Past Events

Let C be a class of graphs. We say that C has a "polynomial separator property" if there there exists a constant d such that for every G in C, the number of minimal separators in G is at most |V(G)|^d. It is known that the maximum weight independent set problem can be solved in polynomial…

A Fano problem is an enumerative problem of counting r-dimensional linear subspaces on a complete intersection in P^n over a field of arbitrary characteristic, whenever the corresponding Fano scheme is finite. A classical example is enumerating lines on a cubic surface. We study the monodromy of…

The problem of mixing via incompressible flows is classical and rich with connections to several branches of analysis including PDE, ergodic theory, and topological dynamics.  In this talk I will discuss some recent developments in the area and then present a…

Z/2 harmonic forms are closed and coclosed 1-forms with values in a real line bundle that is defined on the complement of a cxdimension 2 subvariety of a Riemannian manifold with their norms being zero on the same subvariety. These objects are now known to appear (in dimensions 2-4) in diverse…

Let P be a polygon in the plane with integer vertices. Suppose that the area of P is A and that P  has I interior lattice points and B lattice points on the boundary. Alexander Pick showed that A = (2I…

Abstract:  Z/2 harmonic forms are closed and coclosed 1-forms with values in a real line bundle that is defined on the complement of a cxdimension 2 subvariety of a Riemannian manifold with their norms being zero on this same subvariety. These objects are now known…

Let R be a commutative ring (with identity) and A an n × n matrix over R. Suppose there exist n × n matrices P, Q invertible over R for which PAQ is a diagonal matrix…

In 2016, Gukov, Putrov and Vafa conjectured the existence of invariants of 3-manifolds which are q-series with integer coefficients. They are expected to have a categorification in a sense of Khovanov homology. More recently, in 2019, Gukov and Manolescu studied the analogue of GPV…

In general relativity, the universe is often formalized as a four-dimensional ``space-time”, i.e. a smooth manifold equipped with a signature (3,1) pseudo-Riemannian metric. I give an introduction to general relativity, motivating this formalism…