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Schedule, Notes/Handouts & Videos

Clay Mathematics Institute Introductory Workshop in Algorithmic Number Theory August 14, 2000 - August 23, 2000

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Aug 14, 2000
Monday
08:00 AM - 05:00 PM
  The complexity of Euclid's GCD algorithm
Jeffrey Shallit
08:00 AM - 05:00 PM
  Smooth numbers I
Andrew Granville (Université de Montréal)
08:00 AM - 05:00 PM
  Number field algorithms
Rene Schoof
08:00 AM - 05:00 PM
  Smooth numbers II
Andrew Granville (Université de Montréal)
08:00 AM - 05:00 PM
  Computational class field theory
Henri Cohen
10:00 AM - 11:00 AM
  Solving Pell's Equation
Hendrik Lenstra (Universiteit Leiden)
11:00 AM - 02:00 PM
  Fast Multiplication
Dan Bernstein
02:00 PM - 03:30 PM
  Computational Number Theory: Basic Algorithms
Stan Wagon
03:30 PM - 04:30 PM
  The greatest common divisor
Jeffrey Shallit
Aug 15, 2000
Tuesday
09:30 AM - 11:00 AM
  Smooth numbers and the quadratic sieve
Carl Pomerance (Dartmouth College)
11:00 AM - 02:00 PM
  Applications of fast multiplication
Dan Bernstein
02:00 PM - 03:30 PM
  Elliptic Curves I
Bjorn Poonen (Massachusetts Institute of Technology)
03:30 PM - 04:30 PM
  Computational number theory: Subtler basic algorithms
Stan Wagon
Aug 16, 2000
Wednesday
09:30 AM - 11:00 AM
  The number field sieve
Peter Stevenhagen
11:00 AM - 02:00 PM
  RSA: Past, present, and future
Dan Boneh (Stanford University)
02:00 PM - 03:30 PM
  Primality
Carl Pomerance (Dartmouth College)
03:30 PM - 04:30 PM
  Lattices I
Hendrik Lenstra (Universiteit Leiden)
Aug 17, 2000
Thursday
09:00 AM - 10:00 AM
  Algorithmic number theory before computers
Jeffrey Shallit
Aug 18, 2000
Friday
09:30 AM - 11:00 AM
  Lattices II
Hendrik Lenstra (Universiteit Leiden)
11:00 AM - 02:00 PM
  Lattice basis reduction algorithms in cryptanalysis
Andrew Odlyzko (University of Minnesota)
02:00 PM - 03:30 PM
  Positive applications of lattices to cryptography
Cynthia Dwork
03:30 PM - 04:30 PM
  Protecting communications against forgery
Dan Bernstein
Aug 21, 2000
Monday
09:30 AM - 11:00 AM
  Quantum Computation
Umesh Vazirani (University of California, Berkeley)
11:00 AM - 02:00 PM
  Number Fields
02:00 PM - 03:30 PM
  Elliptic Curves II
Bjorn Poonen (Massachusetts Institute of Technology)
03:30 PM - 04:30 PM
  Zeta functions over finite fields
Daqing Wan
Aug 22, 2000
Tuesday
09:30 AM - 11:00 AM
  Counting smooths: A practical guide
Andrew Granville (Université de Montréal)
11:00 AM - 01:00 PM
  How to get your hands on modular forms using modular symbols
William Stein (University of Washington)
01:00 PM - 02:15 PM
  Infrastructure
Christina Ballentine
02:15 PM - 03:15 PM
  Elliptic curves III
Bjorn Poonen (Massachusetts Institute of Technology)
Aug 23, 2000
Wednesday
09:30 AM - 11:00 AM
  Smooths for smoothness' sake
Andrew Granville (Université de Montréal)
11:00 AM - 02:00 PM
  L-series in algorithmic number theory
Joe Buhler (University of Minnesota)
02:00 PM - 03:30 PM
  Congruent number problems in dimension one and two
Noriko Yui (Queen's University)
03:30 PM - 04:30 PM
  Algorithmic class field theory
Henri Cohen
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