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

Hendrik Lenstra: Solving Pell's Equation
Dan Bernstein: Fast multiplication
Stan Wagon: Computational Number Theory: Basic Algorithms
Jeffrey Shallit: The complexity of Euclid's GCD algorithm
Carl Pomerance: Smooth numbers and the quadratic sieve
Dan Bernstein: Applications of fast multiplication
Bjorn Poonen: Elliptic Curves I
Stan Wagon: Computational number theory: Subtler basic algorithms
Peter Stevenhagen: Number field sieve
Carl Pomerance: Primality
Hendrik Lenstra: Lattices I
Jeffrey Shallit: Algorithmic Number Theory Before Computers
Hendrik Lenstra: Lattices II
Andrew Odlyzko: Lattice basis reduction algorithms in cryptanalysis
Dan Bernstein: Protecting communications against forgery
Umesh Vazirani Quantum Computation
Rene Schoof Infrastructure
Bjorn Poonen Elliptic Curves II
Daqing Wan Zeta Functions over Finite Fields
Andrew Granville: Smooth numbers I
Joe Buhler: L-series in algorithmic number theory
William Stein: How to get your hands on modular forms using modular symbols
Rene Schoof: Number field algorithms
Bjorn Poonen: Elliptic curves III
Andrew Granville: Smooth numbers II
Noriko Yui: Congruent number problems in dimension one and two
Henri Cohen: Computational class field theory

Clay Mathematics Institute Introductory Workshop in Operator Algebras
August 24 - September 2, 2000

Dietmar Bisch Subfactors and Planar Algebras 1
Dietmar Bisch Subfactors and Planar Algebras 2
Dietmar Bisch Subfactors and Planar Algebras 3
Richard Kadison The Theory of Operator Algebras - A Survey 1
Richard Kadison The Theory of Operator Algebras - A Survey 2
Richard Kadison The Theory of Operator Algebras - A Survey 3
Richard Kadison The Theory of Operator Algebras - A Survey 4
Richard Kadison The Theory of Operator Algebras - A Survey 5
Richard Kadison The Theory of Operator Algebras - A Survey 6
Richard Kadison The Theory of Operator Algebras - A Survey 7
Richard Kadison The Theory of Operator Algebras - A Survey 8
Richard Kadison The Theory of Operator Algebras - A Survey 9
Richard Kadison The Theory of Operator Algebras - A Survey 10
Michael Pimsner Introduction to K-theory for Operator Algebras 1
Michael Pimsner Introduction to K-theory for Operator Algebras 2
Michael Pimsner Introduction to K-theory for Operator Algebras 3
Michael Pimsner Introduction to K-theory for Operator Algebras 4
Michael Pimsner Introduction to K-theory for Operator Algebras 5
Michael Pimsner Introduction to K-theory for Operator Algebras 6
Michael Pimsner Introduction to K-theory for Operator Algebras 7
Michael Pimsner Introduction to K-theory for Operator Algebras 8
Marc Rieffel Non-commutative geometry 1
Marc Rieffel Non-commutative geometry 2
Marc Rieffel Non-commutative geometry 3
Thomas Schucker The standard model of gravitational, electro-magnetic, weak and strong forces
Thomas Schucker The almost commutative version of the standard model
Dimitri Shlyakhtenko Introduction to Free Probability Theory 1
Dimitri Shlyakhtenko Introduction to Free Probability Theory 2
Dimitri Shlyakhtenko Introduction to Free Probability Theory 3
Antony Wassermann/Valerio Toledano Laredo Operator Algebras and Conformal Field Theory 1
Antony Wassermann/Valerio Toledano Laredo Operator Algebras and Conformal Field Theory 2
Antony Wassermann/Valerio Toledano Laredo Operator Algebras and Conformal Field Theory 3
Antony Wassermann/Valerio Toledano Laredo Operator Algebras and Conformal Field Theory 4
Antony Wassermann/Valerio Toledano Laredo Operator Algebras and Conformal Field Theory 5
Antony Wassermann/Valerio Toledano Laredo Operator Algebras and Conformal Field Theory 6
Antony Wassermann/Valerio Toledano Laredo Operator Algebras and Conformal Field Theory 7
Antony Wassermann/Valerio Toledano Laredo Operator Algebras and Conformal Field Theory 8
Antony Wassermann/Valerio Toledano Laredo Operator Algebras and Conformal Field Theory 9
Antony Wassermann/Valerio Toledano Laredo Operator Algebras and Conformal Field Theory 10
Antony Wassermann/Valerio Toledano Laredo Operator Algebras and Conformal Field Theory 11

