Abstracts

Week of November 2, 2025

November 3, 2025
Geometric Analysis and Application Area rigidity for the regular representation of surface groups. 3:45pm -

Abstract:  Starting from the celebrated results of Eells and Sampson, a rich and flourishing literature has developed around equivariant harmonic maps from the universal cover of Riemann surfaces into nonpositively curved target spaces. In particular, such maps are known to be rigid, in the sense that they are unique up to natural equivalence. Unfortunately, this rigidity property fails when the target space has positive curvature, and comparatively little is known in this framework. In this talk, given a closed Riemann surface with strictly negative Euler characteristic and a unitary representation of its fundamental group on a separable complex Hilbert space H which is weakly equivalent to the regular representation, we aim to discuss a lower bound on the Dirichlet energy of equivariant harmonic maps from the universal cover of the surface into the unit sphere S of H, and to give a complete classification of the cases in which the equality is achieved. As a remarkable corollary, we obtain a lower bound on the area of equivariant minimal surfaces in S, and we determine all the representations for which there exists an equivariant, area-minimizing minimal surface in S. The subject matter of this talk is a joint work with Antoine Song (Caltech) and Xingzhe Li (Cornell University).

 
Group Actions and Dynamics Global Rigidity of Codimension One Actions 4:00pm -
KT 203

Abstract: This talk concerns the geometric classification of smooth, locally free, codimension-one actions of higher-rank simple Lie groups $G$ on closed manifolds. Under a natural ergodic assumption, we prove a rigidity theorem giving a sharp dichotomy. Every such action is either: 

-Equivariantly diffeomorphic to the suspension of an action of a parabolic subgroup of $G$. 
-Finitely and equivariantly covered by the standard action on $G/\Gamma\times S^1$, where $\Gamma\leq G$ is a uniform lattice.

This result is in the spirit of the Zimmer program.
November 4, 2025
Geometry & Topology Bending, Entropy and proper affine actions of surface groups. 4:30pm -
KT 207

Abstract: The entropy of a quasifuchsian group agrees with the Hausdorff dimension of its limit set, and the entropy gives rise to an analytic function on the space of marked quasifuchsian groups. We find an unbounded open neighborhood of the Fuchsian locus in quasifuchsian space so that the only critical points of the entropy function lie on the Fuchsian locus. We also find an open neighborhood of the Fuchsian locus so that (the adjoint of) any quasifuchsian group in the neighborhood arises as the linear part of a proper affine action of the surface group on the Lie algebra of SL(2,C).

Both of these results are obtained by studying the infinitesimal behavior of bending deformations of quasifuchsian groups. This is joint work with Martin Bridgeman and Andres Sambarino.

Seminar talk is supported in part by the Mrs. Hepsa Ely Silliman Memorial Fund.
Geometry, Symmetry and Physics The geometry of spherical objects in 2-Calabi-Yau categories 4:30pm -
KT 801

Abstract: In the first part of the talk, I’ll give an introduction to the 2CY categories associated to Coxeter systems, stability conditions on them, and the relevance of these objects in the study of Artin-Tits braid groups.  In the second part of the talk, I’ll explain how the spherical objects in these categories have a PL structure closely related to the geometry of the stability manifold.  (Joint work with Asilata Bapat and Anand Deopurkar).
November 5, 2025
Colloquium A rigidity theorem for complex Kleinian groups. 4:00pm -
KT 101

Abstract: 

It is natural to ask what geometric/dynamical restrictions on discrete subgroups of Lie groups produce restrictions on the isomorphism type of the group. For example, Canary and Tsouvalas showed that certain growth conditions on singular values of group elements give rise to bounds on the cohomological dimension of the group. Farre, Pozzetti  and Viaggi introduced a restriction on subgroups of PSL(d,C) which guaranteed that they must be isomorphic to convex cocompact subgroups of PSL(2,C). 

We introduce a slightly stronger condition which guarantees that the  subgroup of PSL(d,C)  is isomorphic to a uniform lattice in PSL(2,C). If, in addition, the subgroup is strongly irreducible, then we show that it is the image of a uniform lattice in PSL(2,C) by an irreducible representation of PSL(2,C) into PSL(d,C). We may regard this as a global version of a classical local rigidity result of Ragunathan.

This is joint work with Tengren Zhang and Andy Zimmer.

Seminar talk is supported in part by the Mrs. Hepsa Ely Silliman Memorial Fund.
November 6, 2025
Analysis Self-interacting walks in high dimensions 4:00pm -
Zoom

Abstract:

A self-interacting random walk is a random process evolving in an environment which depends on its history. In this talk, we will discuss a few examples of these walks including the Lorentz gas, the mirror walk, the once-reinforced walk and the cyclic walk in the interchange process. I will present methods to analyze these walks in high dimensions and prove that they behave diffusively. The talk is based on joint works with Allan Sly, Felipe Hernandez, Antoine Gloria, Gady Kozma and Lenya Ryzhik.
Quantum Topology and Field Theory TBA 4:30pm -
KT 801

TBA
November 7, 2025
Friday Morning Seminar Friday Morning Seminar 10:00am -
KT 801

We have impromptu and (sometimes) scheduled talks, on topics in probability, combinatorics, geometry, and dynamics.

Everyone is welcome! 
November 8, 2025
GATSBY Singularity of measures for Cannon-Thurston maps 10:45am -
KT 101