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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 CryptographyCynthia Dwork: Encryption - Part ICynthia Dwork: Interactive Proofs & Zero KnowledgeMoni Naor: Pseudo-Random Functions and PermutationsMoni Naor: Committments and ApplicationsMoni Naor: Good Encryption Schemes

## Number-Theoretic Cryptography Workshop

October 16 - 20, 2000

Gerhard Frey: Discrete logarithm systems based on polynomial ordersJoseph H. Silverman: Lattices and cryptography in theory and practiceUeli Maurer: Index search, discrete logarithms, and Diffie-HellmanAntoine Joux: Tripartite Diffie-Hellman using pairing on elliptic curvesKristin Lauter: Microsoft Research: Genus three curves over finite fieldsNeil Koblitz: Security and efficiency issues in elliptic curve cryptographyMing-deh Huang: Discrete logarithm problems arising from curve based cryptographyJohannes Buchmann: Identification and signatures based on class groupsMichael Anshel: The Arithmetica Key exchangeDon Coppersmith: Solving low-degree polynomialsGlenn Durfee: Cryptanalysis of RSA using lattice-based root finding techniquesPhong Nguyen: The orthogonal lattice and its applications to cryptanalysisArjen Lenstra: The XTR public key systemDan Bernstein: Design and implementation of a public-key signature systemDaniele Micciancio: Improving lattice based cryptosystems using the Hermite Normal FormMoni 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

MSRI: Spring 2000## Non-Workshop Lectures

Lectures from Other Organizations: 2002 - 2003

Lectures from Other Organizations: 2000 - 2001

Lectures from Other Organizations: 1998 - 1999

Lectures from Other Organizations: 1996 - 97

Lectures for the General Public