The Panorama Of Mathematics, A conference in honor of S. S. Chern
September 14-16, 2000

Robert Bryant,On the Geometry of Differential Equations
Jeremy Gray, A Hundred Years of the Hilbert Problems
Phillip Griffiths, Abel's Differential Equations
Isadore Singer, Hermitian Line Bundles in String Theory and M Theory
Leonard Adleman, DNA Computation
Richard Karp, Mathematical Challenges from Genomics and Molecular Biology

Simple C*-algebras and Non-commutative Dynamical Systems
September 25, 2000 to September 29,2000

Robert T. Powers New results concerning semigroups of *-endomorphisms of B(H)
Ian Putnam The Lefschetz formula for hyperbolic dynamical systems and non-commutative topology
George Elliott A brief survey of progress on the classification problem for amenable C*-algebras
Mikael Rordam A characterization of the nuclear, separable C*-algebras that absorb the Cuntz algebra O'
Thierry Giordano Some extremely amenable groups
Claudia Pinzari Noncommutative pressure and the variational principle for Cuntz-Krieger-type C*-algebras
Jean Bellissard The gap labelling theorem for aperiodic media
Erling Stormer The variational principle for a class of asymptotically abelian C*-algebras
Kenneth J. Dykema Simple C*-algebras arising as free products
Guihua Gong On the classification of simple inductive limit C*-algebras
Peter Friis The Brown-Douglas-Fillmore Theorem revisited
Palle Jorgensen Decidability of isomorphism for ordered simple dimension groups
Joachim Zacharias Entropy and quasi-free C*-dynamics for Cuntz-Pimsner algebras
Etienne Blanchard Purely infinite C*-algebras: The Hausdorff case
Nathanial Brown Topological entropy of free product automorphisms
Jean N. Renault Singly generated dynamical systems and their C*-algebras
Ola Bratteli The infinite distance between AF flows and flows allowing continuous symmetry breaking
Huaxin Lin Simple C*-algebras with tracial topological rank zero
Anatoly Vershik Constructions of factor representations for some locally finite groups
Masamichi Takesaki Characteristic square, extended modular automorphisms and grading
William Arveson Interactions in non-commutative dynamics
Simon Wassermann Tensor products of reduced free product algebras
Marcelo Laca A C*-algebraic dynamical system from number theory
Marius Dadarlat Embeddings of exact C*-algebras
Jesper Villadsen Comparison of projections and unitary elements in simple C*-algebras
Shaloub Razak Classification of simple stably projectionless C*-algebras
Eberhard Kirchberg The passage to non-simple algebras
Claire Anatharaman-Delaroche Exact groupoids
Klaus Thomsen A second order pairing between K-theory and traces
Boris Tsirelson New examples of product systems
Dan Kucerovsky Weyl-von Neumann theorems: An abstract approach
Marie Choda Dynamical completely positive approximation entropy of exact C*-algebras
Serban Stratila The commutation theorem for tensor products over subalgebras
Andrew Dean An invariant for actions of the reals on a UHF algebra
Dimitri Shlyakhtenko Cuntz-Pimsner C*-algebras and reduced amalgamated free products
Cornel Pasnicu Tensor products of C*-algebras with the ideal property
Sergey Neshveyev Comparing entropy of a system and its subsystem
Soren Eilers Invariants for C*-algebras with one/two/many ideals
Bruce Blackadar Scaling elements revisited
Ruy Exel KMS states on Cuntz-Krieger algebras over infinite matrices

Short Course on Foundations of Cryptography
October 14 - 15, 2000

Cynthia Dwork: Foundations of Cryptography
Cynthia Dwork: Encryption - Part I
Cynthia Dwork: Interactive Proofs & Zero Knowledge
Moni Naor: Pseudo-Random Functions and Permutations
Moni Naor: Committments and Applications
Moni Naor: Good Encryption Schemes

