Department of

Mathematics


Seminar Calendar
for events the day of Thursday, October 10, 2019.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, October 10, 2019

12:00 pm in 243 Altgeld Hall,Thursday, October 10, 2019

You can “hear” the shape of a polygonal billiard table

Chandrika Sadanand (Illinois Math)

Abstract: Consider a polygon-shaped billiard table on which a ball can roll along straight lines and reflect off of edges infinitely. In work joint with Moon Duchin, Viveka Erlandsson and Chris Leininger, we have characterized the relationship between the shape of a polygonal billiard table and the set of possible infinite edge-itineraries of balls travelling on it. In this talk, we will explore this relationship and the tools used in our characterization.

4:00 pm in 235 Altgeld Hall,Thursday, October 10, 2019

Nonlocal Problems with the Fractional Laplacian and Their Applications

Yanzhi Zhang   [email] (Missouri University of Science and Technology)

Abstract: Recently, the fractional Laplacian has received great attention in modeling complex phenomena that involve long-range interactions. However, the nonlocality of the fractional Laplacian introduces considerable challenges in both analysis and simulations. In this talk, I will present numerical methods to discretize the fractional Laplacian as well as error estimates. Compared to other existing methods, our methods are more accurate and simpler to implement, and moreover they closely resembles the central difference scheme for the classical Laplace operator. Finally, I will show some applications of nonlocal problems involving the fractional Laplacian.