My Research Group

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, physics and other fields.

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.

Group Leader

Peter Bubenik

  • topological data analysis – theory and applications

Affiliated Faculty

Cory Brunson

  • computational topology, geometric statistics, systems medicine

Current Postdocs

Jonathan Bush

  • topological data analysis

Matthew Wheeler

  • topological data analysis, deep neural networks, mathematics in biology and medicine

Current Graduate students

jose

Jose Bouza

  • Department of Computer and Information Science and Engineering
  • topological data analysis,  computer vision, deep learning
 alex

Alexander Elchesen

  • topological data analysis – theory and applications
kuz

Iryna Hartsock

  • topological data analysis – theory and applications

Current Undergraduate Students

escobar

Jenesis Escobar

Vishweshwar Ramakumar

Alumni

Former Postdocs

 michael

Michael Catanzaro

  • Group member as postdoc 2016-2018
  • Assistant Professor, Iowa State University
  • Applied topology, stochastic topology, mathematical physics
hull

Michael Hull

  • Group member as postdoc 2018-2019
  • Assistant Professor, University of North Carolina – Greensboro
  • Geometric group theory, topological data analysis
thomas

Ashleigh Thomas

  • Group member as postdoc 2019-2021
  • topological data analysis, multi-parameter persistent homology, mathematical biology

Former Graduate Students

 

Leo Betthauser

Parker Edwards

  • Group member as graduate student 2016-2020
  • PhD, University of Florida, Department of Mathematics, 2020
  • Dissertation: A New Palette for Persistence Landscapes
  • Robert and Sara Lumpkins Postdoctoral Research Associate at University of Notre Dame

Alexander Wagner

Nikola Milicevic

  • Group member as graduate student 2016-2021
  • PhD, University of Florida, Department of Mathematics, 2021
  • Dissertation: Embedding, Approximating, and Visualizing Persistence Modules
  • Postdoctoral Scholar, Pennsylvania State University

Former Undergraduates

cesar

Cesar Cardoso

  • Group member as undergraduate student 2019-2020
  • now a graduate student at University of Notre Dame, Data Science MS
david

David Freeman

  • Group member as undergraduate student 2019-2020
  • now a PhD student in Atmosphere Ocean Science and Mathematics at NYU’s Courant Institute of Mathematical Sciences
 patel

Dhruv Patel

  • Group member as undergraduate student 2015-2017 and graduate student 2017-2018
  • now a graduate student at University of North Carolina at Chapel Hill, Department of Statistics
 copy

Sam Rizzo

  • Group member as undergraduate student 2016-2018
  • now a graduate student at Vanderbilt University, Department of Mathematics
 whittle

Benjamin Whittle

  • Group member as undergraduate student 2015-2018
  • working for Ernst and Young
cillero

Ana Pilar Ysasi Cillero

  • Group member as an undergraduate student, 2019
  • Visiting student from Spain
  • currently a graduate student at the University of Chicago, Master of Science in Analytics

Past Visitors

 vergili

Tane Vergili

  • Group member as visiting researcher, 2016-2017
  • Faculty in the Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey