In recent work of Baas-Dundas-Richter-Rognes, the authors define 2-vector bundles and prove that their classifying spaces, K(Vect) is equivalent to the algebraic K-theory of the connective K-theory spectrum ku. In this talk we will give an introduction to bicategories and 2-vector spaces, explain the construction of the classifying space K(Vect). Finally we will explain how some extra structure in the bicategory of 2-vector spaces translate into an infinite loop space structure on K(Vect).

In this talk, we will first discuss the topology of the Frobenius complex, the order complex of a poset motivated by the classical Frobenius problem. Specifically, we will determine the homotopy type of the Frobenius complex in certain cases using discrete Morse theory. In the second half of the talk, we will extend the classical excedancestatistic of the symmetric group to the affine symmetric group and determine the generating function of its distribution. The proof involves enumerating lattice points in a skew version of the root polytope of type $A$.

There will be a reception for Eric at 4:00 p.m. in POT 745.

A cornerstone theorem of free groups is the Nielsen-Schreier theorem - that every subgroup of a free group is itself free. In this talk we'll explore this result via Nielsen's proof and then discuss the statement of the Andrew-Curtis conjecture. This is an open problem that is a natural extension of the tools developed by Nielsen to prove the Nielsen-Schreier theorem, yet a proof has eluded mathematicians for nearly 50 years (and continues to do so!) The talk should be accessible to everyone with an interest in algebra.

I will give an elementary introduction to wall crossing phenomena from the point of view of string theory. In particular I will explain how simple kinematics of molecule-like bound states in this context leads to remarkably universal wall crossing formulae that have been uncovered in recent years.