: Mikhail Skopenkov "TBA"
Abstract:
November 20, 2025: Juliette Bruce "Cohomology of Locally Symmetric Varieties"
Abstract: In this talk, I will introduce recent developments in understanding the rational cohomology of locally symmetric varieties by constructing tropicalizations of these spaces. While tropical geometry provides the main framework, I will emphasize how these tropicalizations offer new tools and insights relevant to topology, particularly in understanding the cohomology of moduli spaces and arithmetic groups.
November 13, 2025: Irving Dai "TBA"
Abstract:
November 6, 2025: Ivan Dynnikov "TBA"
Abstract:
September 25, 2025: Eric Ling "Singularities, topology, and rigidity in cosmological spacetimes satisfying the null energy condition"
Abstract: We consider globally hyperbolic spacetimes with compact Cauchy surfaces (i.e., Riemannian manifolds which appear as time slices within the spacetime) in a setting compatible with the presence of a positive cosmological constant. More specifically, for 3+1 dimensional spacetimes which satisfy the null energy condition and contain a future expanding compact Cauchy surface, we establish a precise connection between the topology of the Cauchy surfaces and the occurrence of past singularities. Our proof makes use of the Penrose singularity theorem along with the fact that every aspherical closed 3-manifold admits a finite covering with positive first Betti number, which is a consequence of the positive resolution of the virtual Haken conjecture. We also obtain several rigidity results when the spacetime does not contain past singularities and the Cauchy surface is only everywhere noncontracting. This is joint work with Greg Galloway and with Carl Rossdeutscher, Walter Simon, and Roland Steinbauer.