2008-2009

Maria Pavlvoskaia

**Monday, December 1
Millikan 213
(Pomona College), 3:00 PM**

**Title: **The geometry of
continued fractions

Abstract: Lagrange's theorem states that a continued fraction is periodic if and only if it is the root of a quadratic polynomial. The geometric interpretation of this fact is related to the action of SL(2,Z) operators on integral lattices. I researched the geometric characteristics of continued fractions related to these operators. I'll talk about the geometric interpretation of continued fractions, some general results in the field, present some open problems and the results of my research.