**email:**
ptoste (at) umich.edu

**office:**
1852 East Hall

I am a 5th year PhD student in mathematics at the University of Michigan. My advisor is Andrew Snowden.

I'm interested in questions on the interface between topology, combinatorics, and representation theory. For me, the bridge between these areas usually involves homological algebra. I like to think about configuration spaces, subspace arrangements, representations of FI-like categories and twisted commutative algebras, operads, Koszul duality, and representations of posets.

Stability in the Homology of Deligne-Mumford Compactifications, * preprint. *

This paper studies the moduli space of stable marked curves from the point of view of representation stability.

Lattice Spectral Sequences and Cohomology of Configuration Spaces, * preprint. *

The Distribution of Gaps between Summands in Generalized Zeckendorf Decompositions, with Amanda Bower, Rachel Insoft, Shiyu Li, and Steven Miller, * Journal of Combinatorial Theory, Series A. (135 (2015), 130--160). *

The Average Gap Distribution for Generalized Zeckendorf Decompositions, with Olivia Beckwith, Amanda Bower, Louis Gaudet, Rachel Insoft, Shiyu Li and Steven Miller, * the Fibonacci Quarterly (51 (2013), 13--27).*

Inclusion Exclusion and Rep Stability for Non-Manifolds

Cutting and Pasting, Michigan math club talk