Week of September 14, 2025

September 15, 2025
Geometric Analysis and Application Harmonic maps into Euclidean buildings Benjamin Dees - Brown University 3:45pm -
KT 906
Geometry, Symmetry and Physics On the de Rham-Hitchin system Siqing Zhang - Yale University 4:30pm -
KT 801
September 16, 2025
Geometry & Topology Limit sets of degenerate coaffine surface groups James Farre - Max Planck Institute Leipzig 4:30pm -
KT 207
Algebraic Geometry Quantizations and their representations, lecture 4 Ivan Loseu - Yale University 10:25pm -
KT 801
September 17, 2025
Colloquium The Zigzag Strategy for Random Band Matrices Vova Riabov - IST Austria - Future University Hakodate, Japan 4:00pm -
KT 101
September 18, 2025
Algebraic Geometry Quantizations and their representations, lecture 5 Ivan Loseu - Yale University 10:25am -
KT 801
Analysis Available Seminar Slot 4:00pm -
Quantum Topology and Field Theory Turaev-Viro invariant from U_q(sl(2;R)) Tian Yang - Texas A & M University 4:30pm -
KT 801
September 19, 2025
Friday Morning Seminar Friday Morning Seminar 10:00am -
KT 801

Abstracts

Week of September 14, 2025

September 15, 2025
Geometric Analysis and Application Harmonic maps into Euclidean buildings 3:45pm -
KT 906

Abstract: This talk will discuss regularity results for harmonic maps into a certain kind of metric space, called Euclidean buildings.  This will include a discussion of what these spaces are, the behavior of harmonic maps into these spaces, and the connection to superrigidity results for lattices.  We will discuss previously known regularity results before presenting a recent theorem of Breiner, Mese, and myself which generalizes these considerably. 
Geometry, Symmetry and Physics On the de Rham-Hitchin system 4:30pm -
KT 801

The de Rham-Hitchin system is a deformation of the Hitchin system in prime characteristic. It plays a main role in the prime characteristic Non Abelian Hodge Theory, relating Higgs bundles and connections. In this talk, I will survey what I know about the geometry and topology of the de Rham-Hitchin system, emphasizing how it relates to complex geometry and number theory. We start by motivating some correspondences on the category level using p-curvatures. Then we do some moduli theory to get a correspondence at the moduli space level. Finally, we deduce some consequences on the cohomologies of the moduli spaces.
September 16, 2025
Geometry & Topology Limit sets of degenerate coaffine surface groups 4:30pm -
KT 207

We are interested in surface subgroups of the coaffine subgroup of GL(4,R) via their actions on 3-dimensional projective space.  Many such surface subgroups are (projective)-Anosov and preserve a properly convex subset of projective space, on which they act with compact 3-manifold quotient with surface boundary.  In this talk, we explain how to identify the boundary of the locus of Anosov representations in terms of the shape of the unit ball for the “stable norm” on homology with respect to the relevant asymmetric metric on the surface.  We use this description and certain dual best Lipschitz maps to describe the structure of the limit sets for these degenerate surface groups.  There is, in particular, an oriented geodesic lamination of maximal stretch whose endpoints are all crushed to the same point in the limit set.  This is joint work with Marit Bobb.
Algebraic Geometry Quantizations and their representations, lecture 4 10:25pm -
KT 801

I will start discussion of classification of quantizations concentrating on the symplectic case.
September 17, 2025
Colloquium The Zigzag Strategy for Random Band Matrices 4:00pm -
KT 101

Random band matrices have entries concentrated in a narrow band of width W around the main diagonal, modeling systems with spatially localized interactions.

We consider one-dimensional random band matrices with bandwidth W >> N^½, general variance profile, and arbitrary entry distributions. We establish complete isotropic delocalization, quantum unique ergodicity (eigenstate thermalization), and Wigner-Dyson universality in the bulk of the spectrum. The key technical input is a family of local laws capturing the spatial decay of resolvent entries, established using a combination of Ornstein-Uhlenbeck dynamics and Green function comparison (the Zigzag strategy). Based on joint work with László Erdős.
September 18, 2025
Algebraic Geometry Quantizations and their representations, lecture 5 10:25am -
KT 801

I will define conical symplectic singularities and give some examples. Then I’ll discuss their quantizations.
Analysis Available Seminar Slot 4:00pm -
Quantum Topology and Field Theory Turaev-Viro invariant from U_q(sl(2;R)) 4:30pm -
KT 801

Abstract:  We define a family of Turaev-Viro type invariants of hyperbolic 3-manifolds with totally geodesic boundary from the 6j-symbols of the modular double of U_q(sl(2; R)), and prove that these invariants decay exponentially with the rate the hyperbolic volume of the manifolds and with the “1-loop term” the adjoint twisted Reidemeister torsion of the double of the manifolds. This is a joint work with Tianyue Liu, Shuang Ming, Xin Sun and Baojun Wu.
September 19, 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!