DIMACS Workshop on Unusual Applications of Number Theory

January 10 - 14, 2000
DIMACS Center, Rutgers University, Piscataway, NJ

Organizing Committee:

Melvyn B. Nathanson, chair, Lehman College (CUNY) and IAS, nathansn@ias.edu

George Andrews, Pennsylvania State University, andrews@math.psu.edu,

David Chudnovsky, Polytechnic University of New York, david@gateway.imas.poly.edu

Ronald L. Graham, AT&T Labs and University of California at San Diego, rgraham@cs.ucsd.edu

Jeffrey C. Lagarias, AT&T Labs, jcl@research.att.com

Victor S. Miller, Institute for Defense Analyses, victor@idaccr.org

Andrew M. Odlyzko, AT&T Labs, amo@research.att.com

Carl Pomerance, Bell Labs, carlp@research.bell-labs.com

Workshop Program:

Monday, January 10

8:30 - 8:50 	Breakfast Registration

8:50 - 9:00     Welcome and greeting
                Fred S. Roberts, Director of DIMACS

9:00 - 9:30     Bahman Kalantari
                New Formulas for Approximation of
                PI and Other Transcendental Numbers

9:40 - 10:30	Bruce Fleischer, IBM
                Hardware Mathematical Facilities of IBM Mainframe Computers


10:30 - 11:00	Coffee

11:00 - 11:50	David and Gregory Chudnovsky, Polytechnic University
                One Bit World

12:00 - 12:30	Sinan Gunturk, Princeton University
                Number Theoretical Error Estimates in a
                Quantization Scheme for Bandlimited Signals

12:30 - 2:00	Lunch

2:00 - 2:50 	John Milnor, State University of New York - Stony Brook
                From Manifolds to Number Theory

3:00 - 3:30	Eric Bach, University of Wisconsin
                P-Adic Secant Algorithms

3:30 - 4:00	Coffee

4:00 - 4:30	Gretchen Ostheimer, Hofstra University
                Practical Algorithms for Infinite Matrix Groups

4:40 - 5:30	David Ingerman, The Institute for Advance Study
                Fermat primes and symmetries of the void

Tuesday, January 11

8:30 - 9:00     Breakfast and Registration

9:00 - 9:40	Audrey Terras, University of California - San Diego
                Finite Quantum Chaos

9:50 - 10:30	Harold Stark, Institute for Advanced Study
                Zeta Functions of Graphs and Coverings

10:30 - 11:00	Coffee

11:00 - 11:30	Siddhartha Sahi, Rutgers University
                Some properties of Askey-Wilson polynomials

11:40 - 12:30	Barry McCoy, SUNY - Stony Brook
                Roger--Ramanujan identities in physics

12:30 - 2:00	Lunch

2:00 - 2:50	George E. Andrews, Pennsylvania State University
                Positivity questions in partitions and the
                Friedman-Joichi-Stanton conjecture

3:00 - 3:30	Jeffrey C. Lagarias, AT&T Labs-Research
                Spectral sets, tilings and exponential polynomials

3:30 - 4:00	Coffee

4:00 - 4:30	Charles Radin, University of Texas
                Relations in SO(3) supported by geodetic angles

4:40 - 5:30	Paula Cohen, CNRS France/IAS
                Non-commutative number theory

6:30 - 8:30	Workshop Banquet at the Holiday Inn in South Plainfield

Wednesday, January 12

8:30 - 9:00     Breakfast and Registration

9:00 - 9:40	Krishnaswami Alladi
                Gollnitz's (Big) theorem, reformulations,
                applications, and extensions

9:50 - 10:30	Alexander Berkovich
                Variations on the Borwein Conjecture

10:30 - 11:00	Coffee

11:00 - 11:30	Carlos Julio Moreno, City University of New York
                The Value of the Gauss Sum

11:40 - 12:30	Jose A. Dias da Silva, University of Lisbon
                Linear Algebra and Additive Theory

12:30 - 2:00	Lunch

2:00 - 2:50	James Lepowsky, Rutgers University
                Vertex operator algebras and the zeta function

3:00 - 3:30	Francis Edward Su, Harvey Mudd College and Cornell University
                Random Walks with Badly Approximable Numbers

3:30 - 4:00	Coffee

4:00 - 4:50	John Friedlander, University of Toronto
                Exponential sums and cryptography

5:00 - 5:30	Sinai Robins, Temple University
		The Linear diophantine problem of Frobenius

Thursday, January 13

8:30 - 9:00     Breakfast and Registration

9:00 - 9:40	Renling Jin, The College of Charleston
                The use of infinite large integers in the
                study of finite integers - The applications of
                nonstandard analysis to upper Banach density problems

9:50 - 10:30	Neil Hindman, Howard University
                Some (usually easy) algebraic proofs of (usually hard)
                results in Ramsey Theory

10:30 - 11:00	Coffee

11:00 - 11:30	Janos Pach, NYU
                The discrete moment curve

11:40 - 12:30	Vitaly Bergelson, Ohio State University
                Polynomial ergodic theorems, Ramsey theory and IP-sets

12:30 - 2:00	Lunch

2:00 - 2:50	Alexander Leibman, Ohio State University
                Ergodic Ramsey Theory and nilpotent groups

3:00 - 3:30	Per Enflo, Kent State University
                On the dynamics of homeomorphisms of n-dimensional manifolds -
                how well can the future be predicted?

3:30 - 4:00	Coffee

4:00 - 4:30	Shuhong Gao, Clemson University
                Decomposition of polytopes and polynomials

4:35 - 5:25	Elon Lindenstrauss, The Institute for Advanced Study
                Some relations between theorems of Freiman and Rusza
                in additive number theory and ergodic theory

5:30 - 6:00     Gregory Frieman, Tel Aviv University
                Applications of the Structure Theory of Set Addition

Friday, January 14

8:30 - 9:00     Breakfast and Registration

9:00 - 9:50	Malcolm Williamson, Center for Communications Research
                Public Key Cryptography: History and Open Questions

10:00 - 10:30	Victor S. Miller, Center for Communications Research
                Elliptic Curves and their use in Cryptography

10:30 - 11:00	Coffee

11:00 - 11:30	Kristin Lauter, Microsoft
                The number of rational points on genus
                3 curves over finite fields

11:40 - 12:30	Joseph Silverman, NTRU Cryptosystems, Inc.
                Lattices, Cryptography, and the NTRU
                Public Key Cryptosystem

12:30 - 2:00	Lunch

2:00 - 2:50	Dorian Goldfeld, Columbia University
                Zeta Functions as One-Way Functions with 
                Applications to Cryptography

3:00 - 3:30	Michael Anshel, CCNY-CUNY
                Constructing Public Key Cryptosystems Via
                Combinatorial Group Theory

3:30 - 4:00	Coffee

4:00 - 4:30	Joshua Brandon Holden, Duke University
                Online Analysis of Algorithms for Computing
                Quadratic Irregularity

4:40 - 5:30	Jeffrey Shallit, University of Waterloo, Canada
                Formal Languages and Number Theory

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