************Intensive Lectures****************
15:00-16:00 in July 10 (Tue)
16:30-17:30 in July 10 (Tue)
15:00-16:00 in July 11 (Wed)
16:30-17:30 in July 11 (Wed)
10:30-11:30 in July 12 (Thur)
PLACE: E6-1, ROOM 4415
SPEAKER: Dawei Chen (Boston College)
TITLE: Moduli of differentials
Abstract:
An Abelian differential defines a flat metric such that the underlying Riemann surface can be realized as a polygon whose edges are pairwise identified via translation. Varying the shape of such polygons induces a GL(2,R)-action on the moduli space of Abelian differentials, called Teichmueller dynamics, whose study has provided fascinating results and opened new avenues to many fields in mathematics. In the first lecture I will give an accessible introduction to this subject, with a focus on its connections to billiard dynamics, enumerative geometry, and arithmetic geometry. In the remaining lectures I will explain how to use techniques in algebraic geometry to study various problems in Teichmueller dynamics, including compactification, birational geometry, cycle class computation, etc. A number of recent developments and open problems will be mentioned.
