# Video Lectures

### The many facets of complexity of Beltrami fields in Euclidean space

Daniel Peralta-Salas

Beltrami fields, that is vector fields on $\mathbb R^3$ whose curl is proportional to the field, play an important role in fluid mechanics and magnetohydrodynamics (where they are known as force-free fields). In this lecture I will review recent...

### Mather-Thurston’s theory, non abelian Poincare duality and diffeomorphism groups

Sam Nariman

I will discuss a remarkable generalization of Mather’s theorem by Thurston that relates the identity component of diffeomorphism groups to the classifying space of Haefliger structures. The homotopy type of this classifying space played a...

### Local flexibility for open partial differential relations

Bernhard Hanke

We discuss the problem of extending local deformations of solutions to open partial differential relations to global deformations and formulate conditions under which such extensions are possible. Among others these results are applied to study...

### Parallel Repetition for the GHZ Game: A Simpler Proof

Uma Girish

We give a new proof of the fact that the parallel repetition of the (3-player) GHZ game reduces the value of the game to zero polynomially quickly.  That is, we show that the value of the n-fold parallel repetition of the GHZ game is at most n^{-...

### Overtwisted = Tight in 3 dimensions

Francisco Presas Mata

We prove the equivalence of Eliashberg overtwisted $h$—principle and  the Eliashberg-Mishachev classification of contact structures in the tight $3$-ball. I.e. we prove that simple algebraic topology computations takes us from one result to the...

### Looking at Euler flows through a contact mirror: Universality, Turing completeness and undecidability

Eva Miranda

The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. Recently, Tao [6, 7, 8] launched a programme to address the global existence problem for the Euler and Navier-Stokes equations...

### Detecting non-trivial elements in the spaces of Legendrian knots via Algebraic K-theory

This talk is based on a joint work with Thomas Kragh. Using the generating function theory we split inject homotopy groups of pseudo-isotopy and/or h-cobordism spaces into various spaces of Legendrian manifolds, e.g. the space of Legendrian unknots...

### Reducible fibers and monodromy of polynomial maps

For a polynomial f??[x], Hilbert's irreducibility theorem asserts that the fiber f?1(a) is irreducible over ? for all values a?? outside a "thin" set of exceptions Rf. The problem of describing Rf is closely related to determining the monodromy...

### Existence of an unbounded nodal hypersurface for smooth Gaussian fields in dimension d > 2

Hugo Duminil-Copin

For the Bargmann--Fock field on Rd with d>2, we prove that the critical level lc(d) of the percolation model formed by the excursion sets {f?l} is strictly positive. This implies that for every l sufficiently close to 0 (in particular for the nodal...