Abstract: I will discuss a recent conjecture formulated in an
ongoing project with Jan Vonk relating the intersection numbers of
one-dimensional topological cycles on certain Shimura curves to the
arithmetic intersections of associated real...
We prove the existence and the linear stability of Cantor families
of small amplitude time quasi-periodic standing water waves
solutions, namely periodic and even in the space variable $x$, of a
bi-dimensional ocean with finite depth under the...
Abstract: Wiles' work on modularity of elliptic curves over the
rationals, used as a starting point that odd, irreducible
represenations $G_Q \rightarrow GL_2 (F_3)$ arise from
cohomological cusp forms (i.e. new forms of weight $K \geq 2$).
Abstract: We will discuss joint work with Calegari, Caraiani,
Gee, Helm, Le Hung, Newton, Scholze, Taylor, and Thorne that proves
potential automorphy of symmetric powers of rank two compatible
systems of weight zero. As a consequence, we deduce...
Abstract: We prove an ordinary modularity lifting theorem for
certain non-regular 4-dimensional symplectic representations over
totally real fields. The argument uses both higher Hida theory and
the Calegari-Geraghty version of the Taylor-Wiles...
Abstract: In usual Hida theory, one constructs a module over
weight space whose specialitzation to sufficiently regular weight
is a space over classical ordinary modular forms. The goal of
higher Hida theory is to construct a perfect complex of...
We present an explicit pseudorandom generator with seed length
$\tilde{O}((\log n)^{w+1})$ for read-once, oblivious, width $w$
branching programs that can read their input bits in any order.
This improves upon the work of Impaggliazzo, Meka and...
Abstract: We will describe new algorithms to compute an explicit
finite simplicial model for compact, congruence locally symmetric
spaces and Hecke actions thereon. Joint work with Aurel Page.
Abstract: I will introduce the mod p derived spherical Hecke
algebra of a p-adic group, and discuss its structure via a derived
version of the Satake homomorphism. Then, I will survey some
speculations about its action on the cohomology of...
Abstract: I will report on ongoing computations, with G. Dispinescu
and W. Niziol, of the p-adic etale cohomology of the Drinfield
tower, and applications to the p-adic local Langlands
correspondence.
