The PI plans to study several questions in representation theory and algebraic geometry which are related to the ``wonderful compactification'' of adjoint groups and (more generally) the complete symmetric varieties. More specifically, the PI will continue his work on Lusztig's G-stable-piece decomposition and the connection to representation theory. On the geometric side, the Frobenius splitting properties and normality of the closures of G-stable pieces will be studied by the PI together with collaborators. On the side of representation theory, the PI will focus on understanding the behavior at infinity of the character sheaves.
The PI's research is in the area of representation theory. Representation theory is an area of modern algebra concerned with understanding symmetries by means of matrices and has many applications in chemistry and physics. The PI's work will focus on using methods of algebraic geometry to obtain new results in representation theory. The PI's research will hopefully reveal the close relations between representation theory and algebraic geometry and is likely to have an impact on both areas.
