# Research////////////////////////////////////////////

My research interests include topological and geometric combinatorics, stochastic topology, topological statistical mechanics, and geometric group theory. I am also interested in topological data analysis and applications of algebraic topology in general.

My research has frequently been supported by NSF. I am currently the PI on a TRIPODS+X:RES grant on "Thermodynamic Phases and Configuration Space Topology" (2019–2021), and an RTG grant on "Algebraic Topology and its Applications" (2016–2021)). I am also Senior Personnel on a TRIPODS Phase I grant on "Discovering Structure, Shape, and Dynamics in Data" (2017–2020).

Almost all of my mathematical writing is available in preprint form on the arXiv.

### Papers

*To appear in Random Structures & Algorithms*. arXiv:1901.08488.

*Geombinatorics*. Aug 2019. arXiv:1807.10231.

*International Mathematics Research Notices (IMRN)*. May 2019. arXiv:1201.0425.

*Experimental Mathematics*. Jun 2018. arXiv:1710.05683.

*Journal of Applied and Computational Topology*. Jun 2018. arXiv:1409.4734.

*Discrete & Computational Geometry*. Apr 2018. arxiv:1509.03871.

*Book chapter for Handbook of Discrete & Computational Geometry (3rd edition)*. Nov 2017. arXiv:1607.07069.

*Annals of Applied Probability*. Oct 2017. arXiv:1509.04347.

*Discrete & Computational Geometry*. May 2017. arXiv:1308.6232.

*Homology, Homotopy and Applications*. Jan 2016. arXiv:1501.03759.

*Random Structures & Algorithms*. Jan 2016. arXiv:1301.1324.

*Geombinatorics*. Jul 2015. arXiv 1409:1278.

*AMS Contemporary Volumes in Mathematics, Algebraic Topology: Applications and New Directions*. Nov 2014. arXiv:1301.7165.

*Annals of Mathematics*. Aug 2014. arXiv:1207.0149.

*Journal of Topology*. Feb 2014.

*Homology, Homotopy and Applications*. May 2013. arXiv:1009.4130.

*International Mathematics Research Notices (IMRN)*. Feb 2013. arxiv:1108.3061.

*Journal of Topology and Analysis*. Nov 2012. arXiv:1012.5316.

*Annals of Combinatorics*. Oct 2012.

*Physical Review E*. Jan 2012. arxiv:1301.7165.

*Discrete & Computational Geometry*. Jan 2011. arXiv:0910.1649.

*Journal of the American Mathematical Society*. Jan 2011. arXiv:0711.2704.

*Geombinatorics*. Oct 2009. arXiv:0811.2449.

*Journal of Combinatorial Theory, Series A*. Sep 2007. arXiv:math/0512077.

*Geombinatorics*. Oct 2005.