The black hole information paradox — whether information escapes
an evaporating black hole or not — remains one of the greatest
unsolved mysteries of theoretical physics. The apparent conflict
between validity of semiclassical gravity at low...
Let N and p greater than or equal to 5 be primes such that p
divides N−1. In his landmark paper on the Eisenstein ideal, Mazur
proved the p-part of the BSD conjecture for the p-Eisenstein
quotient J(p) of J0(N) over Q. Using recent results and...
I will explain how various results in arithmetic statistics by
Bhargava, Gross, Shankar and others on 2-Selmer groups of Jacobians
of (hyper)elliptic curves can be organised and reproved using the
theory of graded Lie algebras, following earlier...
Wiles’s proof of the modularity of (semistable) elliptic curves
over the rationals and Fermat’s Last Theorem relied on his
invention of a modularity lifting method. There were two strands to
the method:
I will present joint work with V. Paškūnas and G. Böckle
concerning deformation rings for mod p Galois representations of
p-adic local fields. After giving a short introduction to the
subject, I will explain our main result which says that
framed...
A surprising property of the cohomology of locally symmetric
spaces is that Hecke operators can act on multiple cohomological
degrees with the same eigenvalues. We will discuss this phenomenon
for the coherent cohomology of line bundles on modular...
Joint IAS/Princeton University Number Theory Seminar Topic:
Abelian varieties not isogenous to Jacobians Speaker: Jacob
Tsimerman Affiliation: University of Toronto Date: December 01,
2021 Katz and Oort raised the following question: Given an...
In 1986, Hooley applied (what practically amounts to) the
general Langlands reciprocity (modularity) conjecture and GRH in a
fresh new way, over certain families of cubic 3-folds. This
eventually led to conditional near-optimal bounds for the
number...
The unbounded denominators conjecture, first raised by Atkin and
Swinnerton-Dyer, asserts that a modular form for a finite index
subgroup of SL2(ℤ) whose Fourier coefficients have bounded
denominators must be a modular form for some congruence...
