## A Party for Which People? The Democrats from Andrew Jackson to Barack Obama and Beyond

## Front propagation in a nonlocal reaction-diffusion equation

We consider a reaction-diffusion equation with a nonlocal reaction term. This PDE arises as a model in evolutionary ecology. We study the regularity properties and asymptotic behavior of its solutions.

## Equivariant and nonequivariant contact homology

I will discuss joint work with Hutchings which constructs nonequivariant and a family floer equivariant version of contact homology. Both theories are generated by two copies of each Reeb orbit over Z and capture interesting torsion information. I will then explain how one can recover the original cylindrical theory proposed by Eliashberg-Givental-Hofer via our construction.

## Multiplicity One Conjecture in Min-max theory

I will present a proof with some substantial details of the Multiplicity One Conjecture in Min-max theory, raised by Marques and Neves. It says that in a closed manifold of dimension between 3 and 7 with a bumpy metric, the min-max minimal hypersurfaces associated with the volume spectrum introduced by Gromov, Guth, Marques-Neves are all two-sided and have multiplicity one.

## Gap and index estimates for Yang-Mills connections in 4-d

In this talk I want to discuss two related questions about