# Upcoming Events

How many edges can you place in a graph on n vertices without creating a triangle? Some trial and error suggests that the best thing to do is to split your vertices into two classes of size n/2 and to connect all pairs in different classes, and indeed this is best possible. Starting from this…

A *parking function *of length *n *is a sequence *a*1*,** **a*2*,** **. . . , a**n** *of positive integers whose increasing rearrangement *b*1 ≤ *b*2 ≤ · ·…

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…

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…

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…

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 *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 *= (2*I…*