# Video Lectures

We will discuss a complete computation of Savelyev's homomorphism associated to any coadjoint orbit of a compact Lie group G, where the domain is restricted to the based loop homology of G. This gives at the same time some applications to the...

We will discuss the existence of rational (multi)sections and unirulings for projective families f:X?P1 with at most two singular fibres. Specifically, we will discuss two ingredients for constructing the above rational curves. The first is local...

In this talk, I will discuss recent joint work with D. Cristofaro-Gardiner and B. Zhang showing that a generic area-preserving diffeomorphism of a closed surface has a dense set of periodic points. This follows from a result called a “smooth closing...

In this talk, we prove an upper bound on the average number of 2-torsion elements in the class group of monogenised fields of any degree n?3 and, conditional on a widely expected tail estimate, compute this average exactly. As an application, we...

In this talk, as a continuation of my talk in the Members’ Colloquium but with a specialized audience in mind, I will discuss in more detail some of the general geometric and dynamical structures underlying the theoretical aspects of the restricted...

Traditionally, objects of study in symplectic geometry are smooth - such as symplectic and Hamiltonian diffeomorphisms, Lagrangian (or more generally, isotropic and co-isotropic) submanifolds etc. However, in the course of development of the field...

In the first half of the talk I will review Gromov's work on convex integration for open differential relations. I will put particular emphasis on comparing various flavours of ampleness and, in particular, I will note that the different flavours...

In this talk we consider the classical Monge-Amp´ere equation in two dimensions in a low-regularity regime:

(0.1) det D 2u = f on D ? R2 .

We will assume that f is a given strictly positive, smooth function, but we want to assume as...

Let f be an embedding of a non compact manifold into an Euclidean space and p_n be a divergent sequence of points of M. If the image points f(p_n) converge, the limit is called a limit point of f. In this talk, we will build an embedding f of a...