RTG: Algebra, Geometry, and Topology at UIC

University Of Illinois At Chicago, Chicago IL

Investigators

Abstract

The Research Training Group in Algebra, Geometry, and Topology at the University of Illinois at Chicago (UIC) will conduct a suite of activities spanning educational levels from high school to postdoctoral. Faculty will lead graduate and postdoctoral research in algebraic geometry, commutative algebra, topology, and algebraic topology. Activities will include conferences, learning seminars, and workshops to bridge the gap between coursework and current research. Undergraduate students will be involved in mathematical research through projects in a Mathematical Computing Laboratory and summer research opportunities. Professional development workshops will help students and postdoctoral fellows prepare for success in their future careers. To recruit the next generation of talented students into the mathematical sciences, the project activities will include high school research projects, Sonia Kovalevsky Day workshops, an Undergraduate Mathematics Symposium, and participation in the UIC Math Olympiad Project enrichment program for gifted students in grades 7-12. The program will develop mentoring activities in association with the UIC Emerging Scholars Program and the Association for Women in Mathematics to improve retention and to increase the proportion of female and minority students and postdocs in the mathematical workforce. The field of algebraic geometry is among the most fundamental and active areas of research mathematics. Algebraic geometers study the properties of geometric objects defined by algebraic equations, using tools from algebra, analysis, and topology. Techniques in algebraic geometry have developed into important tools for resolving questions in number theory, complex geometry, string theory in mathematical physics, cryptography, and computer-aided geometric design. This Research Training Group (RTG) project will train undergraduates, graduate students, and postdoctoral fellows in algebraic geometry and the related fields of commutative algebra, topology, and algebraic topology. The RTG activities aim to integrate these young researchers into the mathematical community. It is expected that the students and postdoctoral researchers trained in the program will make significant contributions to these important fields, including the understanding of moduli spaces, birational geometry, characteristic-p techniques, and the topology of three- and four-manifolds. 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.