Department of

Mathematics


Seminar Calendar
for events the day of Wednesday, December 10, 2014.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, December 10, 2014

11:00 am in 441 Altgeld Hall,Wednesday, December 10, 2014

Introduction to Spectral Networks, II

Daniele Alessandrini (Heidelberg)

Abstract: Abstract: I will give an introduction to the theory of Spectral Networks, developed by Gaiotto, Moore and Neitzke during their research about supersymmetry. These objects have an independent interest for mathematicians, mostly in the theory of surfaces. They can be described as combinatorical objects on the surface, or, equivalently as some orbits associated to a conformal structure on the surface and a collection of holomorphic differentials. The main focus will be on how to use these objects to give coordinates on the moduli spaces of representations of surface groups. These coordinates generalise Fenchel-Nielsen coordinates and Fock-Goncharov coordinates in an especially intriguing way. This is the second of a three lecture series.

3:00 pm in 347 Altgeld Hall,Wednesday, December 10, 2014

Electrical Networks and Electrical Lie Theory

Yi Su   [email] (University of Michigan Math)

Abstract: Curtis-Ingerman-Morrow studied the space of circular planar electrical networks. Lam and Pylyavskyy introduced an electrical Lie algebra such that the positive part of the corresponding electrical Lie group E_{A_{2n}} acts on circular planar electrical networks via some natural combinatorial operations. Inspired by these operations Lam gave a cell decomposition of the space of electrical networks, which is the analogue of type A Bruhat decomposition. In this talk, I will introduce mirror symmetric circular planar electrical networks, and present some analogous results about this new class of networks and its relation to type B electrical Lie theory. If time permitting, I will talk about the structure of electrical Lie algebras of type C and D.

4:00 pm in 245 Altgeld Hall,Wednesday, December 10, 2014

Geometric extensions of Galois representations

Patrick Allen (Northwestern University)

Abstract: Representations of the absolute Galois group of the rationals play a central role in modern algebraic number theory due to their connection with arithmetic geometry and the Langlands program. A philosophy of Grothendieck gives an obstruction to the existence of "geometric" extensions of Galois representations, and this is made precise in a conjecture of Bloch and Kato. I will give an introduction to these ideas, and then discuss my proof of the Bloch--Kato conjecture in many cases for adjoint representations of automorphic Galois representations.

4:00 pm in 245 Altgeld Hall,Wednesday, December 10, 2014

No lecture

(Department of Mathematics, University of Illinois at Urbana-Champaign)