Abstracts

Week of October 5, 2025

October 6, 2025
Geometry, Symmetry and Physics Parabolic 1-dimensional sheaves on del Pezzo surfaces and applications to the Chern filtration 4:30pm -
KT 801

The cohomology of moduli spaces of 1-dimensional sheaves on del Pezzo surfaces carries a perverse filtration, from which curve counting invariants of CY 3-folds can be extracted. Conjecturally, the perverse filtration matches a second filtration, defined in terms of tautological classes, called the Chern filtration. I will explain this conjecture, what is currently known, and some consequences. In the second part of the talk I will explain some new ideas to prove properties of the Chern filtration by using parabolic sheaves. In particular, I will discuss the top Chern degree and chi-independence phenomena. The talk is based on joint work in progress with W. Lim and W. Pi.
October 7, 2025
Geometry & Topology A notion of extended Theta-positivity representation 4:30pm -
KT 207

We study a notion of extended positive representations of surface groups. Examples include maximal representations (Burger—Iozzi—Wienhard), positive representations (Fock—Goncharov), and cusped Hitchin representations (Canary—Zhang—Zimmer). We discuss conditions under which these representations are Anosov or relatively Anosov. We prove that extended positivity is a closed condition, and open in certain subspace of the character variety. Moreover, we describe the boundary of the closure of extended positive representations into a semisimple Lie group G in the real spectral compactification of Hom(\Gamma,G) (introduced by Burger—Iozzi—Parreau—Pozzetti), showing that it consists of extended positive representations into extensions of G over real closed fields. This is joint work with Xenia Flamm, Nicolas Tholozan, and Tengren Zhang.
October 8, 2025
Colloquium Amplituhedra and Origami 4:00pm -
KT 101

Abstract: I will explain a proof of the BCFW triangulation conjecture which states that the cells appearing in the Britto–Cachazo–Feng–Witten (BCFW) recursion triangulate the amplituhedron (in full generality at all loop levels). The key ingredient is a relation to origami crease patterns which are planar graphs with faces colored black and white, embedded in the plane so that the sum of black (equivalently, white) angles at each vertex is 180°. Along the way, we prove conjectures of Chelkak–Laslier–Russkikh and Kenyon–Lam–Ramassamy–Russkikh on the existence of such origami embeddings of arbitrary planar graphs, which originated from the works of Kenyon and Smirnov on the conformal invariance of the dimer and Ising models.

Seminar talk is supported in part by the Mrs. Hepsa Ely Silliman Memorial Fund.
October 9, 2025
Analysis Available Seminar Slot 4:00pm -
Quantum Topology and Field Theory Abelianization of Virasoro blocks and tau functions 4:30pm -
KT 801

Abstract: I will explain a new scheme for construction of conformal blocks for the Virasoro algebra at central charge c=1. One application is a new recipe for producing isomonodromic tau functions. This scheme is joint work with Qianyu Hao. The talk is intended to be self-contained (you don’t have to know in advance what a conformal block or a tau function are). 
October 10, 2025
Friday Morning Seminar Braid variety cluster structures and 3D plabic graphs 10:00am -
KT 801

Abstract: I will explain the combinatorics behind the cluster algebra structure on braid and Richardson varieties. This generalizes the previously known constructions for positroid varieties and double Bruhat cells. The cluster algebra is described in terms of a 3-dimensional generalization of Postnikov’s plabic graphs, and the underlying quiver is induced by the intersection form of the Goncharov–Kenyon conjugate surface associated to a 3D plabic graph. Joint work with T. Lam, M. Sherman-Bennett, and D. Speyer.