Conference: Billiards and Stars: Geometry and Dynamics

The conference “Billiards and Stars: Geometry and Dynamics” is going to take place in Guanajuato, Mexico on August 10-14, 2026. It will focus on recent developments and interactions of two broad mathematical domains: one of them is mathematical foundations of Celestial Mechanics, the area rooted in sky observations since antiquity, later boosted by Newton's discoveries, and flourished during the last century with novel applications of topology, geometry, control theory, and dynamics to study both regular and chaotic motions of celestial bodies, as well as the discovery of many explicit solutions to seemingly intractable problems. The other area is that of Mathematical Billiards, a class of dynamical systems owing its birth to Poincare and Birkhoff and which recently developed into a remarkable domain of symplectic geometry and dynamical systems. This event is going to bridge research communities that rarely meet, to inspire young researchers, and broaden participation across demographics and regions. The conference will foster interaction of scientists and students working in those domains, which share a remarkable geometric structure: both areas involve the study of trajectories governed by geometric and topological constraints. The study of periodic orbits, conserved quantities, and chaos in these systems has produced tools of broad applicability in topology, mechanics, Hamiltonian systems, and discrete dynamics, it inspired new approaches in mathematical physics and robotics. Its recent successes are related to discoveries of new classes of periodic orbits, partial proofs of the Birkhoff conjecture on its integrable cases, and discovery of new billiard-type systems in fluid dynamics. The conference will also celebrate the 70th birthdays of two world experts in those respective domains, Richard Montgomery and Sergei Tabachnikov. The conference website is https://www.cimat.mx/~gil/GD2026/ This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria. NSF Award ID: 2609520 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Maxim Arnold | Institution: University of Texas at Dallas, RICHARDSON, TX | Award Amount: $20,000 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2609520 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2609520.html