Paul Philippe
Institut Camille Jordan, Université Jean Monnet, Saint-Etienne
Institut Camille Jordan, Université Jean Monnet, Saint-Etienne
My main interests lie in Kazhdan-Lusztig theory, buildings and Kac-Moody groups over discretely valued fields.
On the one hand, affine Kazhdan-Lusztig theory relates the representation theory of a reductive group over a discretely valued field to the geometry of its affine flag variety and to the combinatorics of its Bruhat-Tits building.
On the other hand, Kac-Moody groups are infinite-dimensional generalizations of reductive groups for which there exists an analog of Bruhat-Tits buildings, named masures.
The main goal of my PhD is to define Kazhdan-Lusztig polynomials for Kac-Moody groups over discretely valued fields, using masures. Along the way, I also grew a particular interest for the geometric incarnation of Kazhdan-Lusztig theory, through perverse sheaves and their application in representation theory.
Keywords: root systems, Kac-Moody groups, Kazhdan-Lusztig theory, Bruhat-Tits buildings, masures, Hecke algebras, DAHA
I was a student of the Ecole Normale Supérieure de Lyon from september 2018 to july 2022 for my Bachelor and Master.
In 2021-22 I followed the advanced master program "Groups, geometry and dynamics", which I obtained with honors.
I also participated to an exchange program with Trinity College, Cambridge, in which I obtained a Master of Advanced studies (Part III) with distinction.
You can find a more detailed resume here.