You are cordially invited to the Department of Mathematics Colloquium
Speaker: Karim Adiprasito (Jussieu Institute of Mathematics, Paris Rive Gauche (IMJ-PRG))
“Lattice polytopes and their Lefschetz properties”
Abstract: Ehrhart theory is the theory studying how many lattice points are contained in the dilate of a given (lattice) polytope; it has rich applications to combinatorial problems, and deep connections to algebraic geometry, representation theory and more. Some of the most fundamental problems remain open.
We developed a new approach to understanding the fundamental class of associated semigroup algebras via Parseval-Rayleigh identities. This leads to the resolution of several combinatorial conjectures, such as unimodality of the $h^\ast$-polynomial for large classes of lattice polytopes, among them integrally closed Gorenstein polytopes.
Based on joint work with Papadakis and Petrotou. If time permits, I will also give glimpses of upcoming work that involves in addition Katz and Oba.
Biography: Karim Adiprasito is a leading researcher in combinatorics and discrete geometry. He earned his Ph.D. in 2013 at the Free University of Berlin under Günter M. Ziegler and currently serves as Directeur de Recherche at the CNRS, based at Sorbonne University in Paris. His major contributions include the resolution of long-standing problems in polytope theory and matroid Hodge theory—among them the proof of the g-conjecture for simplicial spheres and the log-concavity of the characteristic polynomial of matroids (with June Huh and Eric Katz). He has been awarded the European Prize in Combinatorics (2015), the New Horizons Prize in Mathematics (2019), and the EMS Prize (2020) for his outstanding early-career achievements.
Date: Wednesday, November 12, 2025
Time: 15:40-16:40 (GMT+3)
Place: Zoom and video conference in the Mathematics Seminar Room, SA-141
To request the event link, please send a message to gokhan.yildirim@bilkent.edu.tr