20250926 Oliver Fabert

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.