Web Page of the Ottawa-Carleton Number Theory Seminar
- Saban Alaca: salaca at math.carleton.ca
- Damien Roy: droy at uottawa.ca
October 19, 2012, 2:00-3:00pm, U. of Ottawa, room 327 in Tabaret Hall
- Speaker: Damien Roy (U. of Ottawa)
- Title: Diophantine approximation with sign constraints
- Abstract: Let a and b be real numbers such that 1, a and b are linearly independent over Q.
A classical result of Dirichlet asserts that there are infinitely many triples of integers (x,y,z) such that
|z+ax+by| < max(|x|,|y|,|z|)-2. In 1976, W. M. Schmidt asked what
can be said under the restriction that x and y are positive. Upon denoting by g=1.618 the golden ratio,
he proved that there are triples (x,y,z) satisfying this condition for which the product
|z+ax+by|.max(|x|,|y|,|z|)g is arbitrarily small. Although, at that time, Schmidt did not rule out
the possibility that g be replaced by any number smaller than 2, Moshchevitin proved few months ago
that it cannot be replaced by a number larger than 1.947. In this talk, we present a construction showing
that the result of Schmidt is in fact optimal.
December 20, 2012, 2:30-3:30pm, U. of Ottawa, room KED B015 (585 King Edward)
- Speaker: Fabien Pazuki (U. de Bordeaux)
- Title: Explicit calculations with the Faltings height.
- Abstract: Let A be an abelian variety over a number field. One can define a real number h(A)
called the differential height or Faltings height of A. This number has a lot of interesting properties,
and played a crucial role in the proof of the Mordell conjecture. We will focus on certain of these
properties, for example the explicit comparison with the theta height of A, and we will explain what
arithmetical information about A one can get.
Seminars from previous years