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Two knots are said to be homology concordant if they are smoothly concordant in a homology cobordism. One can define a quotient group using homology concordance similarly…

We explore one facet of an old problem: the approximation of hyperbolic conservation laws by viscous counterparts. While qualitative convergence results are well-known, quantitative rates for the inviscid limit are less common. In this talk, we consider the simplest case: a one-dimensional…

 The well-known Simons cone suggests that singularities may exist in a stable minimal hypersurface in Riemannian manifolds of dimension greater than 7, locally modeled on stable minimal hypercones. It was conjectured that generically they can be perturbed away. In this talk, we present a way to…

Abstract: In General Relativity, an impulsive gravitational wave is a localized and singular solution of the Einstein equations modeling the spacetime distortions created by a strongly gravitating source.

I will present a local theory of the Cauchy problem in U(1)-symmetry for rough data…

Let f :  Y -->X  be a proper flat morphism of algebraic varieties. Grothendieck and Dieudonné showed that the smoothness of f can be detected at closed points of X. Using André–Quillen homology, André showed that when X is excellent, the same conclusion holds when f is a closed flat morphism…

Consider a large random permutation satisfying some constraints or biased according to some statistics. What does it look like? In this seminar we make sense of this question by presenting the notion of permuton convergence. Then we answer the question for different choices of random permutation…

Abstract: Faltings proved the statement, previously conjectured by
Shafarevich, that there are finitely many abelian varieties of
dimension n, defined over a fixed number field, with good reduction
outside a fixed finite set of primes, up to isomorphism. In joint work
…