I am a die-hard combinatorialist. My current research is in geometric combinatorics with connections to applied algebraic geometry and optimization. I am studying slack ideals of polytopes and matroids. In particular, we are interested in correspondence between the algebraic properties of the slack ideals and the geometric and combinatorial structure of the polytopes and matroids. 

I also still like to think about problems and objects that have applications in digital communication. In the past, I have studied Golay sequences and arrays, peak sidelobe levels of binary sequences, and I wrote my Master's thesis on the subject of complex equiangular lines (also known as SIC-POVMs to those studying quantum information theory).


In Autumn 2018, I started a graduate student optimization seminar at the University of Washington. I organized the seminar for the 2018-2019 academic year. 

  • August 2018: Visiting student, University of Coimbra, Portugal

  • July 2018ISMP, Bordeaux, France (25 minute talk in ''Algebraic and geometric aspects of semidefinite programming'' session)

  • June 2018ECCO 18, Barranquilla, Colombia (25 minute talk in ''Polytopes'' session)

  • May 2018Discrete Math Seminar, Simon Fraser University, Burnaby, Canada

  • April 2018AMS Sectional Meeting, Portland State University, Portland, Oregon (25 minute talk in ''Special Session on Commutative Algebra'')

  • March 2018Discrete Geometry Seminar, Freie Universität Berlin, Germany

  • February-March 2018Visiting Student, MPI, Leipzig, Germany (50 minute talk in ''Seminar on Nonlinear Algebra'')


Here is the current version of a Macaulay2 package that can be used to construct and manipulate slack ideals. If you find errors in it, please email me. 
Examples files from The slack realization space of a matroid will be posted here soon.

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