# Upcoming Events

Abstract: In 1977, Berry conjectured that eigenfunctions of the Laplacian on manifolds of negative curvature behave, in the high-energy (or semiclassical) limit, as a random superposition of plane waves. This conjecture, central in quantum chaos, is still completely open.

In this talk,…

A Fano variety X can be reconstructed from its bounded derived category D^b(X). How to use this fact to extract

concrete geometric information from D^b(X)?

In this talk, I will survey one such approach, via certain subcategories of D^b(X) called Kuznetsov components, and stability…

There has recently been much activity within the Kardar-Parisi-Zhang universality class spurred by the construction of a canonical limiting object, the parabolic Airy sheet, by Dauvergne-Ortmann-Virág [DOV]. The parabolic Airy sheet provides a coupling of parabolic Airy_2 processes — a universal…

Abstract: The \ell-torsion conjecture states that the size of the \ell-torsion subgroup Cl_K[\ell] of the class group of a number field K is bounded by Disc(K)^{\epsilon}. It follows from a classical result of Brauer-Siegel, or even earlier result of Minkowski, that the class number |Cl_K| of a…

An expander graph is a well-connected finite graph, with one consequence being that random walks mix extremely quickly on them. While it is relatively easy to show that they exist, and in some sense most graphs are expanders, constructing explicit examples is non-trivial. Margulis gave the first…

An oriented knot is called negative amphichiral if it is isotopic to the reverse of its mirror image. Such knots have order at most two in the concordance group, and many modern concordance invariants vanish on them. Nevertheless, we will see that there are negative amphichiral knots with…

The problem we consider is motivated by a work by B. Nachtergaele and

H.T. Yau where the Euler equations of fluid dynamics are derived from

many-body quantum mechanics. A crucial concept in their work is that of

local quantum Gibbs states, which are quantum statistical…