In all known explicit computations on Weinstein manifolds, the
self-wrapped Floer homology of non-compact exact Lagrangian is
always either infinite-dimensional or zero. We will explain why a
global variant of this observed phenomenon holds in broad...
I will explain some recent work on special cases of the
Bloch-Kato conjecture for the symmetric cube of certain modular
Galois representations. Under certain standard conjectures, this
work constructs nontrivial elements in the Selmer groups of...
Let G be a complex reductive group, G∗ its dual Poisson-Lie
group, and g the Lie algebra of G. G-valued Stokes phenomena were
exploited by P. Boalch to linearise the Poisson structure on G∗. I
will explain how Ug-valued Stokes phenomena can be used...
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...
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...
The title of Ferdinand Céline’s novel resumes the fate of the
Saadian sultans’ library and the premonitory curiosity its founder,
Aḥmad al-Manṣūr, is said to have had for the palace Philip II of
Spain was building in the El Escorial. Over the
last...
What can one say about the fields of values of irreducible
complex characters χχ of a given finite group GG? In
particular when GG is a finite (quasi)simple group? What
about the ``McKay situation'', i.e. when the degree of
χχ is coprime to a fixed...
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
quotient...
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...
