ECHT: Electronic Computational Homotopy Theory Research Community

PROJECT SUMMARY Overview Since 2017, the electronic Computational Homotopy Theory (eCHT) research community has brought graduate students, postdoctoral associates, and faculty from around the globe together to interact and collaborate regularly in a virtual environment. The goal of the project is to expand the reach and increase the e?ectiveness of the eCHT community. By its very nature, the project is distributed amongst people at a wide variety of institu- tions. Wayne State University is the host institution. Researchers at U. Colorado, Cornell U., Reed C., Texas A&M U., UCLA, UC San Diego, U. Chicago, UIUC, U. Kentucky, U. of Notre Dame, U. of Rochester, and Wayne State U have commited to participate. The project is managed by a PI, 3 co-PIs, and 8 additional senior personnel. Each year, 2-4 graduate students and 2-4 postdoctoral associates at these, and perhaps other, institutions will be supported by the project. Funded students and associates will have formal advising and mentoring relationships with faculty at their home institutions as well as faculty at other institutions. These students and associates will organize and conduct eCHT activi- ties including graduate courses, reading seminars, research seminars, and an online summer research program targeted at undergraduate students. More broadly, numerous mathemati- cians with interests in computational homotopy theory will participate in various supported activities. Intellectual Merit 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 e?ective computation of these invariants, both for general classes and in very speci?c cases. One central example is the computation of the stable homotopy groups of spheres. The eCHT research community will focus on this type of computational problems in homotopy theory. In the modern era, machine computation is a tool of growing importance in homotopy theory. The eCHT research community will support the use of machines in the study of homotopy theory. The scienti?c content of the proposal can a?ord to be narrowly focused because partici- pants are drawn from a large pool. Broader Impacts Online communities will grow in importance in 21st century pure mathematics research. Online communities can reach new audiences and take advantage of e?ciencies that are not accessible to traditional departments. This project will: • demonstrate to stakeholders that online research communities are a viable and ef- fective means for conducting mathematical research. • experiment with di?erent types of online programs to determine which are the most e?ective at engaging participants and positively impacting their long-term careers. • determine whether online communities are more e?ective than traditional depart- ments at reaching certain audiences, especially with regard to U.S. citizens, na- tionals, and permanent residents and with regard to groups that are historically underrepresented in the mathematical sciences.