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Workshop

Clay Mathematics Institute Introductory Workshop in Algorithmic Number Theory August 14, 2000 - August 23, 2000
Registration Deadline: August 23, 2000 almost 19 years ago
To apply for Funding you must register by: May 14, 2000 over 19 years ago
Parent Program:
Organizers David Bailey, Joe Buhler (chair), Cynthia Dwork, Hendrik Lenstra Jr., Andrew Odlyzko, Bjorn Poonen, William Velez and Noriko Yui
Speaker(s)

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Description
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.
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Funding & Logistics Show All Collapse

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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

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MSRI does not hire an outside company to make hotel reservations for our workshop participants, or share the names and email addresses of our participants with an outside party. If you are contacted by a business that claims to represent MSRI and offers to book a hotel room for you, it is likely a scam. Please do not accept their services.

MSRI has preferred rates at the Hotel Shattuck Plaza, depending on room availability. Guests can call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Institute discount. To book online visit this page (the MSRI rate will automatically be applied).

MSRI has preferred rates at the Graduate Berkeley, depending on room availability. Reservations may be made by calling 510-845-8981. When making reservations, guests must request the MSRI preferred rate. Enter in the Promo Code MSRI123 (this code is not case sensitive).

MSRI has preferred rates at the Berkeley Lab Guest House, depending on room availability. Reservations may be made by calling 510-495-8000 or directly on their website. Select "Affiliated with the Space Sciences Lab, Lawrence Hall of Science or MSRI." When prompted for your UC Contact/Host, please list Chris Marshall (coord@msri.org).

MSRI has a preferred rates at Easton Hall and Gibbs Hall, depending on room availability. Guests can call the Reservations line at 510-204-0732 and ask for the MSRI- Mathematical Science Research Inst. rate. To book online visit this page, select "Request a Reservation" choose the dates you would like to stay and enter the code MSRI (this code is not case sensitive).

Additional lodging options may be found on our short term housing page.

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Schedule, Notes/Handouts & Videos
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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 (Reed College)
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