This award provides funds to support a conference on algebraic graph theory, which will be held at Villanova University during June 2-5, 2014. The organizers planned a wide array of topics; some of them have diverse links to other fields. There is an impressive list of invited participants, including some well-known experts in this area of discrete mathematics, as well as many graduate students, post-docs, and researchers from under-represented groups.

The subject of Algebraic Graph Theory belongs to the broader field of Discrete Mathematics. Just as one regards Calculus as the mathematical language designed to investigate functional behavior over infinite domain space, Discrete Mathematics applies mainly to finite sets. The subject was initiated in the study of Probability and Statistics in the 17th Century, but its main growth took place in the 20th Century due to the advent of computers and theoretical computer science. These days Discrete Mathematics plays an essential and compulsory role in modern society, providing tools and framework for such areas as digital communication, error-correcting codes, internet and social network structure, data mining in large databases, genome sequencing, experimental design, and many others.

Project Report

". The conference was partially supported by NSF Award DMS-1418686, with additional funding provided by the hosting institution. Algebraic graph theory is a substantial subfield of discrete mathematics, conjoining two prominent areas of mathematical investigation: abstract algebra and graph theory. As such, its core tools stem from its mathematical predecessors, amalgamating techniques from group theory, linear algebra, number theory, representation theory, and finite geometry. With the advent of the computer age, the role played by algebraic graph theory has become pivotal. For example, it provides the theoretical framework for the study of computer circuitry design, digital communication flow, Internet infrastructure, data storage, cryptography, assignment and transportation scheduling problems, and so on. Algebraic graph theory has also found recent application in the hard sciences, most notably in biology and chemistry. The conference was hugely successful, in no small part due to fulfillment of our pedagogical and demographic objectives. Specifically, there were 103 attendees from 20 different nations. This included 50 of the world's top experts, with the remaining attendees primarily composed of established specialists from other fields, as well as graduate students/recent PhDs/post-docs. Junior researchers comprised roughly 30% of all invited participants, while females accounted for over 20%. The conference included nine plenary lectures given by distinguished researchers, with another 60 invited talks delivered in parallel-session format. The program provided the opportunity for participants to meet and discuss their ongoing research, to identify new and innovative avenues of exploration, and to create potentially fruitful collaborations as well as revitalize existing ones. Wide-scale dissemination of recent developments in the "applied sector" led to the formulation of some exciting new strategies and methodological advances. Perhaps most significantly, the conference exposed fledging young researchers to a view of the modern landscape of the field, while affording a relaxed and congenial atmosphere within which they could interact freely with the very architects of that landscape. Though not by design, the conference neatly juxtaposed the triennial conference "Geometric and Algebraic Combinatorics" held in Oisterwijk, Netherlands in 1999, 2002, 2005, 2008 and 2011. Accordingly, many participants expressed the hope that the Villanova Conference could take over where the discontinued GAC conference had left off, conforming to the preexisting triennial schedule.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
Standard Grant (Standard)
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Program Officer
Qing Xiang
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Villanova University
United States
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