Future directions in algorithmic number theory
March 24 to March 28, 2003
American Institute of Mathematics,
Palo Alto, California
and Jonathan Pila
This workshop is occasioned by the breakthrough result of
Agrawal, Kayal and Saxena devising an unconditional, deterministic,
polynomial-time algorithm for distinguishing prime numbers from
composite numbers. The solution of one of the basic problems in
the discipline ushers in a new era. The main objective of the workshop
is to consolidate the breakthrough and explore ramifications for other
fundamental algorithmic problems in number theory and finite fields.
In addition the workshop will look to the future of the subject and
chart directions in which developments might occur.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
A list of open problems.
Agrawal: Primality Testing
Agrawal: Finding Quadratic Nonresidues
Bernstein: Proving Primality After Agrawal-Kayal-Saxena
Edixhoven: Point Counting
Gao: Factoring Polynomials under GRH
Kedlaya: Counting Points using p-adic Cohomology
Lauder: Counting Points over Finite Fields
Lenstra: Primality Testing with Pseudofields
Pomerance and Bleichenbacher: Constructing Finite Fields
Silverberg: Applications of Algebraic Tori to Crytography
Stein: Modular Forms Database
Voloch: Multiplicative Subgroups of a Finite Field
Wan: Partial Counting of Rational Points over Finite Fields
Remarks on Agrawal's Conjecture