RTG: Southern California Geometry and Topology Center

University Of California-Irvine, Irvine CA

Investigators

Abstract

This award will support a series of improvements and new additions to the undergraduate, graduate, and postdoctoral training programs at the University of California at Irvine, formalized as the Southern California Geometry and Topology Center (SCGTC). These are aimed primarily at 1) accelerating research progress in geometry and topology--central areas of contemporary mathematical research with long-standing interactions with mathematical physics and increasing interactions with applications as diverse as data science and video game design--and 2) creating a diverse and vertically integrated pipeline connecting undergraduate and graduate studies to cutting-edge research. As a twice-designated minority serving institution, UC Irvine is uniquely positioned to impact recruitment and retention from minority groups at all levels, and the planned recruitment plan incorporates specific outreach to broaden participation of all students. The projects will support training of graduate students and postdocs in cutting edge techniques, vertically integrated mentorship, and interaction and collaboration amongst them, all aiming at further acceleration of this progress. This award will support a broad research program deepening and seeking further relationships between the theory of existence and regularity of geometric PDE, moduli spaces of canonical geometries, and the arithmetic and topology of complex varieties. In addition to the intrinsic value to these subjects, this fundamental research will have implications for mathematical physics, Hodge theory, K-theory/motives, moduli theory, and complexity of polynomials/arithmetic groups/modular functions. The projects will support training of graduate students and postdocs in cutting edge techniques, vertically integrated mentorship, and interaction and collaboration amongst them, all aiming at further acceleration of this progress. The creation and sharing of educational materials resulting from learning seminars, topics courses, and public lectures will serve as resources for the community. Alongside the research, this award will support efforts to broaden and strengthen a pipeline of students from undergraduate to faculty levels, thus increasing participation in this field and in mathematics in general. Through the capstone research projects and improved mentoring the investigators aim to increase placement of undergraduates into graduate programs, thus increasing participation nationwide. The undergraduate curricular reforms aim to provide the broadest possible introduction to fundamental material required for understanding modern approaches in this area, and these new courses have the potential to serve as a national model. The Winter School will aid in training efforts at UC Irvine and provide students nationwide with exposure to cutting-edge research topics. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.