RTG: Geometry and Topology

University Of Notre Dame, Notre Dame IN

Investigators

Abstract

The goal of this Research Training Group project is to establish a comprehensive collection of programs to augment the research training of undergraduates, graduate students, and postdoctoral fellows in the geometry and topology research group at the University of Notre Dame. A Math for Everyone lecture series aims to popularize mathematical ideas within the entire Notre Dame undergraduate community, leading to increased interest in STEM careers. Greater interaction with undergraduates at other institutions through the Math Club exchange program, exposure to advanced material through directed reading with graduate students, and summer undergraduate workshops are intended to get undergraduates to experience the creative aspects of mathematical research. Another program, coupled to the summer undergraduate workshops, will target talented undergraduate mathematics majors, especially from traditionally underrepresented groups, to increase diversity in the mathematics graduate program. Beginning graduate students will have access to a summer program to review necessary background material and build relationships with older graduate students. A unified vision of topology and geometry will be cultivated by the topology and geometry survey series and mini workshops, benefiting postdocs and senior researchers as well as graduate students. Mentoring activities will ensure that graduate students and postdoctoral associates are well-prepared for their future teaching and professional duties. The five investigators have research interests covering a broad range of areas from geometric and global analysis to homotopy theory and quantum field theory. The research activities of this project have the potential to foster unique collaborations between the investigators, their postdoctoral associates, and students, taking advantage of the group's wide mathematical expertise. Research involving loop spaces and field theories will develop new geometric applications to state of the art methods in homotopy theory. These topics dovetail with investigations of manifolds that admit positive Ricci curvature, and a planned study of Kahler-Einstein and other special metrics has connections to physics. Research investigating random Morse functions will develop connections between probability and geometry. The project's activities and programs will foster a unified vision of geometry and topology among the group members.