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

Participant ListView Videos

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.


All talks will be held in Seminar Room 313

WEEK 1: October 9-13, 2023

Thursday, Oct. 12 at 2:00pm
Lecture by Vladimir Matveev (Friedrich-Schiller-Universität Jena, Germany)
Title: Applications of Nijenhuis Geometry: finite-dimensional reductions and integration in quadratures of certain non-diagonalizable systems of hydrodynamic type.

Friday, Oct. 13 at 10:30 am
Lecture by Keagan Callis (University of Maryland, US)
Title: Absolutely Periodic Billiard Orbits of Arbitrarily High Order.

WEEK 2: October 16-20, 2023 

Monday, Oct. 16, 2 pm
Lecture by Marco Mazzucchelli (École Normale Supérieure de Lyon, France)
Title: Locally Maximal Closed Reeb Orbits of Reeb Flows

Tuesday and Thursday from 10am-12pm
Mini-course by Ke Zhang
(University of Toronto, Canada)
Title: KAM and formal methods for convex billiards

WEEK 3: October 23-27, 2023

Monday, Oct. 23 at 2 pm
Lecture by Vadim Zharnitsky (University of Illinois Urbana-Champaign, US)

Title: Billiard systems in potential fields

Thursday, October 26th at 4:00pm in Math Tower room P-131
Mathematics Colloquium by Sergei Tabachnikov
(Penn State University)
Title: Billiards in conics revisited

Friday, Oct. 27 at 10:30 am
Lecture by Irene De Blasi (University of Turin, Italy)
Title: An introduction to Galactic Refraction Billiards

WEEK 4: October 30 – November 3, 2023

Monday October 30 at 2:00pm
Lecture by Sean Gasiorek (Cal Poly)
Title: Dynamics and Periodicity Conditions for the Integrable Boltzmann System

Tuesday, Thursday and Friday from 10am-12pm
Mini-course by Vladimir Dragovic (The University of Texas at Dallas, US)
Title: Integrable Billiards, Extremal Polynomials, and Isoharmonic Deformations.

WEEK 5: November 6-10, 2023

Monday at 2:00pm
Lecture by Gabriele Benedetti (Vrije Universiteit Amsterdam, The Netherlands)
Title: Periodic orbits in non-convex, non-flat billiards

Tuesday, Thursday and Friday from 10am-12pm
Mini-course by 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

Wednesday and Thursday from 10am-12pm
Mini-course by Tere Seara, Pau Martin and Rafael Ramirez-Ros (Universitata Politecnica de Catalunya, Spain)
Title: Exponentially small phenomena in analytic convex billiards

Friday at 10:30am
Lecture by Marco Lenci (Università degli Studi di Bologna, Italy)
Title: Exactness and K-mixing for extensions of dynamical systems, with application to periodic Lorentz gases

WEEK 9: December 4-8, 2023

Tuesday and Thursday from 10am-12pm
Mini-course by Alexey Glutsuyk (CNRS & ENS Lyon)
Title: On algebraically integrable planar, dual and projective billiards

Friday at 10:30am
Lecture by Max Weinreich (Harvard University)
Title: Algebraic billiards and dynamical degrees

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