# Video Lectures

### Hofer geometry of coadjoint orbits and Peterson's theorem

Chi Hong Chow

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...

### Sections and unirulings of families over the projective line

Alex Pieloch

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...

### The smooth closing lemma for area-preserving surface diffeomorphisms

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...

### Monogenic fields with odd class number

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...

### A (slightly deeper) look into the restricted 3-body problem

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...

### Flexibility in C^0 symplectic geometry

Lev Buhovsky

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...

### Ampleness up to avoidance

Alvaro del Pino Gomez

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...

Chris Kochanek

### A topological view on the Monge-Ampere equation without convexity assumptions

Jonas Hirsch

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...

### Regularity of the limit set of embedded Poincaré Disks

Vincent Borelli

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...