Past Events
Khovanov homology extends to an invariant of smooth oriented 4-manifolds, which is defined as a skein module spanned by decorated embedded surfaces, modulo local relations. I will introduce equivariant and Lee versions of these skein modules and compute the latter. This leads to a non-vanishing…
We consider a continuous time simple random walk on a subset of the square lattice with wired boundary conditions: the walk transitions at unit edge rate on the graph obtained from the lattice closure of the subset by contracting the boundary into one vertex. We study the cover time of such walk…
Statistical mechanics models undergoing a phase transition often exhibit rich, fractal-like behavior at their critical points, which are described in part by critical exponents, the indices governing the power-law growth or decay of various quantities of interest. These exponents are…
Fermat identified the integers which are a sum of two squares,
integral or rational: they are exactly those integers which have all
primes congruent to 3 (mod 4) occurring to an even power in their
prime factorization —- a condition satisfied by 0% of integers!
What about the…
I will explain how to draw Kirby diagrams of smooth 4-manifolds and how to do Kirby calculus to change a Kirby diagram without changing the 4-manifold it represents.
Fano hypersurfaces and differential forms via positive characteristic
Abstract: Holomorphic forms are an important birational invariant for studying the geometry of a variety. In characteristic 0, Fano varieties do not have any holomorphic forms. Surprisingly, Koll…
Title: Behavior of some invariants in characteristic p
Abstract: There are many numerical invariants of a ring in
characteristic p measuring its singularity. In this talk, we will
discuss two classical ones, Hilbert-Kunz multiplicity and the
F-signature,…
Abstract
I will present three deformation results, the first of which
is very general and goes back to Gromov, while the other two are
specific to scalar curvature. As applications, we will discuss the
equivalence (up to homotopy) of different boundary conditions for …