Mathematical Billiards: at the Crossroads of Dynamics, Geometry, Analysis, and Mathematical Physics: October 9-December 15, 2023

Participant List

Organized by:
• Misha Bialy (Tel Aviv)
• Milena Radnovic (Sydney)
• Alfonso Sorrentino (Rome Tor Vergata)
• Sergei Tabachnikov (Penn State University)

The last few years have witnessed an impressively high level of advances in the study of the dynamics of mathematical billiards, shedding new light on their profound connections with important problems in geometry, analysis, and mathematical physics. Moreover, billiard-type dynamics is ubiquitous and is significant in the analysis of many physical systems and for real-life applications, for instance in geometric optics.

Some of these questions have recently experienced a renaissance thanks to important breakthroughs that have given a new boost to the research on these topics; it is therefore very timely and even urgent to grasp this moment, in order to capitalize on and further our understanding. The manifold nature of these subjects requires a deep interaction between different – but very much related – research communities. Our program aims to bridge this gap and provide a unique opportunity for this diverse expertise to interact and effectively integrate, a fundamental step in order to tackle several longstanding questions and explore the new interesting directions that are emerging. We plan to organize several activities that should foster this hybridization of knowledge, including introductory courses on selected topics, which could be particularly beneficial for graduate students and early-career researchers, weekly seminars and suitably focused working groups. We also plan to organize an international one-week Workshop: Mathematical billiards: at the crossroads of dynamics, geometry, analysis, and mathematical physics: November 13 – 17, 2023 to present the current state of the research on these topics and the most recent advances.


WEEK 1: October 9-13, 2023
Lectures & Discussions

WEEK 2: October 16-20, 2023
Lecturer: Ke Zhang (University of Toronto, Canada)
Title: KAM and formal methods for convex billiards

WEEK 3: October 23-27, 2023
Lecturer: Peter Albers (Universität Heidelberg, Germany)
Title: Benci-Giannoni type approximation theorem for billiards.

WEEK 4: October 30 – November 3, 2023
Lecturer: Vladimir Dragovic (The University of Texas at Dallas, US)
Title: Integrable Billiards, Extremal Polynomials, and Isoharmonic Deformations.

WEEK 5: November 6-10, 2023
Lecturer: Carlangelo Liverani (Università di Roma “Tor Vergata”, Italy)
Title: Statistical properties of Hyperbolic Billiards

WEEK 6: November 13-17, 2023
Workshop Week

WEEK 7: November 20-24, 2023
Thanksgiving Week

WEEK 8: November 27 – December 1, 2023
Lecturer: Tere Seara, Pau Martin and Rafael Ramirez-Ros (Universitata Politecnica de Catalunya, Spain)
Title: Exponentially small phenomena and billiards

WEEK 9: December 4-8, 2023
Lecturer: Alexey Glutsuyk (CNRS & ENS Lyon)

WEEK 10: December 11-15, 2023
Lectures & Discussions