Geometry and Topology

Speaker: Tudor Dimofte (Perimeter)

"Applications of 3d gauge theory to geometric representation theory"

Time: 15:30

Room: MC 107

I will discuss some ongoing work (with Mat Bullimore, Davide Gaiotto, and Justin Hilburn) on 3d gauge theories with half-maximal supersymmetry ("N=4"). These theories are labelled by a compact group G and a quaternionic representation R. From this data one obtains many geometric objects. Among them are the "Higgs branch" of vacua (a hyperkahler quotient R///G), the "Coulomb branch" of vacua (a modification of the cotangent bundle of the dual complex torus T*(T')), deformation quantizations of these spaces, and Fukaya-like categories of modules for the quantizations. These various objects and their relations generalize many constructions in geometric representation theory, including a phenomenon called symplectic duality (studied by Braden-Licata-Proudfoot-Webster, generalizing the Koszul duality of Beilinson-Ginzburg-Soergel) and a finite version of the AGT correspondence (by Braverman-Feigin-Finkelberg-Rybnikov).

I will give an introduction to some of these ideas.

Noncommutative Geometry

Speaker: (Western)

"Matrix Integrals 2"

Time: 10:30

Room: MC 108

Matrix integrals play an important role in random matrix theory, 2d quantum gravity, and the topology of moduli spaces of Riemann surfaces. In these lectures we shall look at a perturbative expansion for matrix integrals via Feynman graphical methods.

Homotopy Theory

Speaker: Pal Zsamboki (Western)

"Higher Inductive Types (part 1)"

Time: 13:30

Room: MC 107

We introduce the first example of a higher inductive type, S^1, for which we prove a universal property. Then after discussing the interval I, we move on to spheres. We finish with finite CW complexes.

Analysis Seminar

Speaker: Andrew Zimmer (University of Chicago)

"Negatively curved metric spaces and several complex variables "

Time: 15:30

Room: MC 107

In this talk I will discuss how to use ideas from the theory of metric spaces of negative curvature to understand the behavior of holomorphic maps between bounded domains in complex Euclidean space. Every bounded domain has an metric, called the Kobayashi metric, which is distance non-increasing with respect to holomorphic maps. Moreover, this metric often satisfies well-known negative curvature type conditions (for instance, Gromov hyperbolicity or visibility) and one can then use this negative curvature to understand the behavior of holomorphic maps. I will discuss the domains where the Kobayashi metric satisfies negative curvature type conditions and how to use these conditions to prove new results. Some of this is joint work with Gautam Bharali.

Noncommutative Geometry

Speaker: Mitsuru Wilson (Western)

"A Gauss-Bonnet Theorem for the noncommutative 4-sphere"

Time: 10:30

Room: MC 107

Algebra Seminar

Speaker: Adam Topaz (UC Berkeley)

"On the Ihara/Oda-Matsumoto Conjecture"

Time: 16:00

Room: MC 107

One of the key themes in Grothendieck's "Esquisse d'un Programme" is the idea of studying absolute Galois groups via their action on objects of geometric origin. Motivated by this, the conjecture of Ihara/Oda-Matsumoto (I/OM) predicts that the Galois action on geometric fundamental groups of algebraic varieties leads to a combinatorial/topological description of absolute Galois groups. This conjecture was resolved by Pop in the 90's, and several variants/generalizations have since been formulated. In this talk, I will discuss the recent proof of the mod-ell abelian-by-central variant of this conjecture, which follows from studying the Galois action on certain lattices of geometric origin.