Department of

Mathematics

Seminar Calendar
for Symplectic & Poisson Geometry Seminar events the year of Monday, February 11, 2019.

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events for the
events containing

More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
     January 2019          February 2019            March 2019
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5                   1  2                   1  2
6  7  8  9 10 11 12    3  4  5  6  7  8  9    3  4  5  6  7  8  9
13 14 15 16 17 18 19   10 11 12 13 14 15 16   10 11 12 13 14 15 16
20 21 22 23 24 25 26   17 18 19 20 21 22 23   17 18 19 20 21 22 23
27 28 29 30 31         24 25 26 27 28         24 25 26 27 28 29 30
31


Monday, January 28, 2019

3:00 pm in 243 Altgeld Hall,Monday, January 28, 2019

Circle actions on almost complex manifolds with few fixed points

Donghoon Jang (Pusan National University)

Abstract: A circle action on a manifold can be thought of as a periodic flow on a manifold (periodic dynamical system), or roughly a rotation of a manifold. During this talk, we consider circle actions on almost complex manifolds, which are more general than symplectic manifolds. We discuss classification of a circle action on a compact almost complex manifold $M$, when the number $k$ of fixed points is small. If $k=1$, $M$ is a point. If $k=2$, $M$ resembles $S^2$ or $S^6$. If $k=3$, $M$ resembles $\mathbb{CP}^2$. We also discuss when $k=4$ and $\dim M \leq 6$. Techniques include equivariant cohomology and index theory.

Monday, February 4, 2019

12:00 pm in 343 Altgeld Hall,Monday, February 4, 2019

The integration problem for Courant algebroids

Rajan Mehta (Smith College)

Abstract: Courant algebroids originally appeared in the study of constrained Hamiltonian systems, but they are connected to many areas of mathematical physics, including multisymplectic geometry, double field theory, and (my personal interest) 3-dimensional topological field theory. Since a Courant structure involves a bracket that resembles a Lie bracket (but fails to be skew-symmetric), one might expect there to be some groupoid-like structure for which a Courant algebroid is the infinitesimal object. There is reason to believe that the answer should be a "symplectic 2-groupoid," but there are many devils in the details, including even the question of how "symplectic 2-groupoid" should be defined. I will describe various developments in this problem.

Monday, February 11, 2019

3:00 pm in 243 Altgeld Hall,Monday, February 11, 2019

Rigidity of Lie groupoids and foliations

Rui Loja Fernandes (UIUC)

Abstract: I will discuss a result stating that a compact, Hausdorff, Lie groupoid is rigid. i.e., has no non-trivial deformations. As an application of this result, it follows that a compact, Hausdorff foliation is rigid if and only if the generic leaf has trivial 1st cohomology. This is closely related to old stability results for foliations due to Epstein, Rosenberg and Hamilton. This talk is based on joint work with Matias del Hoyo.

Monday, February 18, 2019

3:00 pm in 243 Altgeld Hall,Monday, February 18, 2019

Swindles relating distinct symplectic structures

James Pascaleff (UIUC)

Abstract: An interesting phenomenon in symplectic topology is the existence of multiple non-equivalent symplectic structures on a single manifold. Often, such structures can be distinguished by their Fukaya categories. A natural question is whether there is any relationship between these categories. In this talk I will show that in some simple examples the categories are related by functors that are reminiscent of the Eilenberg swindle.

Monday, April 8, 2019

3:00 pm in 243 Altgeld Hall,Monday, April 8, 2019