Previous Conferences & Workshops

Abstract: In his ladmark 1976 paper "Modular curves and the Eisenstein ideal", Mazur studied congruences modulo p between cusp forms and an Eisenstein series of weight 2 and prime level N. We use deformation theory of pseudorepresentations to study...

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: Given a p-adic reductive group G and its (pro-p) Iwahori-Hecke algebra H, we are interested in the link between the category of smooth representations of G and the category of H-modules. When the field of coefficients has characteristic...

Abstract: Euler systems are compatible families of cohomology classes for a global Galois represenation, which plan an important role in studying Selmer groups. I will outline the construction of a new Euler system, for the Galois representation...

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...

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 $K \geq 2$).In...

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 the...

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...

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...