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Álvaro del Pino Gómez (Utrecht University, The Netherlands)
March 25, 2021 @ 4:00 pm – 5:00 pm CET
Speaker: Álvaro del Pino Gómez (Utrecht University, The Netherlands)
Title: Billiards in subriemannian geometry
Abstract: When one considers manifolds with boundary, billiard dynamics are the natural analogue of standard geodesic dynamics. Namely, instead of having geodesics escape at the boundary, we force them back into the manifold using the reflection law. In other dynamical settings, similar constructions are possible: In 2006, B. Khesin and S. Tabachnikov initiated the study of billiards in the semiriemannian setting, studying the integrability of various tables. In recent years we have also seen the appearance of several billiard setups of symplectic nature. In this talk I will discuss recent work with L. Dahinden in which we look at billiards in subriemannian geometry. I will sketch how the reflection law arises naturally both from the control-theoretical and symplectic perspectives, how the reflection is problematic at tangency points between the distribution and the boundary of the table, and I will introduce some concrete examples. My ultimate goal will be to pose several intriguing open questions.
NOTE: The seminar will be streamed live on our YouTube channel then saved there. If you ask questions, with your video feed on or off, you agree to the use of your image/spoken words for said purpose.