This page was last updated in June 2020.
My curriculum vitae (updated May 2021) also contains a list of my papers.
Research Papers

Efficient Computation of the Multigraded Betti Numbers with Mike Lesnick (in preparation)

Finding Minimal Spanning Forests in a Graph with AbdelRahman Madkour and Phillip Nadolny (St. Olaf students): We propose two algorithms for solving a graph partitioning problem motivated by computational topology. Given a weighted, undirected graph G and a positive integer k, we employ spectral clustering and dynamic programming to find k disjoint trees within G such that each vertex of G is contained in one of the trees and the weight of largest tree is as small as possible. (submitted) links

Approval Voting in Product Societies with Kristen Mazur, Mutiara Sondjaja, and Carolyn Yarnall: In approval voting, individuals vote for all platforms that they find acceptable. We examine scenarios in which voters must make two decisions simultaneously, present a general lower bound on agreement in a twodimensional voting society, and examine specific results for societies whose spectra are cylinders and tori. (published in The American Mathematical Monthly, 2018) links

Interactive Visualization of 2D Persistence Modules with Mike Lesnick: We introduce RIVET, a software tool for the interactive visualization of 2D persistence modules, and present the mathematical foundations for this tool. RIVET efficiently computes barcodes along 1D affine slices of a 2D persistence module, using a novel data structure based on planar line arrangements. links

Towards DomainSpecific Semantic Relatedness: A Case Study from Geography with Shilad Sen, Isaac Johnson, Rebecca Harper, Huy Mai, Samuel Horlbeck Olsen, Benjamin Mathers, Laura Souza Vonessen, and Brent Hecht: This paper describes an undergraduate research project on domainspecific semantic relatedness at the 2014 MAXIMA REU. Focusing on the domain of geography, we showed that algorithms that use geographic signals can outperform standard sematic relatedness algorithms for geographic concepts. (presented at IJCAI 2015) links

A Hadwiger Theorem for Simplicial Maps with P. Christopher Staecker: We define the notion of valuation on simplicial maps between geometric realizations of simplicial complexes, generalizing both the intrinsic volumes and the Lefschetz number. This allows us to prove a Hadwigerstyle classification theorem for all such valuations. (preprint, February 2014) links

Intrinsic Volumes of Random Cubical Complexes with Michael Werman: We give exact polynomial formulae for the expected value and variance of the intrinsic volumes of several models of random cubical complexes. We also prove a central limit theorem for these intrinsic volumes and, for our primary model, an interleaving theorem for the zeros of the expectedvalue polynomials. (published in Discrete and Computational Geometry, 2016) links

Hadwiger Integration of Random Fields: I provide a formula for the expected values of Hadwiger integrals (and, using Hadwiger's Theorem, more general valuations) of Gaussianrelated random fields, which are both theoretically interesting and potentially useful in applications such as sensor networks and image processing. (published in Topological Methods in Nonlinear Analysis, 2015) links

Hadwiger's Theorem for Definable Functions with Yuliy Baryshnikov and Robert Ghrist: We generalize the intrinsic volumes to the valuations on realvalued functions and provide a classification theorem for such valuations, analogous to Hadwiger's classic theorem. (published in Advances in Mathematics, 2013) links

Hadwiger Integration of Definable Functions: This is my Ph.D. dissertation, completed in 2011, in which I define Hadwiger integrals and prove a classification theorem for valuations on definable functions. links
My Erdös number is 3:
me → Michael Werman → Nathan Linial → Paul Erdös
me → Michael Werman → Nathan Linial → Paul Erdös
Expository Articles

Colorful Symmetries with Brian Bargh and John Chase: With a focus on the concept of symmetry, this article explains how to count the number of ways that you can color an icosahedron (or another geometric object) with n colors. (published in Math Horizons, 2014) links

Cycles of Digits: Cyclic permutations of digits that appear in repeating fractions can help students understand important concepts in abstract algebra. (preprint, 2013) links