Number-Theoretic Cryptography Workshop
October 16 - 20, 2000

Gerhard Frey: Discrete logarithm systems based on polynomial orders
Joseph H. Silverman: Lattices and cryptography in theory and practice
Ueli Maurer: Index search, discrete logarithms, and Diffie-Hellman
Antoine Joux: Tripartite Diffie-Hellman using pairing on elliptic curves
Kristin Lauter: Microsoft Research: Genus three curves over finite fields
Neil Koblitz: Security and efficiency issues in elliptic curve cryptography
Ming-deh Huang: Discrete logarithm problems arising from curve based cryptography
Johannes Buchmann: Identification and signatures based on class groups
Michael Anshel: The Arithmetica Key exchange
Don Coppersmith: Solving low-degree polynomials
Glenn Durfee: Cryptanalysis of RSA using lattice-based root finding techniques
Phong Nguyen: The orthogonal lattice and its applications to cryptanalysis
Arjen Lenstra: The XTR public key system
Dan Bernstein: Design and implementation of a public-key signature system
Daniele Micciancio: Improving lattice based cryptosystems using the Hermite Normal Form
Moni Naor: What is a proper cryptographic assumption, or The complexity of refutation

Special Event: October 19, 2000

Anthony E. Sale: Code Breaking in WW II: The Enigma: the Colossus, and Bletchley Park

Emerging Applications of Combinatorial Design
November 5 - 10, 2000

Jeff Dinitz: Scheduling tournaments and leagues

Charles Colbourn: Applications of combinatorial designs in communications and networking

Ronald C. Mullin: A survey of packing and covering designs

Sid Dalal: Factor-covering designs for testing software

Malcolm Greig: Constructing Large Designs

Art Owen: Combinatorial problems arising in high dimensional integration and approximation

Benno Schwikowski: Small and beautiful: Designing DNA sequences for molecular recognition

William Martin: Combinatorics of the ordered Hamming space

Qing Xiang: Recent results on difference sets with classical parameters

Myra Cohen: Ladder orderings for double erasure codes

Lucia Moura: The integer programming approach for generating designs

Peter Gibbons: Computational methods for combinatorial design construction

Vladimir Tonchev: Applications of combinatorial designs in digital communication

Frank Hwang: Using combinatorial designs in the construciton of pool designs for clone screening

Mark Lawrence: The need for speed: Combinatorial implications of an important application of Monte Carlo methods in financial risk management

Toby Berger: Sharp asymptotic bounds on two-stage group testing efficiency

Julie Ward: Designing storage area network fabrics

Martin Tompa: Quality control in manufacturing DNA arrays: A combinatorial design approach

Alan Ling: Some applications of combinatorial designs to extremal graph theory

David Torney: Biologically motivated design problems

Helen Verrall: Hamilton decompositions of directed wrapped butterfly graphs

Tran Van Trung: Selected applications of combinatorial designs

Jonathan Jedwab: Two applications of combinatorial design theory

Subfactors and Algebraic Aspects of Quantum Field Theory
December 4 - 8, 2000

Sergio Doplicher: Aspects of duality

Roberto Longo: Completely Rational Conformal Quantum Field Theory

Michael Mueger: Completely rational CQFTs, local extensions and modular invariants

Marta-T Asaeda: Exotic subfactor and the spindle algebra

Dmitri Nikshych: Bimodule categories of subfactors and representation theory of quantum groupoids

Michel Enock: Inclusions of von Neumann algebras, and quantum groupoids

Sorin Popa (at Evans Hall, Room 60): Universal constructions and functoriality in the theory of subfactors

Adrian Ocneanu: Higher Coxeter systems

Antony Wassermann: Quantum subgroups and vertex algebras

Valerio Toledano Laredo: Connes fusion and KZ equations

Michael Freedman: Anyons in mathematics, computer science and physics

Zhenghan Wang: On TQFT representations of mapping class groups

Richard Borcherds: Vertex algebras are trivial

Dror Bar-Natan: Finite type invariants and a strange breed of planar algebras

Ruth Lawrence: Almost modularity of quantum 3-manifold invariants

Dylan Thurston: Hyperbolic Volume and the Jones Polynomial: A Conjecture

Dirk Kreimer: Combinatorics of quantum field theory

Zeph Landau: Exchange relations planar algebras

Feng Xu: Algebraic coset conformal field theories

Vaughan Jones: E_6 is a breeze, E_8's a tease

Dietmar Bisch: Singly generated planar algebras of small dimension

V.S. Sunder: Spectra of principal graphs

Nobuya Sato: Two approaches in 3-dimensional topological quantum field theories from subfactors

