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...
In the recent breakthrough on the uniform Mordell-Lang problem
by Dimitrov-Gao-Habegger and Kuhne, their key result is a uniform
Bogomolov type of theorem for curves over number fields. In this
talk, we introduce a refinement and generalization of...
This is intended to complement the recent talk of Pham Huu Tiep
in this seminar but will not assume familiarity with that talk. The
estimates in the title are upper bounds of the form |χ(g)|≤χ(1)α,
where χ is irreducible and α depends on the size of...
I will discuss recent work with Harald Helfgott in which we
establish roughly speaking that the graph
connecting nn to n±pn±p with pp a
prime dividing nn is almost "locally Ramanujan". As a
result we obtain improvements of results of Tao and Tao...
A group is said to have bounded generation (BG) if it is a
finite product of cyclic subgroups. We will survey the known
examples of groups with (BG) and their properties. We will then
report on a recent result (joint with P. Corvaja, J. Ren and
U...
Up to a finite covering, a sequence of nested subvarieties of an
affine algebraic variety just looks like a flag of vector spaces
(Noether); understanding this « up to » is a primary motivation for
a fine study of finite coverings.
