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...
In this talk, we prove an upper bound on the average number of
2-torsion elements in the class group of monogenised fields of any
degree n≥3 and, conditional on a widely expected tail estimate,
compute this average exactly. As an application, we...
For a polynomial f∈ℚ[x], Hilbert's irreducibility theorem
asserts that the fiber f−1(a) is irreducible over ℚ for all values
a∈ℚ outside a "thin" set of exceptions Rf. The problem of
describing Rf is closely related to determining the
monodromy...
We study CM cycles on Kuga-Sato varieties over X(N) via theta
lifting and relative trace formula. Our first result is the
modularity of CM cycles, in the sense that the Hecke modules they
generate are semisimple whose irreducible components are...
We consider the standard L-function attached to a cuspidal
automorphic representation of a general linear group. We present a
proof of a subconvex bound in the t-aspect. More generally, we
address the spectral aspect in the case of uniform parameter...
I will discuss some recent progress in analytic number theory
for polynomials over finite fields, giving strong new estimates for
the number of primes in arithmetic progressions, as well as for
sums of some arithmetic functions in arithmetic...
