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 metric geometry, linear algebra, commutative algebra, category theory, representation theory, real analysis, and probability. There are crucial connections with statistics, algorithms, and machine learning. We are also interested in applications in biology, geospatial imaging, 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.

Current Members

jose

Jose Bouza

  • Graduate student, Department of Computer and Information Science and Engineering
bubenik

Peter Bubenik

  • Faculty
 alex

Alexander Elchesen

  • Graduate student
  • topological data analysis, metrics
escobar

Jenesis Escobar

  • Undergraduate student
kuz

Iryna Hartsock

  • Graduate student
  • topological data analysis
 nikola

Nikola Milicevic

  • Graduate student
  • topological data analysis, homological algebra, sheaf theory

Vishweshwar Ramakumar

  • Undergraduate student
thomas

Ashleigh Thomas

  • Postdoctoral fellow
  • topological data analysis, multi-parameter persistent homology, mathematical biology
wheeler

Matthew Wheeler

  • Postdoctoral fellow
  • topological data analysis, deep neural networks, gauge theory

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 208-2019
  • Assistant Professor, University of North Carolina – Greensboro
  • Geometric group theory, topological data analysis

Former Graduate Students

leo

Leo Betthauser

 parker

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

wagner

Alexander Wagner

  • Group member as graduate student 2016-2020
  • PhD, University of Florida, Department of Mathematics, 2020
  • Dissertation: Embedding, Approximating, and Visualizing Persistence Modules
  • Phillip Griffiths Assistant Research Professor at Duke 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