{"id":22,"date":"2012-09-05T11:22:33","date_gmt":"2012-09-05T15:22:33","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/template\/?page_id=22"},"modified":"2026-09-30T06:57:57","modified_gmt":"2026-09-30T10:57:57","slug":"research","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/henry-adams\/research\/","title":{"rendered":"Research"},"content":{"rendered":"\n
\n

Research<\/h2>\n\n\n\n

My research interests are in topology, geometry, and data analysis. More specific subfields of interest include applied topology, computational topology and geometry, combinatorial topology, metric geometry, machine learning, and sensor networks. I advance the study of geometric simplicial complexes (Vietoris-Rips and \u010cech) and Gromov-Hausdorff distances, forming bridges between applied topology and nearby areas of mathematics such as quantitative topology, geometric group theory, Riemannian geometry, metric geometry, optimal transport, equivariant topology, and combinatorics. I apply topology to data analysis, machine learning, and sensor networks, and I have experience working with datasets arising in interdisciplinary research areas such as computational chemistry, computer vision, collective motion in biological systems, sensor networks, and knowledge-guided machine learning.<\/p>\n\n\n\n

I am an editor for the journals Homology, Homotopy and Applications<\/a>, Experimental Mathematics<\/a>, and Foundations of Data Science<\/a>.<\/p>\n\n\n\n

At UF I am a member of the topology research group<\/a>, which hosts regular seminars<\/a>.<\/p>\n\n\n\n

You may find my research papers in my CV<\/a>, on arXiv<\/a>, or on Google Scholar<\/a>. Here is my PhD thesis<\/a> and a research statement<\/a>.<\/p>\n\n\n\n

See Section 4 of the ACM SIGACT News, Open Problems Column, Vol. 48, No. 3, 2017<\/a> for some open (and some “closed”) problems I am interested in.<\/p>\n\n\n\n

I. Books<\/h3>\n\n\n\n\n\n
\n\u25cfCounting Rocks! An Introduction to Combinatorics<\/i>. With Kelly Emmrich, Maria Gillespie, Shannon Golden, and Rachel Pries (2023).
\n[Book Webpage,<\/font><\/a> Book PDF,<\/font><\/a> Videos 2025,<\/font><\/a> Videos 2020]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n

II. Book chapter<\/h3>\n\n\n\n\n\n
\n\u25cfTopological data analysis<\/i>. With Johnathan Bush and Joshua Mirth. Book chapter in Data Science for Mathematicians<\/i>, editor Nathan Carter, Chapman & Hall\/CRC, New York (2020).
\n[Publisher Link,<\/font><\/a> Software,<\/font><\/a> Software tutorial]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n

III. Preprints<\/h3>\n\n\n\n\n\n
\n\u25cfGromov-Hausdorff Distance Between Euclidean Unit Balls.<\/i> With Kushagri Sharma (2026).
\n[arXiv:2609.09652]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfTight upper bound on d<\/i>GH<\/sub>(S1<\/sup>,S2k+1<\/sup>): GPT’s short proof. (2026).<\/i>
\n[arXiv:2608.21587]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfGromov-Hausdorff distance and Jung constant of finite-dimensional normed spaces.<\/i> With Semeon A. Bogatyi, Florian Frick, Daniil A. Ilyukhin, Alexander O. Ivanov, Ivan N. Mikhailov, Alexey A. Tuzhilin, Anton A. Vikhrova (2026).
\n[arXiv:2607.18447]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfVietoris thickenings and complexes of manifolds are homotopy equivalent.<\/i> With Alexandre Karassev and Žiga Virk (2025).
\n[arXiv:2512.23108]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfAn optimal Brouwer’s fixed point theorem for discontinuous functions.<\/i> With Florian Frick (2025).
\n[arXiv:2512.14934]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfQuantifying discontinuity.<\/i> With Florian Frick, Michael Harrison, Nikola Sadovek, Matt Superdock (2025).
\n[arXiv:2511.07636]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfVietoris-Rips complexes of ellipses at larger scales.<\/i> With Julian Carvajal, Jake Rhodes, Niccolo Turillo, Jingkai Ye, Raymond Ying (2025).
\n[arXiv:2511.09471]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfAnti-Vietoris-Rips metric thickenings and Borsuk graphs.<\/i> With Alex Elchesen, Sucharita Mallick, and Michael Moy (2025).
\n[arXiv:2503.08862,<\/font><\/a> Poster]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfGromov-Hausdorff distances between quotient metric spaces.<\/i> With Armando Albornoz, Glenn Bruda, Jianda Du, Lodewyk Jansen van Rensburg, Alejandro Leon, Saketh Narayanan, Connor Panish, Chris Rugenstein, Martin Wall (2024).
\n[arXiv:2410.14938]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfPersistent equivariant cohomology.<\/i> With Evgeniya Lagoda, Michael Moy, Nikola Sadovek, and Aditya De Saha (2024).
\n[arXiv:2408.17331,<\/font><\/a> Slides]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfTime-varying spaces and mobile sensor networks.<\/i> With Tia Karkos (2024).
\n[arXiv:2311.15392]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfVietoris-Rips complexes of regular polygons.<\/i> With Samir Chowdhury, Adam Jaffe, and Bonginkosi Sibanda (2021).
\n[arXiv:1807.10971,<\/font><\/a> Slides]<\/font><\/a> \n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n

