Simple groups, representations, and related topics

University Of Oregon Eugene, Eugene OR

Investigators

Abstract

The conference "Simple Groups, Representations, and Related Topics," will be held July 13-15, 2015 at the Center for Mathematical Sciences, University of Cambridge, UK. This grant partially supports travel expenses for US-based researchers, particularly early career mathematicians, to attend this major international conference addressing one of the core areas of modern algebra (group theory). The conference will bring together leading experts and outstanding young researchers, providing an opportunity to report on and discuss exciting recent advances in the field. It is expected that approximately 80 mathematicians will attend the conference. The meeting will play an important role in the further development of the subject by helping to identify interesting and challenging open problems and new applications. The location and timing has been chosen to be compatible with an independent conference on "Finite Simple Groups and their Applications" to be held the previous week at the University of Warwick, UK. The subject of the conference is related to the study of finite simple groups, which is a classical area of algebra that has been at the heart of research in group theory for two centuries. Simple groups are the basic building blocks of all finite groups, and the classification of finite simple groups (CFSG) is widely regarded as one of the greatest mathematical achievements of the 20th century, involving many researchers over a period of many years. This fundamental theorem has led to many interesting new problems in group theory and beyond, and the development of powerful techniques to solve them. In the last thirty years or so, post-CFSG, there have been great advances in our understanding of the subgroup structure and representation theory of simple groups. These topics are of fundamental importance in their own right, and they are essential for many applications. The meeting will focus on the theory of simple groups, with a particular emphasis on their subgroup structure and representations. The interplay between finite and algebraic simple groups will be a common theme, and we will focus on applications, both in group theory and in other areas of mathematics such as computational algebra, Lie theory, algebraic geometry, number theory, and model theory. For more information see the conference web site https://www.dpmms.cam.ac.uk/~dis20/liebecksaxl/Liebeck-Saxl_2015/Welcome.html