
Fall 2006
Thematic Program in Cryptography
Cryptography Participants Seminar
Tuesdays 23 p.m., held at the Fields Institute, Room 230

Times and dates of courses will be announced when finalized.
Tuesday,
October 10, 2006
2:00 PM
room 230 
Andreas Stein
Approximating Euler Products and an Algorithm for Computing
the Class Number of an Algebraic Function Field
Abstract:
A fundamental problem in the theory of function fields and curves
over finite fields is the effective computation of the class
number h and thus the order of the Jacobian of an algebraic
function field. If the characteristic of the finite field is
small, various recent algorithms solve this problem. Our main
focus will be algebraic function fields of large characteristic,
in which case not much is known about effective computation
of the order of the Jacobian. However, our methods are very
general for any genus and any characteristic. In our talk, we
will first discuss how to perform arithmetic in an algebraic
function fields based on recent results. Then we will provide
tight estimates for the class number via truncated Euler products,
and show how these estimates can be used to develop an effective
method of computing h. 
Thursday, October 5, 2006
2:00  3:00
Fields Library 
Felix Fontain (University of Zurich)
Computing in Divisor Class Groups of Global Function Fields
Abstract:
In this talk, I will present an algorithm from
Florian Hess to effectively compute RiemannRoch spaces of divisors
in global function fields. Then I will describe a unique representation
of divisor classes and an algorithm to effectively compute in
the divisor class group. 
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