Traditionally, academic research communities are built around departments within universities, requiring participants to be in physical proximity. However, modern telecommunications allow people to interact productively in new ways, and online communities will play a growing role in research in the 21st century.

The National Science Foundation recently awarded a Research Training Group (RTG) grant to a multi-institution project that intends to capitalize on communication channels that expanded in the wake of the COVID-19 pandemic. The Illinois Department of Mathematics is pleased to have its own faculty participating in this new frontier of research, via Vesna Stojanoksa, associate professor and co-principal investigator for the project, named “Electronic Computational Homotopy Theory Research Community.” Her co-investigators include Dan Isaksen (Wayne State University), Bert Guillou (University of Kentucky), and J.D. Quigley (Cornell University).

This project will develop online relationships and collaborations, with the goal of creating a self-sustaining online research community in pure mathematics. The major advantages of such a system are that online communities can reach new audiences and take advantage of efficiencies that are not accessible to traditional research communities.

The scientific theme of the project is computational homotopy theory. One aspect of modern homotopy theory is the study of algebraic invariants that inform on the structure of geometric objects. Part of this theory involves the effective computation of these invariants, both for general classes and in very specific cases. One central example is the computation of the stable homotopy groups of spheres. The electronic Computational Homotopy Theory (eCHT) research community will focus on these types of computational questions in homotopy theory and will support machine computation, a tool of growing importance in homotopy theory. The participants in the program will be drawn from an exceptionally large pool.

The eCHT community will conduct online courses, reading seminars, and research seminars, as well as an undergraduate research program. Under the supervision of senior personnel from different institutions, graduate students and postdoctoral associates will manage eCHT activities. Students and postdoctoral associates will be advised and mentored by the senior personnel in a collaborative online environment.

The funding will be used to support graduate students and postdocs at several participating universities, namely Wayne State (where the award is based), but also at the University of Illinois Urbana Champaign. Other participating universities include University of California-Los Angeles, University of California-San Diego, University of Colorado at Boulder, University of Notre Dame, University of Kentucky, Cornell University, University of Rochester, Reed College, and Texas A&M University.