Billiard tables are usually rectangular. What happens if we change their shape? Mathematical billiards are an idealisation of the billiard game in differently shaped "tables" and arise naturally from the study of several problems in physics. We will focus in this talk on billiards in polygonal tables: we will explain how they relate to "flows" on surfaces, why they provide fundamental examples of "slowly chaotic" systems and survey some recent breakthroughs on the study of their chaotic features.
Corinna Ulcigrai was born in Trieste, Italy, in 1980. She obtained her diploma in Mathematics from the Scuola Normale Superiore in Pisa (2002) and defended her PhD in Mathematics at Princeton University (2007), under the supervision of Ya. G. Sinai. In the academic year 2007/08 she spent a semester at the MSRI Institute in Berkeley, California, and a semester at the Institute for Advanced Studies in Princeton. She is Professor in Pure Mathematics at University of Bristol since August 2015. Previously she has been a Lecturer (August 2007 - July 2013) and a Reader (August 2013 - July 2015) at the same University. Corinna Ulcigrai has given major contributions in ergodic theory, dynamical systems and Teichmuller dynamics, focusing her research on the study of chaotic properties of parabolic dynamical systems, which display a "slow" form of chaotic evolution. In particular, in a paper based on her PhD thesis she has solved an important long-standing problem on the ergodic properties of locally Hamiltonian flows on surfaces by showing that typically such flows are not mixing. With K. Fraczek she also proved an important result that surprised leading experts in non-equilibrium statistical mechanics from both mathematics and physics. This result shows that, for a broad class of billiard dynamics that includes the 100 year old Ehrenfest model describing a particle in a period array of square scatterers, the system is not ergodic in most directions. Corinna was awarded the European Mathematical Society Prize in 2012, the Whitehead Prize in 2013 and the Leverhulme Prize in 2014. She has won the ERC Starting Grant "Chaos in Parabolic Dynamics: Mixing, Rigidity, Spectra" (2013).
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