Seminars Sorted by Series

Abstract: In this talk we will present a construction of global existence of small solutions of the modified SQG equations, close to the disk. The proof uses KAM theory and a Nash-Moser argument, and does not involve any external parameters. We...

Abstract: In this talk we consider the pressureless Euler system in dimension greater than or equal to two. Several works have been devoted to the search of solutions which satisfy the following adhesion or sticky particle principle: if two...

Abstract:  It is known since the work of Dyachenko & Zakharov  that for the weakly nonlinear 2d infinite depth water waves, there are no 3-wave interactions and all of the 4-wave interaction coefficients vanish on the non-trivial resonant manifold...

Abstract: We discuss recent mathematical constructions of self-similar gravitational collapse for Newtonian stars governed by the Euler-Poisson system, known as Larson-Penston solutions for the isothermal stars and Yahil solutions for polytropic...

Abstract: The viscosity of a fluid is usually a constant, independent of the stress. There are however in nature several examples of fluids (ice, molten lava, blood, certain polymers, some salt solutions) where viscosity changes under applied forces...

Abstract: Whether the 3D incompressible Euler equations can develop a finite-time singularity from smooth initial data is an outstanding open problem. The presence of vortex stretching is the primary source of a potential finite-time singularity...

Abstract:In his seminal work, Leray demonstrated the existence of global weak solutions, with nonincreasing energy, to the Navier-Stokes equations in three dimensions. In this talk we exhibit two distinct Leray solutions with zero initial velocity...

For any regularity exponent $\beta<\frac 12$, we construct non-conservative weak solutions to the 3D incompressible Euler equations in the class $C^0_t (H^{\beta} \cap L^{\frac{1}{(1-2\beta)}})$.  By interpolation, such solutions belong to $C^0_tB^{s}_{3,\infty}$ for $s$ approaching $\frac 13$ as $\beta$ approaches $\frac 12$.  Hence this result provides a new proof of the flexible side of the Onsager conjecture, which is independent from that of Isett.  Of equal importance is that the intermittent nature of our solutions matches that of turbulent flows, which are observed to possess an $L^2$-based regularity index exceeding $\frac 13$.  The proof employs an intermittent convex integration scheme for the 3D incompressible Euler equations.  We employ a scheme with higher-order Reynolds stresses, which are corrected via a combinatorial placement of intermittent pipe flows of optimal relative intermittency.

I will describe a program aimed at understanding numerics of representations of quantized symplectic resolutions in positive characteristic. A key ingredient is a generalization of the action of the affine braid group on the derived category of...

According to Langlands’ conjectures, algebraic automorphic forms should be parametrized by global Galois representations, and smooth representations of $p$-adic groups should be parametrized by local Galois representations. These parametrizations...

A symplectic singularity has a natural stratification by Poisson leaves, which are symplectic, hence even-dimensional.  Perverse sheaves constructible with respect to this stratification are semisimple if the coefficients are in characteristic zero...

Let G be a semisimple group over an algebraically closed field of large characteristic. There are two important types of rational representations of G: the Weyl modules and the simple modules. We will explain how to go from the first type to the...

The study of totally positive matrices, i.e., matrices with positive minors, dates back to 1930s. The theory was generalised by Lusztig to arbitrary split reductive groups using canonical bases, and has significant impacts on the theory of cluster...

The talk is based on a joint work with Pablo Boixeda Alvarez. We study equivariant Borel-Moore homology of certain affine Springer fibers and relate them to global sections of suitable vector bundles arising from Procesi bundles on Q-factorial...

In 1997, Kuperberg gave a generators-and-relations presentation of the monoidal category Fund, whose objects are tensor products of fundamental representations, for all rank 2 lie algebras. The general case has been an open problem since. It was...

Abstract: In 2000, Arnaud Beauville introduced the notion of symplectic singularities and raised the question of classifying isolated symplectic singularities with trivial local fundamental group: the latter condition is meant to avoid the numerous...

What can one say about the fields of values of irreducible complex characters $\chi$ of a given finite group $G$? In particular when $G$ is a finite (quasi)simple group? What about the ``McKay situation'', i.e. when the degree of $\chi$ is coprime...

I will explain the construction of an action of the Hecke category on the principal block of representations of a connected reductive algebraic group over an algebraically closed field of positive characteristic, obtained in joint work with Roman...

Using the arithmetics of quantum numbers we construct some “approximations” of tilting modules for reductive algebraic groups that might be useful for understanding the generational patterns of tilting characters conjectured by Lusztig and...