When: Tuesday, 12 - 1:30 PM Eastern Standard Time (currently 10 AM - 11:30 PM Arizona Time). In the Fall 2021, the seminar will meet on a biweekly schedule, starting on September 21.

Where: Please see the talk abstract for a Zoom link and passcode. If you would like to be added to the mailing list, please e-mail Boris Khesin or Anton Izosimov.

Description: This seminar will tentatively be around the topics of geometric mechanics and Hamiltonian dynamics, which includes but is not limited to such topics as geometric fluid dynamics and integrable systems. We would like it to be a working group, so that we all, and in particular students, could ask any questions, get to any detail, rather than to just advertise results. The length of the seminar will be a bit longer than usual, from 1 to 1.5 hours, in order to have time for more questions. We might have weekly or biweekly meetings, depending on the presence of speakers. One important feature will be that undergraduate and graduate students and postdocs could get acquainted with each other and start discussing topics of mutual interest between themselves, beyond the seminar setting.

Upcoming talks

Past talks

Spring 2022:
  • Jan 11 -- Eva Miranda, Universitat Politècnica de Catalunya -- To b or not to b: That is the question

Fall 2021:
  • Dec 14 -- Richard Montgomery, UC Santa Cruz -- Bicycling, jet space and metric lines

  • Nov 30 -- Theodore Drivas, Stony Brook -- Simultaneous development of shocks and weak discontinuities from smooth data

  • Nov 16 -- Sergei Tabachnikov, Penn State -- Cusps of caustics by reflection and Legendrian knots

  • Nov 2 -- Marianna Russkikh, MIT -- Dimers and circle patterns

  • Oct 19 -- Klas Modin, Chalmers University of Technology and University of Gothenburg -- Quantized hydrodynamics on the sphere

  • Oct 5 -- Semeon Artamonov, CRM -- Superintegrable systems on moduli spaces of flat connections

  • Sep 21 -- Anton Izosimov, University of Arizona -- Dimers, networks, and integrable systems

Spring 2021:
  • May 11 -- Vladimir Fock, Strasbourg -- Projective structures of Riemann surfaces: description, moduli, properties, generalisations

  • May 4 -- François-Xavier Vialard, LIGM, Université Gustave Eiffel, CNRS -- Unbalanced optimal transport and its connection to the Camassa-Holm equation

  • April 27 -- Francisco Torres de Lizaur, University of Toronto -- Chaos in the incompressible Euler equation on manifolds of high dimension

  • April 20 -- Max Weinreich, Brown -- The pentagram map and algebraic integrability

  • April 13 -- Mikhail Roop, Institute of Control Sciences, RAS, Moscow, Russia -- Singularities in solutions to 1-dimensional gas dynamics equations: multivalued solutions and phase transitions

  • April 6 -- Leonid Monin, University of Bristol -- Hyperelliptic curves with many automorphisms and triangular billiards

  • March 30 -- Open problems session. Speakers: Sergei Tabachnikov (Notes, References), Anton Izosimov, Klas Modin (Notes), Boris Khesin (Notes), and Gerard Misiolek (Notes)

  • March 23 -- Konstantin Aleshkin, Columbia -- Primitive forms without metric and integrable hierarchies

  • March 16 -- Alexey Bolsinov, Loughborough -- On symplectic invariants of integrable Hamiltonian systems

  • March 9 -- Patrick Heslin, Notre Dame -- Some no-gain results for two-point boundary value problems on diffeomorphism groups

  • March 2 -- Sergei Yakovenko, Weizmann Institute of Science -- Local normal forms without group action

  • February 23 -- Maxim Arnold, UT Dallas -- Cross-ratio dynamics

  • February 16 -- Cy Maor, Hebrew University of Jerusalem -- Some geometric aspects in elasticity theory

  • February 9 -- Niklas Affolter, TU Berlin -- Discrete integrability, TCD maps and the pentagram map

  • February 2 -- Robert Cardona, Polytechnic University of Catalonia -- The topology of Bott integrable fluids

  • January 26 -- Gleb Smirnov, ETH Zurich -- Singular points of integrable Hamiltonian systems and Chern classes

  • January 19 -- Leandro Lichtenfelz, University of Pennsylvania -- 3D Euler Equations on Manifolds with Symmetry
Fall 2020:
  • December 15 -- Vladimir Dragovic, University of Texas at Dallas -- Ellipsoidal billiards, extremal polynomials, and combinatorics

  • December 8 -- Martin Bauer, Florida State University -- Weak and strong Riemannian metrics: theory and examples

  • December 1 -- Klas Modin, Chalmers University of Technology and University of Gothenburg -- Geometry of matrix decompositions seen through optimal transport and information geometry

  • November 24 -- Sergei Tabachnikov, Pennsylvania State University -- Four equivalent properties of integrable billiards

  • November 17 -- Ilia Kirillov, University of Toronto -- Classification of coadjoint orbits for symplectomorphism groups of surfaces with boundary

  • November 10 -- Danny Nackan, University of Toronto and Yale University -- Continuous limits of generalized pentagram maps

  • October 27 -- Nicholas Ovenhouse, University of Minnesota -- Poisson brackets for Grassmannian pentagram maps

  • October 20 -- Quinton Aboud, University of Arizona -- The pentagram map and infinitesimal monodromy

  • October 13 -- Cheng Yang, University of Toronto -- Vortex motion of the Euler and Lake equations

  • September 29 -- Francisco Torres de Lizaur, University of Toronto -- A characterization of steady Euler flows