Department of

# Mathematics

Seminar Calendar
for events the day of Monday, February 5, 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.
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Monday, February 5, 2018

1:00 pm in 141 Altgeld Hall,Monday, February 5, 2018

#### Teaching Mathematics in Prison: Education Justice Project Info Session

Abstract: The Education Justice Project offers for-credit U of I courses and other academic programs at Danville Correctional Center, a men’s medium-security prison. Come learn about opportunities to teach mathematics from current and former members of the math department. The students are eager to have more math and science content, and there are many ways to get involved (from one-day workshops to teaching full semester courses).

2:00 pm in 241 Altgeld Hall,Monday, February 5, 2018

#### Lower hyperbolic rank rigidity of quarter-pinched manifolds

###### Christopher Connell (Indiana University)

Abstract: A Riemannian manifold M has higher hyperbolic rank if every geodesic has a perpendicular Jacobi field making sectional curvature -1 with the geodesic. If in addition, the sectional curvatures of M lie in the interval [−1,−1/4], and M is closed, we show that M is a locally symmetric space of rank one. This partially extends work by Constantine using completely different methods. It is also a partial converse to Hamenstädt's hyperbolic rank rigidity result for sectional curvatures at most −1, and complements well-known results on Euclidean and spherical rank rigidity. This is joint work with Thang Nguyen and Ralf Spatzier.

3:00 pm in 243 Altgeld Hall,Monday, February 5, 2018

#### Symplectic groupoids of cluster Poisson structures

###### Songhao Li (University of Notre Dame)

Abstract: Cluster algebras appears as the coordinate ring of many interesting objects. We recall the notion of a cluster ensemble which consists of a cluster A variety and its corresponding cluster X variety. The compatible Poisson structures on these spaces are log-canonical. We construct the symplectic groupoid of the log-canonical Poisson structure on each cluster chart, and lift the cluster mutations to groupoid mutations.

4:00 pm in 245 Altgeld Hall,Monday, February 5, 2018

#### Bound states and ground states in Strichartz functionals

###### Vadim Zharnitsky   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: Strichartz inequalities arise naturally in PDE analysis and represent a basic tool to establish well-posedness results in nonlinear dispersive PDEs. In the quest to obtain the best constants in such inequalities, it is natural to consider minimization of Strichartz functional associated with the inequality. It is conjectured that the minimum is always a Gaussian for a certain class of functionals. I will describe some recent developments on this subject and I will present some of my recent work that was done in collaboration with Gene Wayne (Boston University).

5:00 pm in 241 Altgeld Hall,Monday, February 5, 2018

#### The reduced C*algebra of the free product is simple

###### Li Gao (UIUC)

Abstract: We follow Connes' approach via cocycles proving this classical result.