Department of

Mathematics


Seminar Calendar
for Symplectic & Poisson Geometry Seminar events the year of Friday, September 14, 2018.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
     August 2018           September 2018          October 2018    
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                        30                                         

Monday, September 10, 2018

3:00 pm in 243 Altgeld Hall,Monday, September 10, 2018

Lie 2-groups and their Lie 2-algebras

Eugene Lerman (University of Illinois at Urbana-Champaign)

Abstract: I will introduce Lie 2-groups and Lie 2-algebras and then discuss left-invariant vector fields on Lie 2-groups.

Monday, September 17, 2018

3:00 pm in 243 Altgeld Hall,Monday, September 17, 2018

Pre-Calabi-Yau structures and moduli of representations

Wai-kit Yeung (Indiana University)

Abstract: Pre-Calabi-Yau structures are certain structures on associative algebras introduced by Kontsevich and Vlassopoulos. This incorporates as special cases many other algebraic structures of diverse origins. Elementary examples include double Poisson algebras introduced by Van den Bergh, as well as infinitesimal bialgebras studied by Aguiar. Other examples also arise from symplectic topology as well as from string topology, whose relation with topological conformal field theory can be formulated in terms of pre-Calabi-Yau structures. In this talk, we will define pre-Calabi-Yau structures, and study it in the context of noncommutative algebraic geometry. In particular, we show that Calabi-Yau structures, introduced by Ginzburg and Kontsevich-Vlassopoulos, can be viewed as noncommutative analogue of symplectic structures. Pushing this analogy, one can show that pre-Calabi-Yau structures are noncommutative analogue of Poisson structures. As a result, we indicate how a pre-Calabi-Yau structure on an algebra induces a (shifted) Poisson structure on the moduli space of representations of that algebra.

Monday, November 12, 2018

3:00 pm in 243 Altgeld Hall,Monday, November 12, 2018

Beyond semitoric

Susan Tolman (Illinois)

Abstract: A compact four dimensional completely integrable system $f \colon M \to \mathbb{R}^2$ is semitoric if it has only non-degenerate singularities, without hyperbolic blocks, and one of the components of $f$ generates a circle action. Semitoric systems have been well studied and have many nice properties; for example, the fibers $f^{-1}(x)$ are connected. Unfortunately, although there are many interesting examples of semitoric systems, the class has some limitations. For example, there are blowups of $S^2 \times S^2$ with Hamiltonian circle actions that cannot be extended to semitoric system. We show that, by allowing certain degenerate singularities, we can expand the class of semitonic systems but still prove that $f^{-1}(x)$ is connected. We hope that this class will be large enough to include not only all compact four manifolds with Hamiltonian circle actions, but more generally all complexity one spaces. Based on joint work with D. Sepe.

Monday, November 26, 2018

3:00 pm in 243 Altgeld Hall,Monday, November 26, 2018

To Be Announced

Daniele Sepe (UFF-Rio)

Monday, December 3, 2018

3:00 pm in 243 Altgeld Hall,Monday, December 3, 2018

To Be Announced

Miquel Cuenca (IMPA)

Monday, December 10, 2018

3:00 pm in 243 Altgeld Hall,Monday, December 10, 2018

To Be Announced

Yael Karshon (Toronto)