A new five-year, $1.72 million Research Training Group (RTG) grant from the National Science Foundation's (NSF) Division of Mathematical Sciences expands possibilities for an interdisciplinary Ohio State working group in algebraic topology, applied topology and related fields.

Matthew Kahle, associate professor, mathematics, is the project's principal investigator.

Tamal Dey, professor, mathematics and computer science and engineering (CSE); Michael Davis, professor, mathematics; Facundo Mémoli, associate professor, mathematics and CSE; and Yusu Wang, associate professor, CSE; are co-principal investigators.

In recent years, algebraic topology — the study of shape via algebraic constructions — has found a number of surprising applications both within mathematics and beyond. Most notably, algebraic topology has provided powerful new methods for detecting and describing shape and structure in complex and high-dimensional data.

The NSF-RTG award, shared between the Departments of Mathematics and Computer Science and Engineering, supports work performed in an emergent and highly collaborative, dynamic interdisciplinary research environment. It also provides support for postdocs, graduate students and undergraduate researchers.

“We have a culture of collaboration here. Faculty in the mathematics and CSE departments jointly run the TGDA (Topology, Geometry, and Data Analysis) seminar, have co-authored papers, and have had a successful track record gaining funding for grant proposals written together in the past,” said Kahle. “But this grant will support our activities on a larger scale. It is especially exciting that we will be able to support PhD students and postdocs.”                                                                                           

“We will leverage our new research directions and interdisciplinary collaborations to develop new curricula and programs to provide young mathematicians and computer scientists with the background required to enter research in novel fields,” said Mémoli.                                       

All agree that the heart of the project is an emphasis on mentoring at all levels. "The program also places a strong emphasis on developing writing and communication skills, particularly for postdoctoral researchers and graduate students involved in the research group," Kahle said.

The researchers’ vision is to build an environment that mentors early-stage mathematicians in theoretical core disciplines of topology, as well as applied and interdisciplinary aspects of topology. The curriculum resulting from this project will serve as a model for programs across the country. Inclusion and development of applied areas will train students for innovative careers in both academia and industry.

The grant’s principal investigators recently hosted a conference at Ohio State’s Mathematical Biosciences Institute, “Topology, geometry, and data analysis,” supported by another NSF-DMS grant. Researchers from around the world presented recent and groundbreaking work.