Algebraic groups are fundamental objects in representation theory and number theory. The course will discuss the structure theory of linear algebraic groups over algebraically closed fields. Topics include tori, parabolic subgroups and Borel subgroups, Lie algebras, root data, Weyl group, and classification of simple algebraic groups. If time permits, we will briefly discuss relation between compact Lie groups and algebraic groups.
Pre-requisites include abstract algebra, basic commutative algebra and basic algebraic geometry.
I am a Senior Lecturer in the School of Mathematics and Statistics at the University of Melbourne. I obtained my PhD in 2010 at Massachusetts Institute of Technology, USA, under the direction of George Lusztig. Prior to Melbourne, I was a Boas Assistant Professor at Northwestern University, USA, from 2010 to 2013 and a postdoctoral researcher at the University of Helsinki, Finland, from 2013 to 2015.
My research interest lies in geometric aspects of representation theory, in particular, representations of algebraic groups and geometry of nilpotent orbits, as well as combinatorics that arises from representation theory. My current research focus is to describe character sheaves in the setting of graded Lie algebras and to explore their applications to p-adic groups.