| Speaker: | Georgios Dimitroglou Rizell, Uppsala University |
| Abstract: |
| TBA |
| Speaker: | Ljudmila Kamenova, Stony Brook University |
Speaker: Michael Entov
Title: Filtered Legendrian contact homology and contact dynamics Part I
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.
| Speaker: | Linquan Ma, Purdue University |
| Title: | The Briançon-Skoda theorem |
| Abstract: |
| The Briançon-Skoda theorem is a comparison relating the integral closure of powers of an​ ideal with its ordinary power. The theorem was originally proved via analytic methods for coordinate rings of smooth varieties over the complex numbers. The full algebraic version for all regular local rings was obtained by Lipman--Sathaye. Since then, there have been other proofs and various generalizations to singularities. In this talk, we present a general Briançon-Skoda containment for pseudo-rational singularities in all characteristics. Our proof is quite simple, and it recovers most previously known results. We also answer a conjecture of Huneke on the uniform Briançon-Skoda theorem for all excellent rings as an application of our result and methods. This is based on joint work with Peter McDonald, Rebecca R.G., and Karl Schwede. |
Speaker: Michael Entov
Title: Filtered Legendrian contact homology and contact dynamics Part 2
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.
Speaker: Alessandro Bravetti
Title: Contact Hamiltonian Systems: from mechanics to thermodynamics and moreAbstract: This seminar aims to introduce contact Hamiltonian systems and explain why they have attracted growing interest. Along the way, we review their main structural properties and present applications that showcase their relevance across mechanics, thermodynamics and statistics (optimization and sampling).
Speaker: Michael Entov
Title: Filtered Legendrian contact homology and contact dynamics Part III
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.
Speaker: Dimitroglou Rizell (Uppsala University)
Title: A survey of quantitative results for Legendrian submanifolds
Abstract: We give a survey of results concerning the properties of Legendrian submanifolds of contact manifolds from the perspective of the Chekanov-Hofer-Schelukhin norm, such as (un)boudnedness, bounds on displacement energies, and relations to spectral norms. We also discuss rigidity of C0-limits of Legendrians. This is based upon joint projects with M. Sullivan and R. Leclercq.
Speaker: Eric Bedford, Stony Brook University
Title: Dynamics of rational mappings in dimension 2
| Abstract: |
| We will look at the dynamics of a family of birational maps on R^2 and C^2. Then we will discuss a noninvertible rational map acting in dimension 2. |
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