Department of

Mathematics


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

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Questions regarding events or the calendar should be directed to Tori Corkery.
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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

From academia to nebraskaGlobal

Lucas Sabalka and Josh Brown Kramer   [email] (nebraskaGlobal)

Abstract: Lucas Sabalka (PhD 2006, U of Illinois) and Josh Brown Kramer (PhD 2007, U of Nebraska) discuss their journey from geometric group theory and combinatorics to computer vision and applied mathematics at venture capital software firm nebraskaGlobal. Refreshments provided. All welcome!