IV. Research papers<\/h3>\n\n\n\n\n\n
\n\u25cfHomotopy connectivity of \u010cech complexes of spheres.<\/i> With Ekansh Jauhari and Sucharita Mallick. Discrete & Computational Geometry 76:1742-1762 (2026).
\n[Publisher Link,<\/font><\/a>\narXiv:2502.00122,<\/font><\/a> Slides]<\/font><\/a>\n<\/td>\n		 <\/td>\n\n\n<\/td>\n<\/tr>\n<\/tbody><\/table>\n\n\n\n\n\n
\n\u25cfGromov-Hausdorff distances, Borsuk-Ulam theorems, and Vietoris-Rips complexes.<\/i> With Johnathan Bush, Nate Clause, Florian Frick, Mario G\u00f3mez, Michael Harrison, R. Amzi Jeffs, Evgeniya Lagoda, Sunhyuk Lim, Facundo M\u00e9moli, Michael Moy, Nikola Sadovek, Matt Superdock, Daniel Vargas, Qingsong Wang, Ling Zhou. Accepted to appear in Algebraic & Geometric Topology (2026).
\n[arXiv:2301.00246,<\/font><\/a> Video]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfLower bounding the Gromov-Hausdorff distance in metric graphs.<\/i> With Sushovan Majhi, Fedor Manin, Žiga Virk, Nicol\u00f2 Zava. Proceedings of the 42nd Symposium on Computational Geometry, 3:1-3:16 (2026).
\n[Publisher Link, <\/font><\/a>arXiv:2411.09182, <\/font><\/a> Slides by Nicol\u00f2 Zava]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfTopological preservation in temporal link prediction.<\/i> With Marco Campos, Casey Doyle, Dan Krofcheck, Sarah Simpson, Michael Xi, William Ott. Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science, Proceedings of Machine Learning Research 321:56-78 (2026).
\n[Publisher Link,<\/font><\/a> Open Review]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfHausdorff vs Gromov-Hausdorff distances.<\/i> With Florian Frick, Sushovan Majhi, Nicholas McBride. Discrete & Computational Geometry 75 (2026), 1217-1246.
\n[Publisher Link,<\/font><\/a> arXiv:2309.16648,<\/font><\/a> Slides,<\/font><\/a> Video]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfElementary methods for persistent homotopy groups.<\/i> With Mehmet Ali Batan, Mehmetcik Pamuk, Hanife Varli. Discrete & Computational Geometry 76 (2026), 866-895.
\n[Publisher Link,<\/font><\/a> arXiv:1909.08865]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfVietoris-Rips complexes of torus grids.<\/i> With Adenike Yeside Adetowubo, Hector Barriga-Acosta, Ziqin Feng, John Sterling. Mediterranean Journal of Mathematics 22:173 (2025), DOI 10.1007\/s00009-025-02945-9.
\n[Publisher Link,<\/font> <\/a>arXiv:2502.07134]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfThe connectivity of Vietoris-Rips complexes of spheres.<\/i> With Johnathan Bush and Žiga Virk. Journal of Applied and Computational Topology 9:15 (2025), 1-26, DOI 10.1007\/s41468-025-00214-y.
\n[Publisher Link,<\/font><\/a> arXiv:2407.15818,<\/font><\/a> Slides]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cf\u010cech complexes of hypercube graphs.<\/i> With Samir Shukla and Anurag Singh. Homology, Homotopy and Applications 27 (2025), 83-105.
\n[Publisher Link,<\/font><\/a> arXiv:2212.05871]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfEfficient evader detection in mobile sensor networks.<\/i> With Deepjyoti Ghosh, Clark Mask, William Ott, and Kyle Williams. SIAM Journal on Applied Dynamical Systems 24 (2025), 557-586.
\n[Publisher Link,<\/font><\/a> arXiv:2101.09813,<\/font><\/a> Software]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfThe topology of projective codes and the distribution of zeros of odd maps.<\/i> With Johnathan Bush and Florian Frick. Michigan Mathematical Journal 74 (2024), 775-796.
\n[Publisher Link,<\/font><\/a> arXiv:2106.14677]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfThe persistent topology of optimal transport based metric thickenings.<\/i> With Facundo M\u00e9moli, Michael Moy, and Qingsong Wang. Algebraic & Geometric Topology 24 (2024), 393-447.
\n[Publisher Link,<\/font><\/a> arXiv:2109.15061]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfLower bounds on the homology of Vietoris-Rips complexes of hypercube graphs.<\/i> With Žiga Virk. Bulletin of the Malaysian Mathematical Sciences Society, 47:72 (2024).
