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...
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 $K \geq 2$).
