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

 Graduate student, Department of Computer and Information Science and Engineering






 Graduate student
 topological data analysis, metrics


Jenesis Escobar


 Graduate student
 topological data analysis


 Graduate student
 topological data analysis, homological algebra, sheaf theory


Vishweshwar Ramakumar


 Postdoctoral fellow
 topological data analysis, multiparameter persistent homology, mathematical biology


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

Alumni
Former Postdocs

 Group member as postdoc 20162018
 Assistant Professor, Iowa State University
 Applied topology, stochastic topology, mathematical physics


 Group member as postdoc 2082019
 Assistant Professor, University of North Carolina – Greensboro
 Geometric group theory, topological data analysis

Former Graduate Students
Former Undergraduates

Cesar Cardoso
 Group member as undergraduate student 20192020
 now a graduate student at University of Notre Dame, Data Science MS


David Freeman
 Group member as undergraduate student 20192020
 now a PhD student in Atmosphere Ocean Science and Mathematics at NYU’s Courant Institute of Mathematical Sciences


Dhruv Patel
 Group member as undergraduate student 20152017 and graduate student 20172018
 now a graduate student at University of North Carolina at Chapel Hill, Department of Statistics


 Group member as undergraduate student 20162018
 now a graduate student at Vanderbilt University, Department of Mathematics


Benjamin Whittle
 Group member as undergraduate student 20152018
 working for Ernst and Young


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

 Group member as visiting researcher, 20162017
 Faculty in the Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey
