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. Invited speakers will address a diverse set of topics including graph theory, Ramsey theory, operation research, theoretical computer science, probabilistic combinatorics, simplicial complexes, biostatistics and bioinformatics. The meeting will provide an opportunity for mathematicians from the Mid-South to benefit not only from the lectures but also from personal contacts with the speakers.

The main speaker is Jon Kleinberg from Cornell University. A popular lecturer, he has done great work on networks and is particularly well known for his HITS algorithm, an algorithm for web search that builds on the eigenvector-based methods used by many commercial search engines. Kleinberg is also known for his work on algorithmic aspects of the small world experiment. Among other honors, he received a MacArthur Foundation Fellowship in 2005 and the Nevanlinna Prize in 2006, an award that is given out once every four years along with the Fields Medal; it is the premier distinction in Computational Mathematics. His most recent book, entitled Networks, Crowds, and Markets: Reasoning About a Highly Connected World, was published by Cambridge University Press in 2010.

Two lectures will be aimed at a general audience and high school students from the best schools in the Memphis area will be invited to attend. In the first lecture, Joel Spencer will give a contextual talk positioning Erdos as one of the most significant mathematicians of the 20th century. In the second lecture, Kleinberg will focus on questions related to flow of information through networks, emphasizing mathematical models for information flow in human social networks and their reflections in the on-line world.

Project Report

The conference was a great success, due to a great extent to the NSF grant awarded to the conference, which enabled us to support so many of the participants. Almost all of the visitors to Memphis were accommodated on campus: in dormitories, conference housing and the campus hotels. The conference had ninety-two participants, forty of whom received financial support from the NSF grant. Of the fifty-two participants we did not give any support, thirty-eight were were local participants, University of Memphis students and faculty or faculty from universities in the tri-state area of Tennessee, Arkansas and Mississippi;eleven participants, all professors, traveled here using their own finances, home university support or grant support; and the remaining were local high school students. A total of 35 graduate students took part in the meeting from a great many places: from the University of Memphis, University of Pittsburgh, University of Cambridge, UK, Depauw University, Florida Atlantic University, AMU in Poznan, University of Maryland-College Park, Vanderbilt University, Princeton University, University of Nebraska - Lincoln, Mississippi State, Western Kentucky University, Emory University, University of Illinois--Urbana, and Carnegie Mellon University, as well as a number of community colleges around the nation. Seven undergraduates attended, some from the University of Memphis and others who accompanied graduate students from other colleges and universities. 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. This time we were lucky to have Nevanlinna Prize Recipient John Kleinberg from Cornell University who not only delivered the inspiring 2011 Erdos Lecture but was more than happy to engage on an informal level with high school students who attended. Kleinberg gave an enjoyable, very well attended lecture entitled "The flow of information in complex networks" which centered on the study of complex networks, an area that has emerged over the past several years as a theme spanning many disciplines, ranging from mathematics and computer science to the social and biological sciences.The methods in this area draw in turn on fundamental work in graph theory and the study of random graphs.A recent focus of research has been the development of models that capture some of the qualitative properties observed in large-scale network data; such models have the potential to help us reason, at a general level, about the ways in which real-world networks are organized. His talk focused on a set of research questions related to flow of information through such networks, with a particular emphasis on mathematical models for information flow in human social networks and their reflections in the on-line world. In addition Joel Spencer from NYU gave a captivating talk which painted a historical portrait of Erd?s entitled " Paul Erd?s: his brilliance and appeal" in which he discussed the famously eccentric mathematician as "the most sociable of colleagues". He investigated Erd?s's appeal, that which "caused so many to be drawn to his circle". Spencer also discussed the centrality of his own work with Erd?s to Spencer's own career and to that of countless others. In addition, there was a special segment dedicated to the memory and legacy of Richard Schelp, one of the founding members of the Combinatorics and Graph Theory Group at the University of Memphis who began an intensive collaborative effort with Paul Erd?s in the 1970s. This collaboration, along with work with Memphis students, visitors and other members of the group, would yield a combined total of over 60 papers. The combinatorics conference featured a series of specialized talks from some experts in graph theory and combinatorics and other areas. The speakers included Jozsef Balogh from UIUC, Guantao Chen from Georgia State University, Ebenezer George from University of Memphis, Jon Kleinberg, Dhruv Mubayi from University of Chicago, Isabella Novik from University of Washington, Ramarathnam Venkatesan from Microsoft-India, David Wilson from Microsoft-Redmond and Alstair Windsor from University of Memphis. There were also plenty of opportunities for interaction between speakers and participants, ancillary activities including receptions and parties. Contemporary Combinatorics 2011 was not only an opportunity to explore some of the most innovative ideas in combinatorics shared by some excellent researchers, but it was a powerful moment to remember two of the most significant minds to have contributed to the culture, landscape and history graph theory and combinatorics in Memphis and the rest of the world, Paul Erd?s and Richard Schelp.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Tomek Bartoszynski
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University of Memphis
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