Lusztig's theory of character sheaves for connected reductive
groups is one of the most important developments in representation
theory in the last few decades. In this talk, we will describe a
construction which extends this "depth zero" picture to...
We develop on a new strategy based on point-set topology, which
allows us to produce a purely p-adic statement for the
crystallinity properties of rigid flat connections.
Let X be a proper, smooth rigid space and G a commutative rigid
group. We study the relationship between G-representations of the
fundamental group of X and G-Higgs bundles on X. This is joint work
with Ben Heuer and Mingjia Zhang.
An old open question in symplectic geometry asks whether all
normalised symplectic capacities coincide for convex domains in the
standard symplectic vector space. I will show that this question
has a positive answer for smooth convex domains which...
Given a family of motives, the de Rham realization (a certain
vector bundle with integrable "Gauss-Manin" connection) can be
compared to the crystalline realizations for various primes p, but
the resulting Frobenius structures cannot be directly...
We ask the question, “how does the infinite q-Pochhammer symbol
transform under modular transformations?” and connect the answer to
that question to the Stark conjectures. The infinite q-Pochhammer
symbol transforms by a generalized factor of...
I will discuss infinite-dimensional linear programs producing
bounds on the spectral gap in various settings. This includes new
bounds on the spectral gap of hyperbolic manifolds as well as the
Cohn+Elkies bound on the density of sphere packings...
In this talk, we introduce the analytic de Rham stack for rigid
varieties over Qp
(and more general analytic stacks). This object is an
analytic incarnation of the (algebraic) de Rham stack of Simpson,
and encodes a theory of analytic D-modules...
