Research Interests

Discrete geometry, combinatorics, combinatorial and finite group theory. I work in the area of abstract polytopes on extremal problems ("Find the smallest abstract polyhedron with p-gonal faces meeting q at each vertex"), classification problems ("Describe all 3-orbit skeletal polyhedra"'), and properties of combinatorial and algebraic constructions applied to polytopes ("Determine the structure of the smallest regular 4-polytope that covers the pyramid over a polyhedron").

Dissertation

Internal and external invariance of abstract polytopes

Publication List

Talks

  • Open problems on k-orbit polytopes, Symmetries in Graphs, Maps, and Polytopes, Morelia, Mexico, June 2018.
  • Small polyhedra with prescribed symmetry, Pick My Brain Seminar at Northeastern University, Boston, MA, January 2018.
  • Non-flat regular polytopes and restrictions on chiral polytopes, Symmetries of Discrete Structures in Geometry, at Casa Matematica Oaxaca, Oaxaca, Mexico, August 2017
  • The search for small polytopes, 2da Escuela en Simetrías de Estructuras Combinatorias, UNAM, Cuernavaca, Mexico, July 2017.
  • Tight chiral polyhedra, AMS Special Session on Geometry and Combinatorics of Polytopes, Rutgers University, New Brunswick, NJ, November 2015.
  • The search for tight polytopes, Discrete Geometry Seminar at Northeastern University, Boston, MA, March 2014.
  • Orbit graphs and transitivity of k-orbit polytopes, AMS Special Session on Discrete Geometry of Polytopes, Boston, MA, April 2013.
  • Minimal equivelar polytopes, MIT Combinatorics Seminar, Cambridge, MA, November 2012.
  • Minimal equivelar polytopes, Seminar in Geometry, Algebra, Singularities, and Combinatorics at Northeastern University, Boston, MA, November 2012.
  • Constructing abstract regular polytopes with external symmetries, UMass Boston Mathematics Colloquium, Boston, MA, May 2012.
  • Constructing abstract regular polytopes with external symmetries, WPI Mathematics Colloquium, Worcester, MA, January 2012.
  • Constructing self-dual and self-Petrie polyhedra, AMS Special Session on Combinatorial Geometry of Polytopes at the Joint Meetings of the AMS, Boston, MA, January 2012.
  • Constructing self-dual chiral polytopes, Workshop on Symmetry in Graphs, Maps and Polytopes at the Fields Institute, Toronto, Canada, October 2011.

CV

Research Statement

 

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