School of Mathematics

The classification of geometric structures on manifolds naturally leads to actions of automorphism groups, (such as mapping class groups of surfaces) on "character varieties" (spaces of equivalence classes of representations of surface groups).

Reproducibility is vital to ensuring scientific conclusions are reliable, but failures of reproducibility have been a major issue in nearly all scientific areas of study in recent decades. A key issue underlying the reproducibility crisis is the...

A compact four dimensional completely integrable system f:M→R2 is semitoric if it has only non-degenerate singularities, without hyperbolic blocks, and one of the components of generates a circle action. Semitoric systems have been extensively...

Consider the action of a group on a finite-dimensional vector space. Given some natural conditions on the group, Hilbert showed a famous "duality" between invariant polynomials and closures of group orbits. Namely, the orbit closure of a vector is...

I will discuss some quantitative aspects for Legendrians in a (more or less) general contact manifold. These include lower bounds on the number of Reeb chords between a Legendrian and its contact Hamiltonian image, the non-degeneracy of the Chekanov...

In this talk we introduce a type of surgery decomposition of Weinstein manifolds we call simplicial decompositions. We will discuss the result that the Chekanov-Eliashberg dg-algebra of the attaching spheres of a Weinstein manifold satisfies a...

The notion of positive (non-negative) contact isotopy, defined by Eliashberg and Polterovich, leads to two relations on the group of contactomorphisms. These relations resemble the causal relations of a Lorentzian manifold. In this talk we will...