Previous Conferences & Workshops

Abstract: The Allen-Cahn equation behaves as a desingularization of the area functional. This allows for a PDE approach to the construction of minimal hypersurfaces in closed Riemannian manifolds. After presenting and overview of the subject, I will...

The Erdos-Rado sunflower conjecture is one of the tantalizing open problems in combinatorics. In my talk, I will describe several attempts on how to get improved bounds for it. These will lead to surprising connections with several other...

Abstract: This will be an overview of spacetime aspects of mean curvature includingtrapped surfaces, marginally outer trapped surfaces, and the role that they playin the spacetime positive energy theorem and Penrose inequality. We willsurvey the...

The workshop focused on recent advances related to the variational theory of the area functional and regularity of minimal varieties. Topics included minimal surfaces, constant mean curvature surfaces, the...

Through geometrical models, perturbation techniques and sometimes analytical approaches, it has been possible to establish a dictionary between "a taxonomy of generic dynamical phenomenons" and a list of "simple mechanisms or dynamical...

The classical Lagrange and Markov spectra encode the features of certain Diophantine approximations problems. The first systematic study of these spectra was done by Markov in 1880. Since then, these objects attracted the attention of several...

In this talk we will survey recent progress on the Beresticky-Caffarelli-Nirenberg Conjecture in Space Forms; that is, let $\Omega$ be an open connected domain of a complete connected Riemannian manifold ($M,g$) and consider the OEP given by
\begin...

Preliminary I will expose a technique developed with T. Rivi\`{e}re to prove energy identities (weak compactness) for sequences of solutions of any conformally invariant problem of second order in dimension 2, see [1]. Then after introducing some...

The Unique-Games Conjecture is a central open problem in the field of PCP’s (Probabilistically Checkable Proofs) and hardness of approximation, implying tight inapproximability results for wide class of optimization problems.

We will discuss PCPs...