Past Events
The Betti numbers of the Hilbert scheme of points on a smooth, irreducible projective surface have been computed by Gottsche. These numbers stabilize as the number of points tends to infinity. In contrast, the Betti numbers of moduli spaces of semistable sheaves on a surface are not known in…
What is the effect of excluding an induced subgraph on the global structure of a graph? While there do not seem to be general structural consequences, a conjecture of Erdős and Hajnal says that graphs with forbidden induced subgraphs behave very differently from general graphs; more…
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…