Department of

# Mathematics

Seminar Calendar
for events the day of Monday, February 8, 2016.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, February 8, 2016

2:00 pm in 345 Altgeld Hall,Monday, February 8, 2016

#### Split Lagrangian spaces in field theories

###### Ivan Contreras (UIUC)

Abstract: A Lagrangian (i.e. maximally isotropic) subspace of a symplectic space is called split if it has an isotropic complement. In finite dimensions, all Lagrangian subspaces are split, but there are more things to say when the symplectic space is infinite dimensional, e.g. a Hilbert or Frechet space, and depending whether the symplectic structure is weak or strong. In this talk we will discuss some aspects of the theory of split canonical relations, in particular, compositions and reductions, in the framework of Lagrangian field theories with boundary. We will prove that the evolution relations arising from certain topological theories are split.

4:00 pm in 245 Altgeld Hall,Monday, February 8, 2016

#### Arithmetic $L$-functions and modular forms

###### Patrick Allen (Department of Mathematics, University of Illinois)

Abstract: In number theory it is common to package information associated to an arithmetic object into a complex analytic function called an $L$-function, the prototypical example of which being the Riemann zeta function. The analytic properties of these $L$-functions often imply interesting things about the original arithmetic object. But complex analysis alone often can't prove the analytic properties we want, and one needs a new idea: the Langlands philosophy implies that a broad class of arithmetic $L$-functions should be equal to ones coming from inherently more analytic objects, known as automorphic forms. We will discuss some instances of this philosophy, and its implications, in the case of modular forms.

5:00 pm in 241 Altgeld Hall,Monday, February 8, 2016

#### Classification of Baumslag-Solitar group von Neumann algebras

###### Stephen Longfield (UIUC Math)

Abstract: Since the introduction of von Neumann algebras, a program to classify group von Neumann algebras has been underway. Though many questions in this direction remain open, new techniques developed in the last 15 years have yielded several interesting results. This talk will follow the 2014 paper of Meesschaert and Vaes, in which the authors apply the powerful deformation/rigidity theory of Popa to partially classify the von Neumann algebras of the Baumslag-Solitar groups.