Department of

Mathematics


Seminar Calendar
for Symplectic & Poisson Geometry Seminar events the year of Tuesday, March 26, 2019.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
    February 2019            March 2019             April 2019     
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                        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

Shifted Poisson structures on differentiable stacks

Ping Xu (Pennsylvania State University)

Abstract: We will discuss shifted (+1) Poisson structures on differentiable stacks in terms of Lie groupoids. In particular, we will describe various examples and show their connection with momentum mapping theory in symplectic geometry. This is a joint work with Francesco Bonechi, Nicola Ciccoli, and Camille Laurent-Gengoux.

Monday, April 29, 2019

3:00 pm in 243 Altgeld Hall,Monday, April 29, 2019

Symplectic capacities and the Minkowski sums of ellipsoids

Ely Kerman (UIUC)

Abstract: I will describe a new and elementary analysis of the Reeb flow on the boundary of the Minkowski sum of symplectic ellipsoids. This is made possible by an elegant parameterization of this boundary due to Chirikjian and Yan. Two immediate applications include an interesting manifestation of the "two to infinitely many" theorem of Hofer-Wysocki-Zehnder for closed Reeb orbits on strictly convex hyper surfaces, and a quick proof of the fact that the higher Ekeland-Hofer capacities, unlike the first one, fail to satisfy a Brun-Minkowski type inequality. This is a report on joint work in progress with Yuanpu Liang.

Monday, May 6, 2019

3:00 pm in 243 Altgeld Hall,Monday, May 6, 2019

To Be Announced

Guillem Cazassus (Indiana University)