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Speaker:    Michael Entov
Title:   Filtered Legendrian contact homology and contact dynamics part IV
Abstract:   In this mini-course, I will discuss how a filtered version of the Legendrian contact homology (a major machinery and object of study in contact topology) can be used to obtain new information about contact Hamiltonian flows on contact manifolds. The applications concern conformal factors of contactomorphisms and trajectories of contact Hamiltonian flows connecting two disjoint Legendrian submanifolds or starting on one of them and asymptotic to the other.This is a joint work with L.Polterovich.

Title:

Parametric Gromov width in Liouville domains

Speaker:   Filip Brocic, University of Augsburg Abstract:   In the talk, I will introduce the notion of the parametric Gromov width motivated by the classical camel theorem. The main theorem is a method how to bound the parametric Gromov width in the case of Liouville domains using the structure of the BV algebra on the persistence module that recovers symplectic cohomology. After presenting the theorem, I will cover the main applications, mainly using the string topology on cotangent bundles. In particular, I will give a new proof of the camel theorem using our methods. Time permitting, I will explain the method of the proof of the main theorem. This talk is based on the joint work with Dylan Cant.

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

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:   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.

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.