Department of

# Mathematics

Seminar Calendar
for events the day of Monday, March 14, 2016.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    February 2016            March 2016             April 2016
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1  2  3  4  5  6          1  2  3  4  5                   1  2
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Monday, March 14, 2016

2:00 pm in 345 Altgeld Hall,Monday, March 14, 2016

#### PMCTs (Poisson manifolds of compact types)

###### Marius Crainic (Utrecht)

Abstract: I will give a brief overview on the recent joint work with R.L. Ferandes and D.M. Torres on Poisson manifolds of compact types. While Poisson manifolds generalize symplectic manifolds as well as (duals of) Lie algebras, the "compactness" we are referring to generalizes compactness of symplectic manifolds as well as compactness of Lie groups. While general Poisson structures are very flexible and there is quite little one can say about them in full generality, the compact ones come with some very rich and beautiful geometry. In particular, one discovers new connections with Lie theory, integral affine geometry, symplectic topology, orbifolds, integrable systems, gerbes, Duistermaat-Heckman measures and formulas etc, all interacting in a very interesting way. Returning to (duals of) Lie algebras, one may say that a large part of the very fundamental results on compact Lie groups are of a purely Poisson geometric nature: one just has to feed the dual of the Lie algebra into the theory of PMCTs (therefore making use only of the Poisosn structure). Since the list of interesting properties of PMCTs is very large, this talk will be rather superficial: just an overview of the most important features of PMCTs.

3:00 pm in 190 ESB,Monday, March 14, 2016

#### The Fluid Manifest: Topological sigma models and dissipative hydrodynamics

###### Makund Rangamani (UC Davis Physics)

Abstract: I will discuss the construction of Wilsonian effective field theories in mixed states of a quantum field theory.  We will abstract a set of topological symmetries that underpin the Schwinger-Keldysh path integral construction and demonstrate that in thermal backgrounds, these give sufficient constraints on the low energy dynamics.  As an application of the formalism we will construct an effective action for relativistic dissipative hydrodynamics.

4:00 pm in 245 Altgeld Hall,Monday, March 14, 2016

#### Introduction to dispersive partial differential equations

###### Nikolaos Tzirakis (Department of Mathematics, University of Illinois)

Abstract: My aim at this talk is to provide a short introduction to some basic methods employed in the area of nonlinear dispersive partial differential equations in the setting of a few model equations like nonlinear Schrodinger and Korteweg-de Vries equation.

5:00 pm in 241 Altgeld Hall,Monday, March 14, 2016

#### Quantum Expander

###### Li Gao (UIUC Math)

Abstract: Expanders are graphs with low degrees and high connectivity. They have been extremely useful, especially in applied direction. In this talk, I will talk about quantum expanders, which are the natural generalizations of expander graphs in quantum information and quantum computation theory. In particular, I plan to present G. Pisier's work on the connection of quantum expanders and geometry of operator space.

5:00 pm in 245 Altgeld Hall,Monday, March 14, 2016