This conference will bring together a group of outstanding mathematicians who work on topics loosely related to combinatorics, understood in the widest sense. The meeting will give a chance to mathematicians from the Mid-South to benefit not only from the lectures but also from personal contacts with the speakers. This is bound to be very inspiring for all the participants, especially for those who otherwise do not do not have a chance to come into close contact with some of today's the leading mathematicians. The main speaker at the conference is Gregory Margulis of Yale University, who has done much brilliant work in combinatorics, differential geometry, ergodic theory, dynamical systems and discrete subgroups of Lie groups. For his great contributions to mathematics he was awarded a Fields Medal in 1978, and a Wolf Prize in 2005. There will be several other excellent mathematicians and speakers at the meeting; they have been chosen because they are not only powerful research mathematicians, but also wonderful expositors and very approachable people. Among other speakers, we shall have Alexander Barvinok of University of Michigan, who has proved outstanding results about distance geometry, convexity and algorithms related to them; Ralph Faudree, one of the most frequent collaborators of the late Paul Erdos, who has done much work on Ramsey theory and extremal graph theory; Oliver Riordan of the University of Oxford, one of the most brilliant combinatorialists in the world, who has contributed to many areas, most recently to the theory of convergent sequences of sparse graphs; Laszlo Szekely of the University of South Carolina, who is well known for his very elegant contributions to discrete geometry; Slava Krushkal of the Unversity of Virginia, who has done outstanding work on polynomials of surfaces related to the Tutte polynomial; Tsz Ho Chan of the University of Memphis, the young analytic number theorist, who has worked on pair correlation of the zeros of the Riemann zeta function, diophantine approximation and the distribution of primes, Andras Gyarfas of the Computer and Automation Institute in Budapest, the prolific combinatorialist, who has done much work on applications of Szemeredi's Lemma, and Jean-Paul Thouvenot, a Director at CNRS in Paris, one of the foremost people working on ergodic theory and dynamical systems.
Two of the lectures will be aimed at a general audience, including good high school students. In the first lecture, Ralph Faudree will not only introduce the audience to the immense contributions Paul Erdos made to mathematics, but will also paint a personal picture of Erdos, one of the most colourful mathematicians of the 20th century. In the second lecture Gregory Margulis will attempt to bring difficult mathematical ideas concerning geometry within reach of the audience. Unlike the East Coast or the Bay Area on the West Coast, the Mid-South cannot boast of many high-level mathematical conferences; the Contemporary Combinatorics 2010 meeting in Memphis goes some way towards redressing the balance. The formula whereby personal contacts between the lecturers and the other participants is greatly encouraged has been found very successful so far, so this is what we are planning for this year as well. There is no doubt that listening to lectures by Gregory Margulis, Alexander Barvinok, Oliver Riordan and others, and, especially, talking to them during the conference will be very inspiring for young and established mathematicians alike.
The Contemporary Combinatorics conference, the thirteenth in the Paul Erd?s Lecture Series, was held in Memphis on March 19--20, 2010. The Institute of Combinatorics within the Department of Mathematical Sciences at the University of Memphis presents the Lecture Series each year in honor of the past relationship of its founding members with the world famous mathematician Paul Erd?s. The event was comprised of three major segments - the 2010 Erd?s Lecture, the foundational/historical talk about the life and significance of Erd?s, and the Combinatorics Conference which consists of a series of specialized talks highlighting recent advances, ideas and research which draws from or builds upon the work of Erd?s. Overall, the conference was a great success, a wonderful moment in the history and culture of mathematics. The conference had eighty-three total registered participants. Graduate students and researchers came from a great many places including University of Portugal, Florida Atlantic University, University of Memphis, Mississippi State, Western Kentucky University, Emory University, University of Illinois--Urbana, University of Chicago and Carnegie Mellon University, as well as a number of community colleges around the nation. A few undergraduates also attended, some from the University of Memphis and others who accompanied graduate students from other colleges. 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. Gregory Margulis, who is not only a Fields Medalist but also a Wolf Prize Winner, delivered the 2010 Erd?s Lecture highlighting the interaction between number theory and homogeneous dynamics in his talk entitled ``Homogenous dynamics and number theory". This ``public" talk was aimed at a rather general audience. In addition to Erd?s Lecture, there were nine other inspiring lectures delivered by excellent mathematicians: Alexander Barvinok, University of Michigan, ``Gaussian and almost Gaussian formulas for the number of integer points in polyhedra" Tsz Ho Chan, University of Memphis, ``On sequences of integers none of which divides the product of $k$ others" András Gyárfás, SZAKI, Budapest, Hungary, ``The afterlife of a remark of Erd?s and Rado" Krushkal, University of Virginia, ``The Tutte and chromatic polynomial relations for planar and surface graphs" Jean Paul Thouvenot, University of Paris, ``On the norm correspondence of nonconventional ergodic averages" Paul Werbos, National Science Foundation, ``Mathematical foundations of prediction under complexity" László Székely, University of South Carolina, ``The Lovász Local Lemma -- a new tool for asymptotic enumeration?" Oliver Riordan, University of Cambridge, UK, ``The survival probability of multi-type branching processes" Gregory Margulis, Yale University, ``A random Minkowski theorem" In addition to the rather technical lectures described above, Ralph Faudree of the University of Memphis gave a talk to a large general audience of about 130 people, including high school students and the community, entitled ``The Erd?s I Knew". Using a series of pictures and stories, he presented a personal account of the activities of Paul Erd?s in Memphis. In the end he painted a very colorful picture of Erd?s, revealing the ``brilliance, humanity, and wit of the extraordinary mathematician who contributed so much to the University of Memphis". The Contemporary Combinatorics Conference was a unique and significant addition to the group of conferences offered in combinatorics in 2010. Furthermore, unlike other areas of the States like the East Coast or the Bay Area on the West Coast, the Mid-South cannot boast of many high-level mathematical conferences; the Contemporary Combinatorics 2010 meeting in Memphis went some way towards redressing the balance. Young researchers and mathematicians benefitted from the lectures and from personal contacts with the speakers, and groundbreaking ideas in combinatorics and an important figure in mathematical history were made accessible to people with little or no mathematical background.
