Video Lectures

I use the same title for different talks, changing the selection of topics and the level of detailedness for each topic:) This is a survey talk based on joint projects with D. Chen, S. Ivanov, late Ya. Kurylev, M. Lassas, J. Lu, and, if time permits...

Cieliebak and Eliashberg showed that there is a special class of flexible symplectic structures that satisfy an h-principle and hence  have `trivial' symplectic topology. In this talk, I will explain that it is fruitful to think of flexibilization...

We describe a construction of a locally conformal symplectic structure homotopic to any given non-degenerate 2-form and whose Lee form can be any non-exact 1-form. Moreover, each connected component of the boundary, if any, may be chosen to be...

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...