The New York City area has long tradition of great strength in number theory. Recently, this tradition has begun to spread to the rest of the state. This proposal seeks to initiate a regular annual conference in number theory to be held in Upstate New York. The four investigators represent four different leading institutions: Binghamton University, Cornell University, SUNY--Buffalo and the University of Rochester.
Modern number theory focuses on a host of problems; some date back to the ancient Greeks, while others are motivated by contemporary problems in technology, such as data encryption. Number theory research in Upstate New York runs the gamut of many of these topics. At the faculty level research, this proposal will integrate several isolated specialists in the region and create an environment that stimulates collaborations and new directions for future work, while at the same time strengthening ties between researchers in Upstate New York and those near New York City. This will maintain and enrich the intellectual merit of the region's number theory research. It will also help graduate students and post-docs by exposing them to work of leading experts, by allowing them to communicate their own research and interests, and by giving them the chance to interact among themselves.
Since the late '90s the number theory community in upstate New York has grown from a handful of researchers to several to now about a dozen. Starting in 2011 we held annual number theory conferences at Cornell, the University of Rochester, Binghamton University and SUNY at Buffalo. At each conference we had approximately 8 plenary talks by distinguished scholars. We encouraged these speakers to aim their lectures at graduate students. Each conference had about 50 participants, mostly from the upstate area. We emphasized attendance by graduate students and encouraged them to give talks on their research. The period of the conferences, 2011-14 has coincided with a doubling of the number theory population at the four host institutions and hires at several other upstate colleges. This increases in size has led to an increase in the number of local graduate students studying number theory so that we do not have as many isolated students who are forced to learn on their own. The Upstate Number Theory conference will continue from 2015-2018 under the leadership of the new young scholars that the first round of conferences attracts. We expect these conferences will help contribute to a vibrant community of scholarship among professors and students in our field over the next generation helping us to better fulfill our dual missions of scholarship and teaching.