Hi! I am a Visiting Researcher at the Institut des Hautes Études Scientifiques in Paris, France. Previously, I was a Visiting Postdoctoral Fellow at the Max-Planck-Institut fur Mathematik (Bonn, Germany), Sabanci University (Istanbul, Turkey), IHES (2012), and Galatasaray University (Istanbul, Turkey). I got my PhD in Mathematics from The University of Western Ontario (UWO, London, Canada) in August 2011, under the supervision of Lex Renner.
My research interests lie on the interaction between algebraic topology and geometry. Specifically, I apply GKM theory (named after Goresky, Kottwitz, and MacPherson) to the study of spherical varieties. I am particularly interested in normal projective embeddings of reductive groups. Notably, these compactifications can be obtained as projectivizations of reductive monoids. In my doctoral dissertation, I provide a complete combinatorial description of the equivariant cohomology of rationally smooth embeddings (a subclass that includes smooth and certain singular varieties). My results vastly increase the effectiveness of GKM theory as a tool in embedding theory.
In current work, I establish GKM theory in the context of equivariant operational Chow rings (with rational coefficients) and equivariant operational K-theory (with integer coefficients). Moreover, I describe the equivariant operational Chow rings of spherical varieties as dual modules of their corresponding equivariant Chow groups. These results build on previous work by Brion, Fulton, Kimura, MacPherson, Payne, Sottile and Sturmfels. You are welcome to read my MPIM Report and my preprints in the arxiv for more details!
My long term goal is to describe the equivariant intersection cohomology of all normal projective embeddings of reductive groups. Previous work on this direction has been carried out by Peter Fiebig and G. Barthel, J. Brasselet, K. Fieseler and L. Kaup.