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*Sponsored by the SIAM Activity Group on Discrete Mathematics
(SIAG/DM)*

Discrete mathematics is a branch of the mathematical sciences, with a wide range of challenging research problems and important applications in industry. Discrete mathematics has applications to all fields of computer science, and to the physical and biological sciences. It is used extensively in telecommunications, information processing and manufacturing, and many businesses and industries use techniques of discrete optimization to improve the efficiency of their operations.

Discrete mathematics is a dynamic field in both theory and applications. Researchers in discrete mathematics have established important connections with mainstream areas of pure and applied mathematics, and as a consequence, research techniques and problems are drawn from a wide range of different fields, including algebra, topology, geometry, probability, analysis, and logic.

The purpose of this conference is to highlight the major theoretical advances in the field, the development of new tools for discrete mathematics, and the most significant of the new applications of discrete mathematics to problems arising in industry and business. The conference also seeks to bring together participants from the many different environments where discrete mathematics is developed and applied.

- Combinatorics
- Graph theory and matroids
- Combinatorial algorithms
- Coding theory and cryptology
- Ordered sets

and its connections to other disciplines, including:

- Computer science
- Computational biology
- Optimization
- Geometry
- Topology

Mark Ellingham (chair),

Vanderbilt University

Rob Calderbank,AT&T Labs - Research

William Cook,Georgia Institute of Technology

Jim Haglund,University of Pennsylvania

Penny Haxell,University of Waterloo, Canada

Monika Henzinger,Google, Inc

Rolf Möhring,Technische Universität, Berlin, Germany

Ron Shamir,Tel Aviv University, Israel

William T. Trotter,Georgia Institute of Technology

Douglas B. West,University of Illinois

with input from officers of the **SIAG/DM**:

Derek Corneil,

University of Toronto,Canada

Nathaniel Dean,Texas Southern University

Gary MacGillivray,University of Victoria, Canada

What Makes a Finite Network High-Dimensional:
Random Graph Scaling for Finite Graphs

Jennifer Chayes, *Microsoft Research*

Transportation and Integer Programming

Martin Grötschel, *Konrad-Zuse-Zentrum für Informationstechnik
Berlin (ZIB), DFG-Forschungszentrum "Mathematik für Schlüsseltechnologien,"
and Technische Universität Berlin, Germany *

Complex Networks, Search Algorithms, and
the Evolution of the Web

Jon Kleinberg, *Cornell University*

Internet Vulnerabilities: A Look at Some Problems and Possible Solutions

Tom Leighton, *Massachusetts Institute of Technology and Akamai Technologies,
Inc. *

The Structure of Claw-Free Graphs

Paul Seymour, *Princeton University*

Tropical Geometry and Its Applications

Bernd Sturmfels,* University of California, Berkeley*

Old Problems and New Results in Coding Theory

Alexander Vardy, *University of California, San Diego*

A Word Count Statistic in Computational Biology

Michael Waterman*, University of Southern California *

SIAM and the conference organizing committee wish to extend their thanks and appreciation to the National Science Foundation for their support of this conference.

SIAM acknowledges the support provided by Vanderbilt University. In particular, SIAM thanks the Department of Mathematics for hosting the Sunday night reception, the Microcomputer Laboratories of the College of Arts and Science for providing email access, and the Science and Engineering Library for providing library facilities.

Mike Albertson

**Graph Colorings **

Alexander Barg

**Geometric and Combinatorial Methods in Coding Theory**

Anne Bergeron

**Genome Rearrangements**

Tom Bohman and Benny Sudakov

**Probabilistic Combinatorics**

Andreas Brandstädt

**Clique-width of Graph Classes: Properties, Related Concepts, Applications**

Francesco Brenti and Greg Warrington

**Combinatorics of Kazhdan-Lusztig Polynomials, Schubert Varieties and
Lie Algebras**

Guantao Chen and Xingxing Yu

**Cycles and Paths in Graphs, I and II**

Eddie Cheng

**Stable Sets and Stable Multisets**

Fan Chung

**Title TBA**

Jeff Erickson

**Computational Geometry**

Luis Goddyn and C.Q. Zhang

**Flows and Colorings**

James Haglund, Jennifer Morse and Jeffrey Remmel

**Macdonald Polynomials and the Combinatorics of Diagonal Harmonics,
I and II**

Sorin Istrail

**SNPs, Haplotypes, and Disease Associations**

Andre Kündgen and Dhruv Mubayi

**Extremal Combinatorics**

Gary MacGillivray

**Graph Homomorphisms**

John Maharry

**Graph Minors**

Lucia Moura and Brett Stevens

**Design Theory**

James Oxley

**Matroid Theory**

Frank Ruskey

**Sequencing of Combinatorial Objects **

László Székely and Farhad Shahrokhi

**Discrete Geometry, I and II**

William T. Trotter

**Ordered Sets**