Mathematics Graduate Student Colloquium

MGSC Website: http://math.uci.edu/~mgsc/

Newton Polygons of Zeta Functions

Phong Le
Wednesday, April 18, 2007
4:00 pm - 4:50 pm
MSTB 114

Talk Abstract:

Given a set of polynomial equations over a finite field, one may construct an associated zeta function and its L function. Both of these functions are known to be rational, i.e., they are the quotient of polynomials. The L function carries deep number theoretical information about the solutions of the set of equations. This information is geometrically presented in the Newton polygon and an associated polygon, the Hodge polygon. We present the basic objects and tools used to determine when the Newton polygon coincides with the Hodge polygon and what this means number theoretically. We close with some current applications to mirror symmetry.

About the Speaker:

Phong is a fourth year graduate student at UCI. He received his B.A. in mathematics from Goucher College (Baltimore, Maryland) in 2003. His current research involves mirror symmetry and zeta functions. In his free time he likes to cook and play Tetris.

Refreshments:

Pizza will be served after the talk.