Past Events
I will briefly introduce the notion of random graphs and some of their basic properties, mostly focusing on thresholds for increasing properties. I will also introduce "Kahn-Kalai expectation threshold conjecture" and explain the motivation behind it with some examples. If time permits, we will…
Abstract: A vast array of physical phenomena, ranging from the propagation of waves to the location of quantum particles, is dictated by the behavior of Laplace eigenfunctions. Because of this, it is crucial to understand how various measures of eigenfunction concentration respond to the…
Let M be a compact 3-manifold with scalar curvature at least 1. We show that
…
there exists a Morse function f on M, such that every connected component of every fiber of f has genus, area and diameter bounded by a universal constant. This is a joint work with Davi Maximo.
Values of matrix coefficients of p-adic groups can be written in terms of solvable lattice models. But the usual argument for that is ad hoc -- you first know the model and then show that the partition functions match the values of matrix coefficients. In my talk, I'll show how one can start…
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…
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…
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…
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…
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…