[Topology.beta] Tomorrow

[Rot, T.O. (Thomas)]

Hi,

Reminder for Tomorrow. Lots of math!

Thomas


Friday Fish:




+ Speaker: Oliver Fabert (VU)
+ Date: 26 september 2025
+ Time: 11:00
+ Location: Vrije Universiteit: Maryam (NU9-A46)
+ Title: Topology, symplectic topology, … what’s next?
+ Abstract: In topology one uses Morse theory to prove lower bounds
for the number of 0-dimensional objects, namely critical points of
smooth functions on smooth manifolds. In symplectic topology one
uses Floer theory to prove lower bounds for the number of
1-dimensional objects, namely solutions to Hamiltonian ODEs. In this
talk I will outline how the framework of symplectic topology can be
generalized to study 2-dimensional or even higher-dimensional
objects, leading to a class of first-order (Hamiltonian) PDEs
sharing similar rigidity properties. In the same way as the
Hamiltonian ODEs provide a generalized framework for classical
mechanics, our class of Hamiltonian PDEs shall provide a generalized
framework for studying equilibrium states of reaction-diffusion
systems. This is joint work with my PhD student Ronen Brilleslijper.




DDT&G:


Speaker: Fabio Gironella (Nantes)
Title: "On symplectic foliations in high dimensions" (see below for the abstract)
Date: Friday 26 September, 14:30-17:00
Location: Amsterdam, Maryam (NU9-A46)


The schedule will be as follows:


2:30-3:30 p.m.: first part of the seminar (little to no prior knowledge assumed)
4:00-5:00 p.m.: second part of the seminar (slightly more advanced level)


Please notice that the first part of the seminar (2:30-3:30 p.m.) is intended for general mathematical audience, and master students with an interest in geometry and topology are especially encouraged to participate.


Abstract


The end goal of the two-hour presentation is to describe the results of a joint work with Klaus Niederkrueger and Lauran Toussaint, where we give a new obstruction, generalizing a 3-dimensional one due to Novikov in a symplectic-topological direction, for a symplectic foliation to be of a special type, called strong. This is based on the use of pseudo-holomorphic curves theory, which is an essential (and very powerful) tool to prove rigidity phenomena in symplectic topology.
The aim of the first hour of the talk is twofold. First, I will describe the overall idea of (one possible way) of using pseudo-holomorphic techniques to study symplectic manifolds with contact-type boundary, also called symplectic fillings, which is a very common setup in symplectic topology. Then, I will motivate the question underlying our joint work, by explaining (at least one reason) why one should care about (strong) symplectic foliations in high dimensions: they are one of the best candidates of subclass of foliations in high-dimensions to play the role of rigid objects analogously to taut foliations in ambient dimension 3. While giving the context for the rest of the talk in this first hour, I will mention some related problems and questions which are currently also of interest in symplectic topology.
The second hour of the presentation will then be dedicated to explain how the previously mentioned pseudo-holomorphic techniques can be adapted to the symplectically foliated setup in order to give the above claimed new obstruction to strongness of symplectic foliations. Time permitting, I will also sketch an explicit construction of a symplectic foliation which is not strong due to this new criterion, but cannot be deduced to be non-strong with other more elementary criteria.




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