An extension of Gromov compactness theorem ensures that any
family of manifolds with convex boundaries, uniform bound on the
dimension and uniform lower bound on the Ricci curvature is
precompact in the Gromov-Hausdorff topology. In this talk,
we...
What can we say on a convex body from seeing its projections? In
the 80s, Lutwak introduced a collection of measurements that
capture this question. He called them the affine quermassintegrals.
They are affine invariant analogues of the classical...
(work in progress with R. Rouquier) I will present a
computational (yet conjectural) method to determine some
decomposition matrices for finite groups of Lie type. These
matrices encode how ordinary representations decompose when they
are reduced to...
The problem of classification of perverse sheaves on the
quotient h/W for a semisimple Lie algebra g has an explicit answer
which turns out to be related to the algebraic properties of
induction and restriction operations for parabolic
subalgebras...
The Hecke algebra admits an involution which preserves the
standard basis and exchanges the canonical basis with its dual.
This involution is categorified by "monoidal Koszul duality" for
Hecke categories, studied in positive characteristic in my...
I'll present joint work with Tsao-Hsien Chen on the geometry of
real and symmetric matrices. For classical groups, we use
hyperkahler geometry to lift the Kostant-Sekiguchi correspondence
to an equivariant homeomorphism. As an application, we show...
Polymers are macromolecules that cannot cross each other without
breaking their bonds. This leads to polymer chain entanglement
which determines bulk viscoelastic responses of the material.
Understanding the relation between entanglement and...
Triangulated categories play an important role in symplectic
topology. The aim of this talk is to explain how to combine
triangulated structures with persistence module theory in a
geometrically meaningful way. The guiding principle comes from
the...
The Generalized Ramanujan Conjecture (GRC) for GL(n) is a
central open problem in modern number theory. Its resolution is
known to yield several important applications. For instance, the
Ramanujan-Petersson conjecture for GL(2), proven by Deligne...
