Loud & Discrete Mathematics

Since December 2020, I am Privatdozent at the Department of Mathematics and Computer Science of the Freie Universität. In November 2021, I will join the Service d'Enseignement Généraux at the École de Technologie supérieure in Montréal which is within the Université du Québec system as a Lecturer (Maître d'enseignement).

I completed my Habilitation in July 2020. My Habilitation Lecture was on Jones' Unknotting Conjecture.

Between October 2016 and September 2020, I was a Postdoctoral Researcher in the Discrete Geometry workgroup of the Freie Universität Berlin as a member of the SFB Project Discretization in Geometry and Dynamics. I was a junior faculty member of the Berlin Mathematical School and of the Research Training Group Facets of complexity.

Between October 2014 and September 2016, I was a Postdoctoral Research Fellow at the Einstein Institute of Mathematics of the Hebrew University of Jerusalem. My advisor was Eran Nevo. I was also a Postdoctoral Research Fellow of the Fonds Québécois de recherche doing research in collaboration with Francisco Santos at the Universidad de Cantabria.

Between July 2013 and June 2014, I was a Postdoctoral Research Fellow at the Freie Universität Berlin as a member of the SFB Project Discretization in Geometry and Dynamics.

Between October 2010 and July 2013, I did my doctoral studies in Mathematics under the supervision of Professor Günter M. Ziegler. My thesis focused on discrete geometry and algebraic combinatorics, namely on the theory of polytopes and their interaction with the theory of Coxeter groups.


Research interests

My speciality lies in unifying computational, combinatorial, and geometric methods to create novel frameworks to study structures in algebra, geometry, and quantum physics. In particular, my research merges large-scale computational experimentations and abstract modelizations to tackle open problems related to Coxeter and reflection groups, polytopes (in particular the permutahedra, associahedra and their generalizations), triangulations, and simplicial complexes.

In general, I appreciate particularly problems related to the following themes:

  • Algebra: representation theory, Coxeter groups, infinite root systems, Lie groups, cluster algebras
  • Combinatorics: counting problems, combinatorics on words, lattice theory, relation to algebraic structures
  • Convex Geometry: triangulations, realization spaces of polytopes, permutahedra, associahedra and their generalizations
  • Computational geometry and algebra: generation problems, isomorphism problems, complexity, visualization tools

Although not an expert, I appreciate to hear about

  • Quantum physics
  • Computational complexity, imagery, tilings, fractals
  • Toric varieties and lattice polytopes
  • Tropical geometry
  • Hyperbolic geometry

My Projects