In this talk, I will present a formulation of the Gross-Zagier
formula over Shimura curves using automorphic representations with
algebraic coefficients. It is a joint work with Shou-wu Zhang and
Wei Zhang.
The classical result on the uniqueness of black holes in GR, due
to Hawking, which asserts that regular, stationary solutions of the
Einstein vacuum equations must be isometric to an admissible black
hole Kerr solution, has at its core a a highly...
I will first discuss the orientability of the moduli spaces of
J-holomorphic maps with Lagrangian boundary conditions. It is known
that these spaces are not always orientable and I will explain what
the obstruction depends on. Then, in the presence...
Among the bounty of brilliancies bequeathed to humanity by
Srinivasa Ramanujan, the circle method and the notion of mock theta
functions strike wonder and spark intrigue in number theorists
fresh and seasoned alike. The former creation was honed...
We give a survey of recent results on conjectures of Heath-Brown
and Serre on the asymptotic density of rational points of bounded
height. The main tool in the proofs is a new global determinant
method inspired...
In the early 80's, Shimura made a precise conjecture relating
Petersson inner products of arithmetic automorphic forms on
quaternion algebras over totally real fields, up to algebraic
factors. This conjecture (which is a consequence of the Tate...
