Moment zeta functions, I

Speaker: 

Professor Daqing Wan

Institution: 

UCI

Time: 

Tuesday, January 9, 2007 - 2:00pm

Location: 

MSTB 254

This will be a series of two introductory lectures on the
distribution of closed points on a scheme of finite type
over the integers. Both general properties and important
examples will be discussed, with an emphasis on p-adic
variation for zeta functions over finite fields.

Brumer's Conjecture for Extensions of Degree 2p

Speaker: 

Barry Smith

Institution: 

UCSD

Time: 

Tuesday, January 30, 2007 - 12:00pm

Location: 

MSTB 254

An explicit expression for the L-function evaluator associated to an abelian extension K/k of number fields of degree 2p will be discussed. Instances will be given where this expression can be used to determine pieces of the ideal class group of K that are annihilated by this L-function evaluator.

Error-correcting codes on low rank surfaces

Speaker: 

Marcos Zarzar

Institution: 

University of Texas

Time: 

Thursday, May 25, 2006 - 3:00pm

Location: 

MSTB 254

Motivated by the construction made by Goppa on curves, we present some error-correcting codes on algebraic surfaces. A surface whose Neron-Severi group has rank 1 has a "nice" intersection property that allows us the construction of a good code. We will verify this on specific examples. Surfaces with many points and rank 1 are not easy to find. We were able, though, to find also surfaces with low rank and many points, and these gave us good codes too. Finally, we present a decoding algorithm for these codes. It is based on the realization of the code as a LDPC code, and it is inspired on the Luby-Mitzenmacher algorithm.

Tame polynomials and exponential sums

Speaker: 

Antonio Rojas-Leon

Institution: 

UCI

Time: 

Thursday, May 11, 2006 - 3:00pm

Location: 

MSTB 254

Given an arbitrary polynomial f in n variables over a finite field k, it is known that for a generic linear form l the exponential sum associated to f(x)+l(x) is pure. However, the proof is non-constructive and gives no explicit description of the set of such l's. In this talk we will give some results and conjectures related to the problem of giving an explicit geometric description of this set.

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