Decomposition theorem for perverse sheaves on algebraic
varieties, proved by Beilinson-Bernstein-Deligne-Gabber, is one of
the most important and useful theorems in the contemporary
mathematics. By the Riemann-Hilbert correspondence, we may
regard...
A theme that cuts across many domains of computer science and
mathematics is to find simple representations of complex
mathematical objects such as graphs, functions, or distributions on
data. These representations need to capture how the object...
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...
