Impact of Computation on Number Theory, July 30 - August 3, 2014

Pennsylvania State Univ University Park, University Park PA

Investigators

Abstract

A conference on the impact of computation on number theory will take place July 30 to August 3, 2014, at the National Center for Theoretical Sciences (NCTS), in Hsinchu, Taiwan. The purpose of this conference is to gather international experts to share experiences in how computation has impacted their research in number theory (broadly understood), to present cutting-edge results, and to discuss the future role of computation in number theory. Support from this award will partially defray the expenses of the invited speakers and invited participants from the US. Calculation has always played a significant role in number theory. Beginning in the middle of the last century and continuing today, machine computation has played an increasingly prominent role. Many important statements in number theory, like the conjecture of Birch and Swinnerton-Dyer and the formula of Gross and Zagier, were formulated based on extensive data collected from computation. In situations where we lack a deeper understanding, such as in Grothendieck's theory of dessins d'enfants, the only way to gain understanding is to compute examples first. It is hoped that this conference will shed light on how important conjectures in number theory were discovered, how to comb through numerical data to detect phenomena, how to take advantage of modern technology to assist future research, and to learn the types of problems better suited for numerical explorations. One of the goals for the conference is to broaden participation by inspiring young participants and to encourage them to build connections with people from all over the world. A three-week course in arithmetic geometry and number theory will serve as a good prelude and preparation for the conference for graduate students. Conference web site: http://math.cts.nthu.edu.tw/Mathematics/2014ICNT.htm