EMSW21-RTG: Unified Approach to Training in Geometry

University Of Texas At Austin, Austin TX

Investigators

Abstract

Abstract Award: DMS-0636557 Principal Investigator: Daniel S. Freed, Sean M. Keel, Lorenzo A. Sadun, Karen K. Uhlenbeck The UT Geometry Group Research Training Grant is a vertically integrated program to enhance the training of undergraduates, graduate students, and postdoctoral associates at the University of Texas and, through publication on the web, beyond. The nine faculty members of the Group will initiate new activities at all levels. Included is a new distinguished lecture series, Perspectives in Geometry, which will be widely disseminated. The Geometry Group at UT has long taken a unified perspective on the field. Our seminars reflect our approach: they include a healthy mix of ideas from algebraic geometry, differential geometry, global linear and nonlinear analysis, representation theory, and topology. Often concepts and inspiration from theoretical physics play a role as well. The RTG training activities are designed to promote this view of geometry and, more broadly, of mathematics and science to young mathematicians. Mathematics, the study of Number and Space, lies at the foundation of science and technology. Geometry, the study of Space, has long had connections with and applications to the real world. In the ancient world measurement was introduced to facilitate commerce; more advanced concepts, such as trigonometry, were introduced to understand the stars. In our modern world advanced ideas in Geometry underlie abstract theories in physics and also have more immediate practical implications, for example in coding theory, computer graphics, etc. Effective training of the next generation of Geometers is vital for the continued development of this field, both within mathematics and for external applications. The University of Texas Geometry Group Research Training Grant (RTG) promotes a unified view of the field. Through local activities in Austin, and via dissemination on the web, the RTG will enhance training at all levels.