Loud & Discrete Mathematics

Since October 2016, I am 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 completed my Habilitation in June 2020. I am 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 research is at the intersection of combinatorics, discrete geometry and group theory. My area of specialization consists of computational, combinatorial, and geometric approaches to study algebraic and topological structures. Particularly, my research is focused on Coxeter 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, relation to algebraic structures
  • Convex Geometry: triangulations, subdivisions, and 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

  • Computational complexity, imagery, tilings, fractals
  • Analytic and algebraic number theory
  • Toric varieties and lattice polytopes
  • Tropical geometry
  • Hyperbolic geometry

My Projects