\n[Publisher Link,<\/font><\/a> arXiv:2309.06222]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfAdditive energy functions have predictable landscape topologies.<\/i> With Brittany Story, Biswajit Sadhu, and Aurora Clark. Journal of Chemical Physics 158 (2023), 164104.
\n[Publisher Link,<\/font><\/a> ChemRxiv Link]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfA Primer on Topological Data Analysis to Support Image Analysis Tasks in Environmental Science.<\/i> With Lander Ver Hoef, Emily King, and Imme Ebert-Uphoff. Artificial Intelligence for the Earth Systems 2 (2023), e220039.
\n[Publisher Link,<\/font><\/a> arXiv:2207.10552]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfGeometric approaches to persistent homology.<\/i> With Baris Coskunuzer. SIAM Journal on Applied Algebra and Geometry 6 (2022), 685-710.
\n[Publisher Link,<\/font><\/a> arXiv:2103.06408]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfMetric thickenings and group actions.<\/i> With Mark Heim and Chris Peterson. Journal of Topology and Analysis 14 (2022), 587-613.
\n[Publisher Link,<\/font><\/a> arXiv:1911.00732]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfVietoris thickenings and complexes have isomorphic homotopy groups.<\/i> With Florian Frick and Žiga Virk. Journal of Applied and Computational Topology 7 (2022), 221-224.
\n[Publisher Link,<\/font><\/a> arXiv:2206.08812]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfOn Vietoris-Rips complexes of hypercube graphs.<\/i> With Micha\u0142 Adamaszek. Journal of Applied and Computational Topology 6 (2022), 177-192.
\n[Publisher Link,<\/font><\/a> arXiv:2103.01040]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfSupport vector machines and Radon’s theorem.<\/i> With Elin Farnell and Brittany Story. Foundations of Data Science 4 (2022), 467-494, DOI 10.3934\/fods.2022017.
\n[Publisher Link,<\/font><\/a> arXiv:2011.00617]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfCapturing dynamics of time-varying data via topology.<\/i> With Lu Xian, Chad Topaz, and Lori Ziegelmeier. Foundations of Data Science 4 (2022), 1-36.
\n[Publisher Link,<\/font><\/a> arXiv:2010.05780]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfThe persistent homology of cyclic graphs.<\/i> With Sophia Coldren and Sean Willmot. International Journal of Computational Geometry and Applications 32 (2022), 1-37.
\n[Publisher Link,<\/font><\/a> arXiv:1812.03374]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfThe middle science: Traversing scale in complex many-body systems.<\/i> With Aurora E Clark, Rigoberto Hernandez, Anna I Krylov, Anders Niklasson, Sapna Sarupria, Yusu Wang, Stefan M Wild, and Qian Yang. ACS Central Science 7 (2021), 1271-1287.
\n[Publisher Link,<\/font><\/a> Supplemental Cover Photo]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfLions and contamination, triangular grids, and Cheeger constants.<\/i> With Leah Gibson and Jack Pfaffinger.\n
Journal version:<\/u> Ellen Gasparovic, Vanessa Robins, and Kate Turner, eds., Research in Computational Topology 2<\/i>, AWM Springer series, volume 30 (2021). [Publisher Link]<\/font><\/a>\n
Conference version:<\/u> In 37th European Workshop on Computational Geometry (2021), 7:1-7:6. [arXiv:2012.06702,<\/font><\/a> Conference Version Link]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfTopology applied to machine learning: From global to local.<\/i> With Michael Moy. Frontiers in Artificial Intelligence; Machine Learning and Artificial Intelligence 4 (2021), 668302.
\n[Publisher Link,<\/font><\/a> arXiv:2103.05796]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfRepresentations of energy landscapes by sublevelset persistent homology: An example with n-alkanes.<\/i> With Joshua Mirth, Yanqin Zhai, Johnathan Bush, Enrique G Alvarado, Howie Jordan, Mark Heim, Bala Krishnamoorthy, Markus Pflaum, Aurora Clark, and Y Z. Journal of Chemical Physics 154 (2021), 114114.
