" Title: Modular representations of algebraic groups and symmetric groups Abstract: This course will be an introduction to some fundamental questions in representation theory. The focus will be on what is known and not known about simple representations of algebraic groups and symmetric groups. I will spend some time revising classical theory (structure theory of connected reductive groups, Weyl modules, Specht modules, tilting modules, affine Weyl groups, linkage principle) and then move on to more modern developments (categorification, derived equivalences, Soergel bimodules, p-canonical basis). Some background in representation theory and algebraic geometry will be assumed." This is a second semester postgraduate course and it will run every Thursday, 3pm-5pm, in Carslaw 352 (we might need to change the room!). Postgraduates and Honours students are particularly encouraged to attend.