Groups Representations and Applications: New Perspectives

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Group Theory is essentially the theory of symmetry for mathematical and physical systems, which underpins much of modern pure mathematics, with major connections to physics, chemistry, and information science. Especially after the completion of the Classification of Finite Simple Groups (CFSG), important and deep connections to areas as varied as topology, algebraic geometry, Lie theory, homological algebra, and mathematical physics, have been discovered and exploited. Still, the area abounds with basic problems and long-standing conjectures. Recent breakthroughs hold out the prospect of finally solving some venerable open problems. In turn, recent results in group- and representation theory have led to substantial progress in a vast number of applications in Lie theory, number theory, algebraic geometry,combinatorics and semigroup theory.All this wealth of new results and directions will be the main theme of the 2020 six-month program "Groups, Representations and Applications: New Perspectives", Jan. 6 - June 30, 2020, at the Isaac Newton Institute for Mathematical Sciences (INI, Cambridge, UK), which features five one-week workshops. The goal of this program is to bring together the leading experts in group and representation theory, on the one hand, and from several key other parts of mathematics on the other, to tackle some of the main problems and to take the many connections between CFSG and other areas of mathematics to the next level. Detailed information is given at the program's website http://www.newton.ac.uk/event/gra. Funding provided by the grant will support US-based participants of the five one-week workshops within the program.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.