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Clay Mathematics Institute Introductory Workshop in Algorithmic Number Theory
Aug 14, 2000 to Aug 23, 2000

Organizer(s)

David Bailey, Joe Buhler (chair), Cynthia Dwork, Hendrik Lenstra Jr., Andrew Odlyzko, Bjorn Poonen, William Velez and Noriko Yui
To apply for funding, you must register by Wed, Aug 23 2000.
This workshop will have lecture series covering the basic areas of algorithmic number theory,
aimed at graduate students and mathematicians without extensive experience in the field.

The topics covered will include:

Basic Number Theoretic Algorithms
Primality and Factorization
Computations in Algebraic Number Fields
Elliptic Curves
Cryptography
Lattice Basis Reduction
Analytic Number Theory Algorithms

A related event follows on the UC Berkeley campus: a 3-day conference in honor of the Lehmers;
see http://www.math.berkeley.edu/lehmer.html for information.

Funding

To apply for funding, you must register by Wed, Aug 23 2000. Click to Register
Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are made typically 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.
Schedule
Monday, August 14, 2000
10:00AM Hendrik Lenstra Solving Pell's Equation
11:00AM Dan Bernstein Fast Multiplication
2:00PM Stan Wagon Computational Number Theory: Basic Algorithms
3:30PM Jeffrey Shallit The greatest common divisor
Tuesday, August 15, 2000
9:30AM Carl Pomerance Smooth numbers and the quadratic sieve
11:00AM Dan Bernstein Applications of fast multiplication
2:00PM Bjorn Poonen Elliptic Curves I
3:30PM Stan Wagon Computational number theory: Subtler basic algorithms
Wednesday, August 16, 2000
9:30AM Peter Stevenhagen The number field sieve
11:00AM Dan Boneh RSA: Past, present, and future
2:00PM Carl Pomerance Primality
3:30PM Hendrik Lenstra Lattices I
Thursday, August 17, 2000
9:00AM Jeffrey Shallit Algorithmic number theory before computers
Friday, August 18, 2000
9:30AM Hendrik Lenstra Lattices II
11:00AM Andrew Odlyzko Lattice basis reduction algorithms in cryptanalysis
2:00PM Cynthia Dwork Positive applications of lattices to cryptography
3:30PM Dan Bernstein Protecting communications against forgery
Monday, August 21, 2000
9:30AM Umesh Vazirani Quantum Computation
11:00AM Number Fields
2:00PM Bjorn Poonen Elliptic Curves II
3:30PM Daqing Wan Zeta functions over finite fields
Tuesday, August 22, 2000
9:30AM Andrew Granville Counting smooths: A practical guide
11:00AM William Stein How to get your hands on modular forms using modular symbols
1:00PM Christina Ballentine Infrastructure
2:15PM Bjorn Poonen Elliptic curves III
Wednesday, August 23, 2000
9:30AM Andrew Granville Smooths for smoothness' sake
11:00AM Joe Buhler L-series in algorithmic number theory
2:00PM Noriko Yui Congruent number problems in dimension one and two
3:30PM Henri Cohen Algorithmic class field theory
Parent Program(s):
Algorithmic Number Theory


Questions about this workshop should be sent either by email to
or by regular mail to:
Clay Mathematics Institute Introductory Workshop in Algorithmic Number Theory
Mathematical Sciences Research Institute
17 Gauss Way, Berkeley, CA
94720-5070.
USA

The Institute is committed to the principles of Equal Opportunity and Affirmative Action.



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