My Research Group | Peter Bubenik

Our research

We study a range of problems in topological data analysis. At the graduate level and beyond, our main focus is on developing tools and their underlying mathematics. At the undergraduate level the main focus is on applying topological data analysis and computations. However, there is a mix of these aspects at all levels.

In addition to using algebraic topology, there are connections with many areas of mathematics, including linear algebra, general topology, metric geometry, commutative algebra, category theory, representation theory, functional analysis, measure theory, and probability. There are crucial connections with statistics, algorithms, and machine learning. We are also interested in applications in biology, computer science, material science, physics and other fields.

Congratulations!

to Nikola Milicevic for accepting a tenure-track Assistant Professor position at the University of Texas El Paso, Department of Mathematical Sciences, starting in Fall 2025
to Wanchen Zhao for winning the Best Poster Award at the Graduate Poster session of the 2025 Joint Mathematical Meetings. Here is her winning poster.
to Johnathan Bush for starting a tenure-track Assistant Professor position at James Madison University, Deparment of Mathematics and Statistics in Fall 2024
to Parker Edwards for starting a tenure-track Assistant Professor position at Florida Atlantic University, Department of Mathematics and Statistics in Fall 2023

Interested in joining?

If you are interested in joining my group, please take a look at my Topological Data Analysis page, my Research page, and some of the references therein. If you are a student at the University of Florida, please email me to schedule at time to meet. If you have been offered admission to UF and are considering your options, please email me to schedule a Zoom meeting. If you are interested in applying to our graduate program, please do so, and mention my name in your application letter. Note that admissions to our graduate program are decided at the department level.

Group Leader

Peter Bubenik

topological data analysis – theory and applications

Current Graduate students

Zach Thomas

topological data analysis – theory and applications

Himanshu Yadav

topological data analysis – theory and applications

Wanchen Zhao

topological data analysis – theory and applications

Alumni

Former Postdocs

Jonathan Bush

Group member as postdoc 2021-2024
Research topics at UF: topological data analysis, metric thickenings, mathematical biology
Subsequent position: Assistant Professor, James Madison University

Matthew Wheeler

Group member as postdoc: 2019-2020
Research topics at UF: topological data analysis, deep neural networks, mathematics in biology and medicine
Subsequent position: Postdoctoral Fellow, University of Florida, College of Medicine

Ashleigh Thomas

Group member as postdoc 2019-2021
Data Scientist, Vericast
Research topics at UF: topological data analysis, multi-parameter persistent homology, mathematical biology

Michael Hull

Group member as postdoc 2018-2019
Research topics at UF: geometric group theory, topological data analysis
Subsequent position: Assistant Professor, University of North Carolina – Greensboro

Michael Catanzaro

Group member as postdoc 2016-2018
Research topics at UF: applied topology, stochastic topology, mathematical physics
Subsequent position: Assistant Professor, Iowa State University
Current position: Senior Scientist, Geometric Data Analytics

Former PhD Students

	Iryna Hartsock Graduate student, 2018-2023 Research at UF: topological data analysis – theory and applications Dissertation: Topology of persistence diagram spaces and stem cell differentiation patterns Postdoctoral Fellow, Moffitt Cancer Center and Research Institute
	Alexander Elchesen Graduate students 2017-2022 topological data analysis – theory and applications Dissertation: Universality of the Wasserstein distances and relative optimal transport Postdoctoral Fellow, Colorado State University
	Nikola Milicevic Group member as graduate student 2016-2021 PhD, University of Florida, Department of Mathematics, 2021 Dissertation: Embedding, Approximating, and Visualizing Persistence Modules Subsequent position: Postdoctoral Scholar, Pennsylvania State University and ICERM Current position: Assistant Professor, University of Texas El Paso
	Parker Edwards Group member as graduate student 2016-2020 PhD, University of Florida, Department of Mathematics, 2020 Dissertation: A New Palette for Persistence Landscapes Subsequent position: Robert and Sara Lumpkins Postdoctoral Research Associate at University of Notre Dame Current position: Assistant Professor, Florida Atlantic University
	Alexander Wagner Group member as graduate student 2016-2020 PhD, University of Florida, Department of Mathematics, 2020 Dissertation: Embedding, Approximating, and Visualizing Persistence Modules Subsequent position: Phillip Griffiths Assistant Research Professor at Duke University Current position: Research Scientist, Teledyne Techonologies
	Leo Betthauser Group member as graduate student 2015-2018 PhD, University of Florida, Department of Mathematics, 2018 Dissertation: Topological Reconstruction of Grayscale Images Current position: Senior Research Scientist at Microsoft Research

Former Masters Students

Jose Bouza

Group member 2018-2021
MS, University of Florida, Department of Computer and Information Science and Engineering
topological data analysis, computer vision, deep learning

Dhruv Patel

Group member as undergraduate student 2015-2017 and graduate student 2017-2018
subsequent position: graduate student at University of North Carolina at Chapel Hill, Department of Statistics

Former Undergraduates

	Arjun Singh Group member as an undergraduate student 2025 research topic at UF: random matrices and brain networks
	Jiun Cho Group member as an undergraduate student 2021-2023 subsequent position: graduate student at University of Florida, Department of Mathematics
	Ryan Elkind Group member as an undergraduate student 2021-2022
	Jenesis Escobar Group member as an undergraduate student 2020-2022
	Max Zhang Group member as an undergraduate student 2020-2021 subsequent position: undergraduate student at Cornell University, Departments of Mathematics and Computer Science
	Vishweshwar Ramakumar Group member as an undergraduate student 2020-2021
	Cesar Cardoso Group member as undergraduate student 2019-2020 subsequent position: graduate student at University of Notre Dame, Data Science MS
	David Freeman Group member as undergraduate student 2019-2020 subsequent position: PhD student in Atmosphere Ocean Science and Mathematics at NYU’s Courant Institute of Mathematical Sciences
	Ana Pilar Ysasi Cillero Group member as an undergraduate student, 2019 Visiting student from Spain subsequent position: graduate student at the University of Chicago, Master of Science in Analytics
	Sam Rizzo Group member as undergraduate student 2016-2018 subsequent position: graduate student at Vanderbilt University, Department of Mathematics
	Benjamin Whittle Group member as undergraduate student 2015-2018 subsequent position: Ernst and Young