The 2012 Contemporary Combinatorics conference will be held on the 17th and 18th of May at the University of Memphis in Memphis, Tennessee. The Institute of Combinatorics at the University of Memphis will again host the event in honor of Paul Erdos's past work and relationship with the founding members of the Institute. In bringing together a group of accomplished researchers loosely connected to Combinatorics, the PI hopes to continue to extend the rare opportunity to interactively experience the power and richness of mathematical inquiry to the Mid South community and surrounding areas. This region now has access to a high class conference, much like those which are plentiful (and expensive) on the East Coast or the Bay Area on the West Coast. The formula whereby personal contacts between the lecturers and the other participants is greatly encouraged has been very successful will continue to be an important element of the 2012 meeting. This year's conference features three major segments: The foundational lecture about the Paul Erdos and his work, two Paul Erdos Lectures, and a Combinatorics Conference with excellent invited speakers.
The aim of this conference is to bring together a group of outstanding mathematicians who work on topics related to combinatorics, understood in the widest sense. There will be two main speakers: Vaughan Jones and Avi Wigderson. Jones is a distinguished professor of mathematics at Vanderbilt University who is best known for his work on von Neumann algebras, knot polynomials and conformal field theory, in particular, for the 'Jones polynomial' of a knot. He was awarded a Fields Medal in 1990. Jones will give a talk on the connection between combinatorics and knot theory. The second major speaker, Wigderson, is not only an excellent pure mathematician, but also one of the best practitioners of theoretical computer science. Wigderson received the Nevanlinna Prize in 1994 for his work on computational complexity. He will give a lecture on the intimate connection between combinatorics and theoretical computer science. The speakers at this conference have been chosen because they are excellent mathematicians, enjoyable lecturers, and very approachable people. In addition to Jones and Wigderson, the speakers include Maria Chudnovsky, Henry Cohn, Eyal Lubetsky, Alan Frieze, and Jacob Fox. The audience will be composed of people from a variety of backgrounds with varying levels of expertise: postdocs, graduate students to senior level academics, and industry researchers from all over the world.
The Contemporary Combinatorics conference, the fifteenth in the Paul Erd?s Lecture Series, was held at the University of Memphis on May 17-18, 2012 and had 113 participants. Fifty participants received some level of funding and sixty-three did not. The conference had great potential impact and intellectual merit. The general interest talks were highly marketed to talented high school students, teachers and to some industry professionals and were well attended. Ideas presented could potentially be integrated into the teaching of science and into advanced high school and graduate study in math, engineering and computer science. In addition, this conference promoted the broad importance of mathematical study to individuals, organizations and institutions and advanced mathematical study to talented high school students, young researchers and community college students, and to many other communities who might not otherwise get chance to be exposed to research of this caliber. And finally this effort stimulated collaborative energy by bringing together some of the most enjoyable lecturers and accomplished and inventive mathematicians in the world. Graduate students took part in the meeting from a great many places: from the University of Memphis, Rhodes College, Rust College, University of Pittsburgh, Depauw University, University of Maryland-College Park, Southeast Missouri University, Vanderbilt University, Princeton University, University of Virginia, UC Irvine, University of Nebraska - Lincoln, Mississippi State, Western Kentucky University, Emory University, University of Illinois--Urbana, Carnegie Mellon University, Columbia University, McGill University, Harvard University and international universities including University of Cambridge, International Institute of Techn. (India), New University Lisbon, Unif. Fed. de Ceará (Brazil), Ghent University, as well as a number of community colleges around the nation. Also in attendance were industry professionals, from FedEx, for example. The main aim of the conference was to bring some outstanding mathematicians to Memphis, who would not only deliver lectures from a great distance, but would be happy to talk to the participants in informal settings as well. The roster originally included four main speakers, Fields Medalist Vaughan Jones, Nevanlinna Prize Winner Avi Wigderson, Peter Winkler, and technology historian George Dyson. However Avi Wigderson experienced a death in his immediate family during the week of the conference and therefore could not attend. Jones is best known for his work on von Neumann algebras, knot polynomials and conformal field theory, in particular, for the Jones polynomial of knots. Jones gave a very enjoyable talk to a large general audience entitled ``Why Flatland is a Great Place to Do Algebra". The talk was well planned and well received, and intended for those without too much mathematics background. It was enhanced by a good number of colorful, relevant anecdotes and images, and traced the speaker's own mathematical voyage in dimensions. Peter Winkler has done notable research in discrete mathematics and is a patent holder in a broad range of applications, ranging from cryptography to marine navigation. Winkler's general talk of broad interest entitled ``Erd?s and the Magic of Randomness" discussed what Winkler called one of ``Paul Erd?s' greatest contributions … his discovery of the value of randomness even in situations where probability seemed to play no role". It culminated in a discussion of the implications inside and outside of the mathematical realm. A very special treat for the general audience was an enlightening talk given by technology historian George Dyson entitled ``Turing's Cathedral: von Neumann and the Dawn of Computing" based upon his book Turing's Cathedral: The Origins of the Digital Universe which traces the ``history of digital computing" by dividing it into ``an Old Testament whose prophets, led by Leibnitz, supplied the logic, and a New Testament whose prophets, led by von Neumann, built the machines". The combinatorics conference featured a series of specialized talks from some experts in graph theory and combinatorics and other areas: Eyal Lubetsky, Microsoft Research, ``Random Triangle Removal" James Campbell, University of Memphis, ``A General Polynomial Multiple Occurrence Theorem" Peter Winkler, Dartmouth College, ``A Cop and Robber solve the Kakeya Needle problem" Jacob Fox, MIT, ``Two Extensions of Ramsey's Theorem" Paul Balister, University of Memphis, ``Hamiltonicity of the $k$-nearest Neighbor Graph" Alan Frieze, Carnegie Mellon University, ``Some Coloring Problems on Random Graphs" Jacques Verstraete, University of California, San Diego, ``Ramsey numbers for triangles in hypergraphs" Cecil Rousseau, University of Memphis, ``Ramsey Numbers for Convex Paths -- a Tragicomedy" Vaughan Jones, Vanderbilt University and University of California, Berkeley, ``Principal graphs and the Classification of Subfactors of Small Index" Maria Chudnovsky, Columbia University, ``Forcing Large Transitive Subtournaments" Henry Cohn, Microsoft Research, ``The Physics of Error-correcting Codes" In addition, there was a poster session which gave students a chance to share their research with peers and senior scientists and to receive feedback. There were also plenty of opportunities for interaction between speakers and participants, ancillary activities including receptions and parties.
