University of Regina

So far, we learned that a deformation problem is controlled by a DG Lie algebra, and that solutions to the deformation problem correspond to Maurer-Cartan (MC) elements. However, different MC elements may yield equivalent deformations! The DG Lie...

In this seminar, we have seen that problems in deformation theory are often controlled by differential graded Lie algebras (dgla). For example, in Martin's talk, we saw how the deformations of an associative algebra are controlled by a dgla structure...

We will describe a discretization of Chern-Simons theory using Whitney forms. Derived moduli spaces are often described using L-infinity algebras and it is interesting to explore how a derived moduli space varies as we modify the 'governing L...

We will discuss the link between Hochschild cohomology and deformations of an algebra A. We will see that the Hochschild cochains of A can be endowed with a differential graded (DG) Lie algebra structure. The Maurer-Cartan equation describes the...

An Azumaya algebra is something that is "locally" isomorphic to a matrix algebra. By varying the sense of "locally", we arrive at different incarnations of the concept. The motivating example is that of central simple algebras over a field. In this...

This is joint work with Uriya First. Azumaya algebras are objects that are locally isomorphic to matrix algebras—over a topological space X, they are bundles of matrix algebras. If the base space X is endowed with a self-map of order 2 (which may be...

What does a random permutation group look like? This talk will start with a brief survey of how we might go about counting subgroups of the symmetric group Sn, and talk about what is known about “most” subgroups. To tackle the general problem, it...

The action of the automorphisms of a formal group on its deformation space is crucial to understanding periodic families in the homotopy groups of spheres and the unsolved Hecke orbit conjecture for unitary Shimura varieties. We can explicitly pin...

Topological quantum field theories (TQFTs) are one of several mathematical approaches to quantum field theory in physics. They were introduced by Atiyah in the 1980s. The cobordism hypothesis, proposed by Baez and Dolan in the 1990s, is a statement...

Periods are numbers that arise as integrals of rational functions with coefficients in Q over sets that are cut out by polynomial inequalities with coefficients in Q. More conceptually, periods are numbers that arise from the natural isomorphism...