PDE CDT Lunchtime Seminar

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
27 February 2020
12:00
Juan Davila
Abstract

I will describe new solutions to the stationary Ginzburg-Landau equation in 3 dimensions with vortex lines given by interacting helices, with degree one around each filament and total degree an arbitrary positive integer. I will also present results on the asymptotic behavior of vortices in the entire plane for a dissipative Ginzburg-Landau equation. This is work in collaboration with Manuel del Pino, Remy Rodiac, Maria Medina, Monica Musso and Juncheng Wei.

  • PDE CDT Lunchtime Seminar
12 March 2020
12:00
Michele Stecconi
Abstract

Invented by Andreas Floer in 1988 to solve Arnold's
conjecture, (symplectic) Floer Homology is a machinery to relate the
existence of periodic trajectories of an Hamiltonian flow on a
symplectic manifold M with the homology groups of M, analougously to
Morse Homology. Indeed this is done by developing an infinite
dimensional Morse theoretic framework adapted to a certain functional
(the action functional) on the loop space of M, whose critical points
are the periodic trajectories of the given hamiltonian flow.
Despite the topological nature of the results, the construction is
technically quite heavy, involving hard analysis and elliptic systems of
PDEs.

Together with Andrei Agrachev and Antonio Lerario we are developing a
method to construct such infinite dimensional homology invariants using
only soft and essentially finite dimensional tools. In my talk I will
present our approach.
The main feature consists in approximating the loop space with finite
dimensional submanifolds of increasing dimension, we do this with the
language of control theory, and then interpret asymptotically the
information provided by classical Morse theory

  • PDE CDT Lunchtime Seminar
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