Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, September 24, 2015.

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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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Thursday, September 24, 2015

11:00 am in 241 Altgeld Hall,Thursday, September 24, 2015

#### Origami Galois representations

###### Rachel Davis (Purdue University)

Abstract: Let $X$ be an elliptic curve over $\mathbb{Q}$. Let $f:Y \rightarrow X$ be an étale cover, ramified only above one point. The pair $(X,f)$ is called an origami. The name comes from a picture that I will draw during the talk. We study the relationship between the pre-images of rational point on $X$ under the map $f$ and Galois representations. This is joint work with Edray Herber Goins.

1:00 pm in 243 Altgeld Hall,Thursday, September 24, 2015

#### Poisson manifolds of compact types

###### Rui Loja Fernandes (UIUC Math)

Abstract: In this talk I will describe a class of Poisson manifolds which play the role of "compact objects" in Poisson geometry. These Poisson structures of compact type are very rigid compared to general Poisson structures: the symplectic foliation has a transverse integral affine structure, its leaf space is an orbifold with a Duistermaat-Eckman type measure, and they have an associated symplectic gerbe, that obstructs realizing them as isotropic quotients of a symplectic manifold. In this talk I will carefully define these objects and give a small tour of their rich geometry. Joint work with M. Crainic (Utrecht) and D. Martinez-Torres (PUC-Rio de Janeiro).

1:00 pm in 347 Altgeld Hall,Thursday, September 24, 2015

#### To Be Announced

###### Seppe Kuehn (UIUC Physics)

Abstract: TBA

2:00 pm in 347 Altgeld Hall,Thursday, September 24, 2015

#### Homogeneous functors and derivatives

###### Sarah Yeakel   [email] (UIUC Math)

Abstract: We'll talk about how homogeneous functors are amazingly similar to their real-valued function analogs by discussing the relationship between homogeneous functors and multilinear symmetric functors. We'll provide formulas for calculating the homogeneous layers of the Taylor tower and the derivatives of a functor, the fundamental theorems of Goodwillie's Calculus III.

4:00 pm in 245 Altgeld Hall,Thursday, September 24, 2015

#### Discrete integrability and cluster algebras

###### Rinat Kedem (Illinois)

Abstract: Classical Liouville integrability has a discrete analogue, with Poisson-commuting integrals of motion with respect to a discrete time evolution. The canonical quantization is a discrete quantum integrable system with commuting, time-independent Hamiltonians. Cluster algebras, introduced by Fomin and Zelevinsky, are a rich source of discrete evolutions with a canonical Poisson structure compatible with the evolution, as described by Gekhtman, Shapiro and Vainshtein. In some cases they are integrable evolutions. In addition to a beginner's guide to cluster algebras and their quantization, I will introduce two examples from the representation theory of quantum groups, T-systems and Q-systems. The story will culminate with the (possibly surprising) appearance of discrete quantum Toda Hamiltonians and family of generalizations, acting on the characters of generalized Weyl modules or fusion products. The entire construction has a deformation beyond quantization, into Macdonald theory, elliptic Hall algebras, spherical DAHAs and other wonderful objects from quantum field theory.

5:00 pm in 1090 Lincoln Hall,Thursday, September 24, 2015

#### IGL Outreach Information Session

Abstract: Come learn more about opportunities for community outreach with the Illinois Geometry Lab! 30 minute information session. Please note the location: 1090 Lincoln Hall