Conference: Group Theory and Number Theory: Interactions

University Of Denver, Denver CO

Investigators

Abstract

This grant is to support travel of participants to attend the conference "Group Theory and Number Theory: Interactions", which will take place October 16-20, 2023 at Princeton University. Bringing together experts in the areas group theory and number theory, this conference will provide new networking opportunities and stimulate important research collaborations between researchers in these two branches of mathematics. Group theory is motivated by the study of symmetries of objects found in many areas of science, art, and technology, from molecular structures, to the spin of particles, to the patterns in cryptosystems, to the structure of musical chords. Number theory is motivated by the study of the integers, prime numbers, integer-valued functions, and generalizations of these objects, and has applications to the same areas as group theory. In many of the key problems in group theory, one sees natural relationships to number theory, and vice versa. Recent advances and open conjectures in the two areas have made it clear that there is a strong benefit to being able to combine the techniques from both. This conference will inspire progress on important questions, while also broadening the tools and ideas available to researchers in both areas, and fostering a new generation of researchers studying interactions of group theory and number theory. Students, early-career researchers, and mathematicians who identify as women and other underrepresented groups will be especially encouraged to participate. One of the most well-known examples with a clear relationship between group theory (and, more specifically, representation theory) and number theory is the Langlands program. The main speakers, representing some of the most influential names and trends currently in the two areas of group theory and number theory, will give talks discussing new results related to the Langlands program, as well as new results on algebraic groups, permutation groups, probabilistic approaches to representation theory and word growth, local-global conjectures in character theory, and other topics that bridge the two areas of group theory/representation theory and number theory. The conference website is: https://sites.google.com/view/tiep60conference/ 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.