Previous Conferences & Workshops

Spherical varieties play an important role in the study of periods of automorphic forms. But very closely related varieties can lead to very distinct arithmetic problems. Motivated by applications to relative trace formulas, we discuss the natural...

We give a gentle introduction to rational and Du Bois singularities in algebraic geometry. Through examples, we will see how birational geometry comes into play with the theory of differential operators. Time permitting, we discuss the sheaf...

A cornerstone result in geometry is the Szemerédi–Trotter theorem, which gives a sharp bound on the maximum number of incidences between $m$ points and $n$ lines in the real plane. A natural generalization of this is to consider point-hyperplane...

The resolutions of Slodowy slices $\tilde{S}_{e}$ are symplectic varieties that contain the Springer fiber $(G/B)_{e}$ as a Lagrangian subvariety. In joint work with R. Bezrukavnikov, M. McBreen and Z. Yun, we construct analogues of these spaces for...

Triangulated surfaces are Riemann surfaces formed by gluing together equilateral triangles. They are also the Riemann surfaces defined over the algebraic numbers. Brooks, Makover, Mirzakhani and many others proved results about the geometric...

In this talk, I will discuss lower bounds for a certain set-multilinear restriction of algebraic branching programs. The significance of the lower bound and the model is underscored by the recent work of Bhargav, Dwivedi, and Saxena (2023), which...

Explain the formulation of the Grothendieck–Riemann–Roch theorem for analytic adic spaces: go through [And23, pp. 32-38] and define all relevant objects and maps. Before explaining the construction of the Chern class map, define the sheaf KU∧p on...

In a recent joint work with S. Iyengar, C. Khare and J. Manning, we use their notion of congruence modules in higher codimension to give a new construction of the bottom class of the rank d=[F:\Q] Euler system attached to nearly ordinary Hilbert...