Abstracts

Week of February 15, 2026

February 16, 2026
Geometric Analysis and Application On Backwards uniqueness for singular mean curvature flows. 3:45pm -
KT 906

Mean curvature flow, the gradient flow of the area functional, is the most natural geometric heat flow for embedded hypersurfaces. Being non linear, the flow develops singularities, at which it stops being smooth. One fundamental, often delicate, question for such non linear flows is that of backwards uniqueness. In this talk I will discuss recent backwards uniqueness results, obtained jointly with Josh Daniels-Holgate, which can address some singularities. I will also compare these results to (commonly more robust) forward uniqueness results, and also to the situation in other equations.   
Geometry, Symmetry and Physics Virtual Hodge numbers of the moduli space of maps to projective space 4:30pm -
KT 801

I will discuss joint work with Terry Song on the calculation of the virtual Hodge numbers (i.e. Hodge—Deligne polynomial, Hodge-Euler characteristic, etc.) of the moduli space of degree-d maps to projective space from smooth n-pointed curves of genus g. Up to Brill—Noether loci in genus g>= 3, I will show how to reduce the calculation to the corresponding invariants of M_g,n. This reduction implies a strong stability statement for the virtual Hodge numbers as functions of the degree d, and suggests homological stability properties of the moduli space generalizing known statements in genus zero.  As an intermediate result, I will outline an analogous calculation for the universal Jacobian over M_g,n. As I will discuss, the theory of symmetric functions is fundamental to our approach.
February 17, 2026
Geometry & Topology Superrigidity of rich representations 4:30pm -
KT 207
In this talk, I will introduce the class of geodesically rich representations. These are representations of (real or complex) hyperbolic lattices that preserve a significant amount of the geometric structure of the associated quotient manifold. When the quotient manifold has robust geometric structure, these representations exhibit rigidity phenomena. In particular, a recent superrigidity theorem for rich representations was used to prove that finite-volume hyperbolic manifolds with infinitely many maximal totally geodesic submanifolds are arithmetic (Bader-Fisher-Miller-Stover). I will discuss a new superrigidity theorem for rich representations that efficiently recovers existing results and addresses target groups that were previously inaccessible.
February 19, 2026
Quantum Topology and Field Theory Skeins, q-series, and modularity 4:30pm -
KT 801

Abstract:  I will describe a construction of a q-series invariant (BPS q-series, also known as the Z-hat invariant) associated to a 3-manifold decorated by an embedded link. These q-series depend only on the class of the link in the skein module, and hence define a homomorphism from the skein module to the space of q-series. The image of this homomorphism is conjectured to exhibit holomorphic quantum modularity, which suggests a new approach to Langlands duality for skein modules via q-series.
February 20, 2026
Learning seminar on Matroids and Algebraic Cycles Learning seminar on Matroids and Algebraic Cycles 2:15pm -
KT 801

TBA