# Upcoming Seminars & Events

## Primary tabs

##### Locally symmetric spaces: p-adic aspects

p-adic period spaces have been introduced by Rapoport and Zink as a generaliza- tion of Drinfeld upper half spaces and Lubin-Tate spaces. Those are open subsets of a rigid analytic p-adic flag manifold. An approximation of this open subset is the so called weakly admissible locus obtained by removing a profinite set of closed Schubert varieties. I will explain a recent theorem characterizing when the period space coincides with the weakly admissible locus. The proof consists in a thorough study of modifications of G-bundles on the curve.

##### TBA-Maria Colombo

##### Attractors: "when inertial waves meet topography..."

##### TB-Federico Buonerba

##### Bulk-Edge Duality and Complete Localization for Chiral Chains

We study one dimensional insulators obeying a chiral symmetry in the single-particle picture where the Fermi energy is assumed to lie within a mobility gap. Topological invariants are defined for infinite (bulk) or half-infinite (edge) systems, and it is shown that for a given bulk system with nearest neighbor hopping, the invariant is equal to the induced-edge-system's invariant.

##### TBA-Ti-Yen Lan

##### The Kuga-Satake construction.

The Kuga-Satake construction associates an abelian variety (the Kuga-Satake variety) to certain weight two Hodge structure, for example the second cohomology group of a K3 surface. I will discuss the construction, and its applications to the Weil conjecture, the Hodge conjecture, and the Tate conjecture (related to K3 surfaces).

##### TBA - Aliakbar Daemi

##### TBA-Gautam Iyer

##### From counting Markoff triples to Apollonian packings; a path via elliptic K3 surfaces and their ample cones

The number of integer Markoff triples below a given bound has a nice asymptotic formula with an exponent of growth of 2. The exponent of growth for the Markoff-Hurwitz equations, on the other hand, is in generalnot an integer. Certain elliptic K3 surfaces can be thought of as smooth generalizations of the Markoff surface. Like the Markoff surface, their group of automorphisms is discrete and infinite. One can therefore investigate the growth rate of a rational point (or curve) on the surface under the action of the group. The exponent of growth is sometimes an integer, and sometimes no