Department of

# Mathematics

Seminar Calendar
for events the day of Monday, December 8, 2014.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    November 2014          December 2014           January 2015
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30


Monday, December 8, 2014

11:00 am in 441 Altgeld Hall,Monday, December 8, 2014

#### Introduction to Spectral Networks, I

###### 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 first of a three lecture series.

3:00 pm in 341 Altgeld Hall,Monday, December 8, 2014

#### Linear analysis on manifolds with cylindrical ends

###### Pierre Albin (UIUC Math)

Abstract: It seems that manifolds with cylindrical ends show up naturally in symplectic geometry. I will recall how analysis on these manifolds compares to analysis on closed manifolds.

4:00 pm in 314 Altgeld Hall,Monday, December 8, 2014

#### Existence theorems for isometric immersions, examples and applications

###### Marie-Amelie Lawn (University of Texas at Austin)

Abstract: One of the fundamental problems in Riemannian geometry is the existence of isometric immersions from one manifold into another, notably resulting in Nash's embedding theorem, and closely tied to general relativity, such as in Choquet-Bruhat's solution to the Cauchy problem. The Gauss, Ricci and Codazzi equations are well-known as the structure equations, meaning that any submanifold of any Riemannian manifold must satisfy them. A classical result (the fundamental theorem of submanifold theory) states that, conversely, they are sufficient conditions for a (semi-)Riemannian n-manifold to admit an immersion in the Euclidean space R^m. Proving fundamental theorems if the ambient space is not of constant sectional curvature is technically very difficult and there are only few other results known. I will discuss fundamental theorems for immersions into new classes of ambient manifolds, namely homogeneous spaces and special warped products, and discuss applications, such as non-existence results of associated families of minimal surfaces, existence of sister surfaces, and a new approach to the Cauchy problem of general relativity in the non-vacuum case.

4:00 pm in 243 Altgeld Hall,Monday, December 8, 2014

#### Understanding Comodules over a Hopf algebra

###### Dileep Menon (UIUC Math)

Abstract: Being able to do homological algebra in the category of comodules over the dual Steenrod algebra is important for computations with the Adams spectral sequence. However, trying to understand what a comodule is can be difficult and non-intuitive. In this talk we give a geometric interpretation of a comodule over a Hopf algebra and use this new framework to understand the statement of the comodule algebra structure theorem.

5:05 pm in 145 Altgeld Hall,Monday, December 8, 2014

#### quantum group channels

###### Marius Junge (UIUC)

Abstract: Second part on quantum group channels and cb-entropy. Depending on Senate, I will start late