2008-2009

Lenny Fukshansky

**Monday, April 13
Millikan 213
(Pomona College), 3:00 PM**

**Title: **Diophantine
approximation on a circle

Abstract: The original problem of
Diophantine approximation, which goes back to the famous 1842 theorem
of Dirichlet, is that of approximating real numbers by rationals with
controlled denominators. Since that time, various generalizations and
extensions of Dirichlet's theorem have been proved in a number of
different directions. In particular, these include Diophantine
approximation with restricted fractions and simultaneous approximations
for points in Euclidean spaces. We will start with the review of the
classical Dirichlet-type results, and then move into Diophantine
approximations by quotients of Pythagorean triples and make a
connection to rational approximations for points on circles and
ellipses. This talk will be completely accessible to undergraduate
students.