Overview: The analysis group at Northwestern University has achieved significant growth in the past few years: its members include Laura DeMarco (complex dynamics: co-PI), Ezra Getzler (index theory, quantum field theory: PI), Elton Hsu (stochastic differential geometry), Aaron Naber (Riemannian geometry: co-PI), Valentino Tosatti (PDE and complex geometry), Ben Weinkove (PDE and complex geometry: co-PI), Jared Wunsch (scattering theory and microlocal analysis: co-PI), and Steven Zelditch (spectral theory and eigenfunctions), while other members of the department (Bryna Kra, ergodic theory, Mihnea Popa, algebraic geometry, and Eric Zaslow, mirror symmetry) work in closely allied areas. It is the ambition of this group to attain national leadership in training students and postdoctoral researchers in this field. This proposal for a Research Training Group is centered on the following initiatives: 1) improving the training of undergraduates at Northwestern University in the general field of analysis, and more particularly of analysis on manifolds; 2) enhancing the range of courses available to our undergraduate students, expanding the range of research experiences for undergraduates, and increasing the fraction of our students completing undergraduate theses; 3) creating a summer workshop for advanced undergraduates and incoming graduate students to increase fluency in the language of modern analysis; 4) holding a series of graduate workshops, combining lecture series by distinguished guest lecturers, lectures by our faculty and postdoctoral fellows, and presentations by students on their research; 5) increasing the number of postdoctoral researchers at Northwestern in the field of analysis on manifolds, especially US citizens, and creating channels for them to mentor undergraduates and graduate students. Intellectual Merit: Developments in several fields of analysis have created increased contacts between the faculty, and students, in this group: Riemannian geometry, Kahler and Hermitian geometry, spectral theory of the Laplacian, and symplectic geometry and Gromov-Witten theory. Our department has become, or is becoming, a national center for research in all of these areas, and is strong in a number of allied disciplines which share techniques with these, such as complex dynamics and stochastic differential geometry. This is a timely moment to offer expanded opportunities for undergraduates at Northwestern to learn more about differential geometry and analysis on manifolds, either because of the intrinsic value of this study, or as preparation for study at the doctoral level. Broader Impacts: There is an urgent need to increase the number of US students interested in pursuing the study of analysis, and more specifically, analysis on manifolds. A first goal of this proposal is to provide a rich educational environment, for both undergraduates and graduate students, in this field, mentored by some of the finest recent PhD recipients in the field, who will in turn receive mentoring from our faculty. The larger goal of the proposal is to increase the number of well-prepared US citizens who pursue careers in the mathematical sciences. Our group is well-placed to contribute to this goal: our university attracts a particularly strong group of undergraduates (through its Integrated Science Program); our graduate program has seen a renewal in its reputation, as witnessed by the regular award of NSF Postdoctoral Fellowships to students emerging from the analysis group; and our department now has a well-established postdoctoral progra
|Effective start/end date||7/1/15 → 6/30/22|
- National Science Foundation (DMS‐1502632)
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