\n[Publisher Link,<\/font><\/a> arXiv:2011.00918,<\/font><\/a> Software]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfAn adaptation for iterative structured matrix completion.<\/i> With Lara Kassab and Deanna Needell.\n
Journal version:<\/u> Foundations of Data Science 3 (2021), 769-791.\n
Conference version:<\/u> 54th Asilomar Conference on Signals, Systems, and Computers (2021), 1451-1456.
\n[Journal Version Link,<\/font><\/a> Conference Version Link,<\/font><\/a> arXiv:2002.02041,<\/font><\/a> Software]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfOperations on metric thickenings.<\/i> With Johnathan Bush and Joshua Mirth. In: Spivak, D., Vicary, J. (eds), Applied Category Theory, Electronic Proceedings in Theoretical Computer Science 333:261-275 (2021).
\n[Publisher Link,<\/font><\/a> arXiv:2101.10489]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfMetric thickenings, Borsuk-Ulam theorems, and orbitopes.<\/i> With Johnathan Bush and Florian Frick. Mathematika 66 (2020), 79-102.
\n[Publisher Link,<\/font><\/a> arXiv:1907.06276,<\/font><\/a> Slides1,<\/font><\/a> Slides2,<\/font><\/a> Poster]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfA fractal dimension for measures via persistent homology.<\/i> With Manuchehr Aminian, Elin Farnell, Michael Kirby, Chris Peterson, Joshua Mirth, Rachel Neville, and Clayton Shonkwiler. In: Baas N., Carlsson G., Quick G., Szymik M., Thaule M. (eds), Topological Data Analysis<\/a>. Abel Symposia, Springer vol 15 (2020), 1-32.
\n[Publisher Link,<\/font><\/a> arXiv:1808.01079,<\/font><\/a> Software]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfOn homotopy types of Vietoris-Rips complexes of metric gluings.<\/i> With Micha\u0142 Adamaszek, Ellen Gasparovic, Maria Gommel, Emilie Purvine, Radmila Sazdanovic, Bei Wang, Yusu Wang, and Lori Ziegelmeier.\n
Journal version:<\/u> Journal of Applied and Computational Topology 4 (2020), 425-454.\n
Conference version:<\/u> Vietoris-Rips and \u010cech complexes of metric gluings<\/i> in Proceedings of the 34th Symposium on Computational Geometry (2018), 3:1-3:15.
\n[Journal Version Link,<\/font><\/a> Conference Version Link,<\/font><\/a> arXiv:1712.06224,<\/font><\/a> Slides]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfMultidimensional scaling on metric measure spaces.<\/i> With Mark Blumstein and Lara Kassab. Rocky Mountain Journal of Mathematics 50 (2020), 397-413.
\n[Publisher Link,<\/font><\/a> arXiv:1907.01379,<\/font><\/a> Poster]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfA torus model for optical flow.<\/i> With Johnathan Bush, Brittany Carr, Lara Kassab, and Joshua Mirth.\n
Journal version:<\/u> Pattern Recognition Letters 129 (2020), 304-310.\n
Conference version:<\/u> On the nonlinear statistics of optical flow<\/i> published in Proceedings of Computational Topology in Image Context, LNCS volume 11382 (2019), 151-165.
\n[Journal Version Link,<\/font><\/a> Conference Version Link,<\/font><\/a> arXiv:1812.00875,<\/font><\/a> Software]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfMetric thickenings of Euclidean submanifolds.<\/i> With Joshua Mirth. Topology and its Applications 254 (2019), 69-84.
\n[Publisher Link,<\/font><\/a> arXiv:1709.02492,<\/font><\/a> Poster]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfOn Vietoris-Rips complexes of ellipses.<\/i> With Micha\u0142 Adamaszek and Samadwara Reddy. Journal of Topology and Analysis 11 (2019), 661-690.
\n[Publisher Link,<\/font><\/a> arXiv:1704.04956,<\/font><\/a> Oberwolfach Preprint,<\/font><\/a> Slides]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfMetric reconstruction via optimal transport.<\/i> With Micha\u0142 Adamaszek and Florian Frick. SIAM Journal on Applied Algebra and Geometry 2 (2018), 597-619.
\n[PDF,<\/font><\/a> Publisher Link,<\/font><\/a> arXiv:1706.04876,<\/font><\/a> Poster,<\/font><\/a> Talk Notes,<\/font><\/a> Slides,<\/font><\/a> Video]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfSweeping costs of planar domains.<\/i> With Brooks Adams and Colin Roberts. In Erin W Chambers, Brittany T Fasy, and Lori Ziegelmeier, eds., Research in Computational Topology<\/i>, pages 71-92, AWM Springer series, volume 13 (2018).
