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.
Abstract: I will discuss the following question: is Langlands
functoriality given by algebraic cycles? After a survey of some
examples of interest, the talk will focus mostly on one case,
namely that of inner forms GL(2) over a totally real field...
Abstract: In this talk, I will give a new construction of the
Morse-Bott cochain complex, where the underlying vector space is
generated by the cohomology of the critical manifolds. This new
construction has two nice features: (1) It requires the...