Abstract: A rather notorious mistake occurs p. 217 in the proof
of Lemma 6.3 of the book "Simple algebras, base change, and the
advanced theory of the trace formula" (1989) by J. Arthur, L.
Clozel. E. Lapid and J. Rogawski (1998) proposed a proof...
Abstract: An important input into modularity lifting theorems is
an understanding of the geometry of Galois deformation rings,
especially local deformation rings with p-adic Hodge theory
conditions at $\ell=p$. Outside of a few cases (ordinary...
Abstract: Zywina showed that after passing to a suitable field
extnesion, every abelian surface $A$ with real multiplication over
some number field has geometrically simple reduction modulo
$\frak{p}$ for a density one set of primes $\frak{p}$. One...
Abstract: In his classical work, Mazur considers the Eisenstein
ideal $I$ of the Hecke algebra $\mathbb{T}$ acting on cusp forms of
weight $2$ and level $\Gamma_0(N)$ where $N$ is prime. When $p$ is
an Eisenstein prime, i.e. $p$ divides the...
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...
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...
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...