Peter Goddard: An axiomatic approach to conformal field theory

Uffe Haagerup: Old and new results on spin models

Akihiro Tsuchiya: Seiberg-Witten differentials as periods of rational elliptic surfaces

Vijay Kodiyalam: Paragroups and Hopf algebras

Masaki Izumi: Non commutative Poisson boundaries and compact quantum group actions

David Evans: Modular invariants from subfactors

Yasuyuki Kawahigashi: Braiding and extension of endomorphisms of subfactors

Hans Wenzl: Braid groups and subfactors

Rosa Orellana: Finite dimensional representations of the braid group of type B and Markov traces

Yoshimichi Ueda: Minimal actions of compact quantum groups and subfactors

Dimitri Shlyakhtenko: Some applications of free probability to subfactor theory

Edward Frenkel: Vertex algebras and the geometric Langlands correspondence

Arithmetic Geometry
December 11 - 15, 2000

Armand Brumer: Odds and ends on curves of low genus

Joseph Wetherell: Chabauty and covers for curves with an automorphism

Michael Stoll: Uniform Chabauty bounds for twists

Alexandra Shlapentokh: Diophantine undecidability of function fields of positive characteristic finitely generated over fields algebraic over a finite field

Greg Anderson: Wick's theorem and the calculation of genus one Jacobians

John Cremona: Reduction of binary forms

Tom Fisher: Descent calculations for the elliptic curves of conductor 11

Catherine O'Neil: The period-index problem

Franz Lemmermeyer: Second 2-descents for y^2 = x^3 - d^2 x

Sylvain Duquesne: Explicit Weierstrass Preparation Theorem in several variables and rational points on the hyperelliptic curve y^2=x^9 - 6x^8 + 31x^7 - 81x^6 + 177x^5 - 176x^4 - 9x^3 + 107x^2 + 19x + 1

Henri Darmon: The calculation of periods on $H_ptimes H$ and Heegner points attached to real quadratic fields: a progress report
Takakazu Satoh: Algorithms for computing zeta functions of elliptic curves over finite fields and related topics.

Fernando Rodriguez-Villegas: Picard-Fuchs equations and computing zeta functions p-adically

Florian Hess: On the computation of the divisor class group of global function fields

Vinay Deolalikar: On splitting rational places in algebraic extensions of function fields over finite fields

Nils Bruin: Explicit covering techniques

Leopoldo Kulesz: Algebraic curves of genus at least 2 with many rational points

Tony Shaska: Curves of genus two covering elliptic curves

William Stein: Visibility of Shafarevich-Tate groups of abelian varieties

Bas Edixhoven: On computing coefficients of eigenforms.

Helena Verrill: Computation of periods of higher weight modular forms

David Kohel: Shimura curve invariants

Ki-ichiro Hashimoto: Q-curves over quadratic fields and jacobian surfaces of GL2-type

Jordan Ellenberg: Ljunggren's equation and modular Q-curves

Joan-C. Lario: Manin ideals for Q-curves

Enrique Gonzalez Jimenez: Modular curves of genus 2

Qing Liu: Rational points of the group of components of a Neron model.

Dino Lorenzini: Special fibers of Neron models

Rania Wazir: A Nagao-type formula for elliptic threefolds

Fabrizio Andreatta: Uniformization of Neron models of semistable Jacobians

Luis V. Dieulefait: Images of three-dimensional Galois representations

Victor Rotger: On the group of automorphisms of Shimura curves and applications

Tom Tucker: Thue equations and the method of Chabauty-Coleman

Charles Doran: From K3 lattices to explicit K3 moduli

Non-Workshop Lectures

Jim Holt: What Trivial Beings Talk About When They Talk About Math
Donald G. Saari: Using chaos and symmetry groups to analyze election and decision procedures
Donald G. Saari: Why Voting Procedures Can Create a Mess; A Mathematician Looks at Elections

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