Principal Investigator: Robion C. Kirby, Peter Teichner
This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
The principal investigators (Robion Kirby and Peter Teichner), with the cooperation of the other senior personnel (Professors Ian Agol, Robert Bryant, Michael Hutchings, Vaughan Jones, John Lott, Constantin Teleman, and Alan Weinstein), propose to establish a research training group of undergraduates, graduate students, postdoctoral fellows, and senior faculty at the UC Berkeley mathematics department in the areas of geometry, topology and operator algebras. The objectives are to improve the recruitment of undergraduates into graduate studies in mathematics, and the training of graduate students and postdoctoral fellows, by establishing a strong, coherent interdisciplinary group in the above areas. These areas are coherent in that they have at their center problems and methods from mathematical physics, such as the count of pseudoholomorphic curves to calculate Seiberg-Witten and Heegaard-Floer invariants of 3- and 4-dimensional manifolds, or the use of Ricci flow for understanding smooth manifolds, or the use of mathematical notions of quantum field theories to describe interesting algebraic topology, like elliptic cohomology.
A major difficulty for young people entering research in mathematics today is the increasingly interdisciplinary nature of the subject and the range of technical tools required. Traditional seminar formats are becoming less effective at training. We will work with the existing strong programs of the mathematics department to create a series of new and restructured activities, ranging from the undergraduate level to advanced research. These will include undergraduate research seminars during the school year led by graduate students under the supervision of senior faculty, undergraduate and graduate summer workshops, elementary level graduate student seminars, a hot topic seminar, and a weekly joint research seminar in which each research talk is preceded by a background lecture.
The areas of geometry, topology and operator algebras covered in this proposal are central to mathematics and mathematical physics. UC Berkeley has an exceptional group of faculty in this area, and a long history of successfully training graduate and undergraduate students. However, these subjects have grown more and more interdisciplinary requiring graduate students to know much more than in the past, and more guidance is required of senior mathematicians. To improve the training of graduate students and postdocs, they should also improve the quality of research that they produce. The cross-group interaction will facilitate a number of interdisciplinary research projects that we intend to pursue, including: Elliptic cohomology and quantum field theory, K-theory and topological field theories, Semi-infinite aspect of elliptic cohomology, and Four-dimensional field theories.
