Since December 2020, I am Privatdozent at the Department of Mathematics and Computer Science of the Freie Universität.
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 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.
- Organizer of the Research Seminar in Discrete Geometry April 2017--March 2020
- Organizer of the VII Encuentro Colombiano De Combinatoria (ECCO 2020)
- Organizer of the Einstein Workshop Geometric and Topological Combinatorics 2018
- Alumnus of the Research Training group Methods for Discrete Structures
- Alumnus of the Berlin Mathematical School
- Student representative of the Berlin Mathematical School 2012
- Organizer of the Polyhedral Combinatorics seminar with Cesar Ceballos 2011-2013
- Organizer of the workshop Coxeter Groups meet Convex Geometry 2012
- Organizer of the BMS Student Conference 2013
- Former student of the LaCIM 2008-2010
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