Abstracts of Talks

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Diophantine Approximation on Quadratic Surfaces

Alexander Gorodnik (Princeton)

We discuss the problem of Diophantine approximation by integer vectors lying on a quadratic surface and determine the optimal order of approximation for generic points. This result is analogous to the Khinchin theorem.

Logarithm Laws for Unipotent Flows

Jayadev Athreya (Princeton)

In joint work with G. Margulis, we prove a logarithm law describing the statistical behavior of excursions into the cusp for unipotent flows on the space of unimodular lattices in R^n. One of the main tools in our proof is a measurable analogue of the Minkowski convex body theorem which may be of independent interest.

Shrinking Target Properties for Translations of Tori

Bassam Fayad (Paris-13)

The only translations that have the Monotone Shrinking Target property are those of constant type.

A Survey of Progress toward the Duffin-Schaeffer Conjecture

A. Haynes (Brandeis)

The Duffin-Schaeffer Conjecture is a central problem in metric number theory which has been studied for well over 50 years. This talk will be expository and its purpose is to discuss some of the ideas that have been successfully used to make significant progress toward proving this conjecture.

LImit Theorems for Birkhoff Sums over Rotations

C. Ulcigrai (Bristol)

We prove a renewal-type limit theorem for denominators of the continued fraction expansion. We use it to show the existence of a limiting distribution for certain trigonometric sums. Such sums are given by Birkhoff sums over rotations of a function with a singularity of type 1/x.