\n[Publisher Link,<\/font><\/a> arXiv:1612.03540]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfPersistence images: A stable vector representation of persistent homology.<\/i> With Sofya Chepushtanova, Tegan Emerson, Eric Hanson, Michael Kirby, Francis Motta, Rachel Neville, Chris Peterson, Patrick Shipman, and Lori Ziegelmeier. Journal of Machine Learning Research 18 (2017), Number 8, 1-35.
\n[PDF of Paper,<\/font><\/a> Publisher Link,<\/font><\/a> arXiv:1507.06217,<\/font><\/a> Software]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfThe Vietoris-Rips complexes of a circle.<\/i> With Micha\u0142 Adamaszek. Pacific Journal of Mathematics 290 (2017), 1-40.
\n[Publisher Link,<\/font><\/a> arXiv:1503.03669,<\/font><\/a> Slides,<\/font><\/a> Poster 1,<\/font><\/a> Poster 2,<\/font><\/a> Talk Video]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfRandom cyclic dynamical systems.<\/i> With Micha\u0142 Adamaszek and Francis Motta. Advances in Applied Mathematics 83 (2017), 1-23.
\n[Publisher Link, arXiv:1511.07832]<\/font><\/a>\n<\/font><\/a><\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfNerve complexes of circular arcs.<\/i> With Micha\u0142 Adamaszek, Florian Frick, Chris Peterson, and Corrine Previte-Johnson. Discrete & Computational Geometry 56 (2016), 251-273.
\n[PDF of Paper,<\/font><\/a> Publisher Link,<\/font><\/a> arXiv:1410.4336]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfEvasion paths in mobile sensor networks.<\/i> With Gunnar Carlsson. International Journal of Robotics Research 34 (2015), 90-104.
\n[Publisher Link,<\/font><\/a> PDF of Paper,<\/font><\/a> Slides,<\/font><\/a> Poster,<\/font><\/a> Talk Video,<\/font><\/a> Highlight,<\/font><\/a> Multimedia]<\/font><\/a> \n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfNudged elastic band in topological data analysis.<\/i> With Atanas Atanasov and Gunnar Carlsson. Topological Methods in Nonlinear Analysis 45 (2015), 247-272.
\n[Publisher Link,<\/font> <\/a>arXiv:1112.1993,<\/font><\/a> Slides,<\/font><\/a> Software,<\/font><\/a> Javadoc,<\/font><\/a> Data]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfJavaplex: A research software package for persistent (co)homology.<\/i> With Andrew Tausz and Mikael Vejdemo-Johansson. Proceedings of ICMS 2014, Han Hong and Chee Yap (Eds), LNCS 8592 (2014), 129-136. Software available at http:\/\/appliedtopology.github.io\/javaplex\/<\/a>.
\n[Publisher Link]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfOn the nonlinear statistics of range image patches.<\/i> With Gunnar Carlsson. SIAM Journal on Imaging Sciences 2 (2009), 110-117.
\n[Publisher Link,<\/font><\/a> PDF of Paper,<\/font><\/a> Data]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n

V. Press and mathematical writings<\/h3>\n\n\n\n\n\n
\n\u25cfHow to Tutorial-a-thon.<\/i> With Hana Dal Poz Kouřimsk\u00e1, Teresa Heiss, Sarah Percival, and Lori Ziegelmeier. Notices of the American Mathematical Society, Volume 68, Number 9, October 2021.
\n[Print Version]<\/font><\/a>
\n\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfHow do I … develop an online research seminar?<\/i> Notices of the American Mathematical Society, Volume 67, Number 8, September 2020.
\n[Print Version]<\/font><\/a>
\n\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfAnne Manning at CSU wrote a nice press release on my work with the Pattern Analysis Lab at CSU, August 11, 2020.
\n[Press Release]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfTopological data analysis of collective motion.<\/i> With Maria-Veronica Ciocanel, Chad M. Topaz, and Lori Ziegelmeier. SIAM News, January\/February Issue, 2020.
\n[Publisher Link,<\/font><\/a> Print Version]<\/font><\/a>\n<\/td>\n		\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n\n\n
\n\u25cfHere is a research highlight<\/a> from 2014.\n<\/td>\n\u00a0<\/td>\n\n\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n

VI. Software tutorials<\/h3>\n\n\n\n