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ABSTRACT
This National Science Foundation award provides support for the CBMS Conference: L-functions and Multiplicative Number Theory, to be held at the University of Mississippi in Oxford, MS on May 20-24, 2019. The conference will feature a series of ten lectures by Professor Kannan Soundararajan from Stanford University who is well known for his prolific and influential research in this area, and also for his skill as a lecturer and expositor. Professor Soundararajan's lectures will culminate in an expository monograph that will be a valuable resource for current and future researchers. The conference will also feature six additional lectures intended to complement and enhance the main lecture series. Approximately thirty participants will be supported, many of whom will be graduate students. The organizers intend to bring together both beginning and more established researchers to stimulate advances and collaboration on this current research topic. The organizers will actively recruit female participants as well as participants from other groups that are underrepresented in the mathematical sciences. In accordance with the NSF-CBMS goals, the host institution is interested upgrading and improving its research efforts, and trying to build a strong research group in number theory.
Number theory is an old and very active branch of mathematics, and the theory of L-functions has played a central role in its modern development. The tools used to study L-functions draw from many fields including analysis, algebra, algebraic geometry, automorphic forms and representation theory, probability and random matrices, and even mathematical physics. The broad theme for the conference will be the value distribution of zeta and L-functions. The lecture series will touch upon several important questions including the maximal size of L-functions, asymptotics for moments of L-values, the distribution of zeros, and non-vanishing of L-functions at special points. Moreover, it will be shown how the techniques used in the study of moments have close counterparts in the understanding of other problems in multiplicative number theory. The lecture series and accompanying monograph will give a broad perspective of this sharply focused research area in a way that will help researchers of all levels understand the major ideas and possible future directions for the field. Information regarding the conference can be found at https://math.olemiss.edu/cbms2019/.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
This project supported the NSF-CBMS Conference: L-functions and Multiplicative Number Theory which took place at the University of Mississippi on May 20-24, 2019. This conference featured 10 lectures by Professor K. Soundararajan of Stanford University who is well known for his prolific and influential research in this area, and also for his skill as a lecturer and expositor. Number theory is an old and very active branch of mathematics, and the theory of L-functions has played a central role in its modern development. The tools used to study L-functions draw from many fields including analysis, algebra, algebraic geometry, automorphic forms and representation theory, probability and random matrices, and even mathematical physics. The broad theme for the conference was the value distribution of zeta and L-functions. The main lecture series touched upon several important questions including the maximal size of L-functions, conjectures for moments of L-values, and the progress towards these conjectures. Moreover, it was be shown how the techniques used in the study of moments have close counterparts in the understanding of other problems in multiplicative number theory. Professor Soundararajan is currently expanding his lecture notes into an expository monograph that will be a valuable resource for current and future researchers.
The conference also featured seven additional lectures that helped complement and enhance the main lecture series. These lectures where given by Vorrapan Chandee (Kansas State University), Alexandra Florea (Columbia University), Xiannan Li (Kansas State University), Kyle Pratt (University of Illinois), Brad Rodgers (Queens University), Caroline Turnage-Butterbaugh (Carleton College), and Matthew P. Young (Texas A&M University). There was also an open problem session led by Ayla Gafni (University of Rochester), and plenty of time for discussion after each lecture. A website on the University of Mississippi Institutional Repository was created which features slides and videos from most of the 17 conference lectures: https://egrove.olemiss.edu/cbms2019/. This information is available on this website under `detailed schedule.'
The grant was able to provide travel support for 32 participants, a majority of whom were graduate students. In total, the conference attracted 65 participants from 8 countries (United States, Canada, United Kingdom, France, Germany, Russia, South Korea, and India). 50 participants came from US institutions. As part of our broader impacts, a goal for the conference was to bring together both beginning and more established researchers to stimulate advances and collaboration on this current research topic. Of the 65 attendees, 16 were tenure or tenure-track faculty, 44 were graduate students and postdocs, 2 were non-tenure-track instructors, and 3 were undergraduates. The organizers actively tried to recruit participants from groups that are underrepresented in the mathematical sciences: 16 participants were female, 2 identified as Black or African-American, and 4 identified as Hispanic or Latino. One participant identified as hearing impaired. We had 20 participants from universities in the Southeast Region of the United States. This data was collected in part via an anonymous web survey we sent the participants.
Last Modified: 07/01/2020
Modified by: Micah B Milinovich
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