Video Lectures

The field of continuous combinatorics studies large (dense) combinatorial structures by encoding them in a "continuous" limit object, which is amenable to tools from analysis, topology, measure theory, etc. While the syntactic/algebraic approach of...

We present some obstructions to the existence of Lagrangian cobordisms in ℝ4. The obstructions arise from studying moduli spaces of holomorphic disks with corners with boundaries on immersed objects called Lagrangian tangles. The obstructions boil...

The question in the title was one of the founding questions in symplectic topology 40 years ago, and despite a lot of progress since that time, it remains widely open. In the talk I will discuss the initial questions, the progress, and the remaining...

A Kakeya Set in (Z/N Z)^n is a set that contains a line in every direction.  It has been known for over a decade that such sets must be large when N is prime (or more generally over any finite field).  This goes back to Dvir's proof of the finite...

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...