Below are my publications and preprints, in reverse chronological order, along with brief informal summaries. My papers and preprints may also be found by searching my name on the arXiv.

- Bott-Taubes/Vassiliev cohomology classes by cut-and-paste topology, submitted. I recover (an integer lattice of) all the "Bott-Taubes/Vassiliev" cohomology classes of Cattaneo, Cotta-Ramusino, and Longoni as integer-valued classes. I also construct mod-p classes which need not be mod-p reductions of integer-valued classes. These methods could lead to counting formula for finite-type invariants, and potentially new nontrivial mod-p invariants (or cohomology classes).
- Milnor invariants of string links, trivalent trees, and configuration space integrals, with Ismar Volic, submitted. We show that the correspondence between trivalent trees and Milnor's link homotopy invariants of string links can be realized by configuration space integrals. This recovers some results of Habegger and Masbaum, but using configuration space integrals instead of the Kontsevich integral. We also produce nontrivial cohomology classes in spaces of links in Euclidean spaces of dimension at least 4.
- Homotopy string links and the kappa-invariant,
with Fred Cohen, Rafal
Komendarczyk, and Clay
Shonkwiler,
*Bull. Lond. Math. Soc.*, 2017. We prove a string-link analogue of a conjecture of Koschorke. This work uses a way of multiplying maps of configurations of points, which is very similar to the multiplication used in my paper below with Budney, Conant, and Sinha. - Embedding
calculus knot invariants are of finite type, with Ryan Budney,
Jim Conant, and
Dev
Sinha,
*Algebr. & Geom. Top*, 2017. We show that the Taylor tower for the knot space (in the sense of Goodwillie functor calculus) yields finite-type knot invariants. An important step is constructing a homotopy-commutative multiplication on the Taylor tower. - Homotopy
Bott-Taubes integrals and the Taylor tower for the spaces of knots and
links,
*J. Homotopy Related Structures*, 2016. This paper originated from the second half of my PhD thesis, with a modification to incorporate the refinement and main result in my paper on the Milnor triple linking number for string links (see below). - A colored
operad for string link infection, joint with John Burke,
*Algebr. & Geom. Top.*, 2015. We generalize Budney's splicing operad from splicing by long knots to infection by long links. We then obtain a decomposition of a subspace of 2-component long links, using a prime decomposition of isotopy classes of 2-component long links, obtained in joint work with Blair below. - A prime
decomposition theorem for the 2-string link monoid, with Ryan Blair and
John Burke,
*J. Knot Theory Ramif.*, 2015. We consider (isotopy classes of) 2-component long links under the operation of stacking. Unlike for knots, this monoid is nonabelian, but we were nonetheless able to obtain a prime decomposition theorem for it. - The Milnor
triple-linking number of string links by cut-and-paste topology,
*Algebr. & Geom. Top.*, 2014. I obtain the Milnor triple linking number for long links via a refinement of the "homotopy-theoretic configuration space integrals" of my PhD thesis. I later used this refinement to obtain many cohomology classes in spaces of knots and links in Euclidean spaces of dimension at least 4 (see above). This paper also describes the triple linking number as roughly the degree of a map from a 6-sphere to a quotient of the product of three 2-spheres. - Configuration
space integrals and the cohomology of the space of homotopy string
links, with Brian Munson and Ismar
Volic,
*J. Knot Theory Ramif.*, 2013. We use configuration space integrals to produce both isotopy classes and link-homotopy classes of long links in 3-dimensional space, as well as cohomology classes in both spaces ofembeddings and spaces of link maps of long 1-manifolds in Euclidean spaces of dimension at least 4. - A homotopy-theoretic view of Bott-Taubes integrals and
knot spaces,
*Algebr. & Geom. Top.*, 2009. This is roughly the first half of my PhD thesis, where I construct cohomology classes in the space of knots, with arbitrary coefficients (or even arbitrary cohomology theories with respect to which a certain "Bott-Taubes bundle" is orientable).

- Systematic identification of statistically significant
network measures, with Etay Ziv, Manuel Middendorf, and Chris
Wiggins,
*Phys. Rev. E*, 2005. We developed a new computational method for producing large numbers of features of a network, by considering words up to a certain length in the adjacency matrix and several operations on it. - Discriminative Topological Features Reveal Biological
Network Mechanisms, with Manuel Middendorf, Etay Ziv, Carter
Adams, Jennifer Hom, Chaya Levovitz, Greg Woods, Linda Chen, and
Chris Wiggins,
*BMC Bioinformatics*, 2004. We mapped networks into a high-dimensional space using the features from the paper above and then applied machine learning techniques to study networks from data, as well as models of them from the literature.