Public holiday

Speaker:   Leonid Polterovich
Title:   Contact Topology meets Thermodynamics Part I
Abstract:   We discuss the occurrence of some notions and results from contact topology in the non-equilibrium thermodynamics. This includes the Reeb chords and the partial order on the space of Legendrian submanifolds.

Joint with M.Entov and L.Ryzhik.

Speaker:   Miguel Sanchez Caja
Title:   Lorentz–Finsler Geometry and its Applications Part I
Abstract:   Session 1: Lorentz–Finsler background1.    Minkowski and Lorentz norms
2.    Finsler, Lorentz–Finsler, and cone structures
3.    Basic Finslerian setting
4.    Symplectic and contact viewpoints for geodesics

Speaker:   Eric Kilgore
Title:   A Legendrian non-squeezing phenomenon
Abstract:   We discuss some embedding rigidity results for Legendrian submanifolds of the pre-quantization of the standard symplectic vector space. In particular, we describe a criterion forbidding the squeezing (by Legendrian isotopy) of a Legendrian \Lambda into a sufficiently small neighborhood of the pre-image of a symplectic plane in the base, formulated in terms of certain categorical invariants associated to \Lambda. As an application, we’ll see that lifts of certain (non-exact!) Lagrangians are not squeezable.

Speaker:   Miguel Sanchez Caja
Title:   Lorentz–Finsler Geometry and its Applications Part II
Abstract:   Session 2: Global Lorentz–Finsler Geometry and the space of cone geodesics1.    Causality theory for a cone structure
2.    Globally hyperbolic cone structures (with timelike boundary)
3.    The space of cone geodesics

Speaker:   Leonid Polterovich
Title:   Contact Topology meets Thermodynamics Part 2
Abstract:   We discuss the occurrence of some notions and results from contact topology in the non-equilibrium thermodynamics. This includes the Reeb chords and the partial order on the space of Legendrian submanifolds.
Joint with M.Entov and L.Ryzhik.

Title:   The Matrix Bootstrap

Abstract:   I will survey recent developments in the matrix bootstrap, a non-perturbative method for solving large N quantum systems, including applications to the c=1 string and BFSS. I will also discuss work in progress with Klebanov and Meshcheriakov on the existence of a Regge trajectory in the adjoint sector of the 1-matrix quantum mechanics.

Speaker:   Miguel Sanchez Caja
Title:   Lorentz–Finsler Geometry and its Applications Part III
Abstract:   Session 3: Applications

1.             Broadpicture of wave propagation

2.             Linksamong Riemannian, Lorentzian and Finsler geometries

3.             Fermat’sprinciple, Snell’s law and discretization

4.             FinslerianRelativity

Title:   PCF correspondences on Riemann surfaces and applications
Speaker:   Dzmitry Dudko, Stony Brook University

Abstract:

We consider certain postcritically finite (PCF) correspondences on a Riemann surface and show that they admit a weak form of hyperbolicity: sufficiently long loops get shorter under lifting at a fixed point and closing. The proof relies on analyzing the tension between the non-uniform contraction induced by the Schwarz lemma and an ``additive correction.'' As an application, we show that apart from the usual Latt'es counterexamples, any PCF rational map on the Riemann sphere with 4 post-critical points possesses finite graph attractors: among graphs of given complexity, there exists a finite invariant collection of isotopy classes of graphs into which every graph is attracted under lifting. Joint work with L. Bartholdi and K. Pilgrim.