Research

I’m interested in various topics in homotopy theory. Lately I’ve been thinking a lot about higher algebra and equivariant homotopy theory. In particular about equivariant dendroidal sets and about connecting Tambara functors to number theory and algebraic geometry.

Fall 2020 I co-organized a reading course on derived algebraic geometry with Roy Magen, joint with Columbia University.

Summer and fall 2020 I organized a reading course on ∞-categories at UPenn out of Charles Rezk’s notes and Jacob Lurie’s Higher Topos Theory.

 

Papers

Triangulations of simplices with vanishing local h-polynomial
Accepted for publication in Algebraic Combinatorics
With Andre Moura, Jason Schuchardt, Sam Payne, and Alan Stapledon
https://arxiv.org/abs/1909.10843

Balanced complexes and effective divisors on \overline{M}_{0,n} 
Communications in Algebra, February 2020.
With José Luis González and Olivia Zhang
https://arxiv.org/abs/1709.10198

The cycle structure of a Markoff automorphism over finite fields
Journal of Number Theory, October 2019.
With Alois Cerbu, Michael Magee, and Luke Peilen.
https://arxiv.org/abs/1610.07077