"This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5)."
The University of Wisconsin Algebraic Geometry and Number Theory Research Training Grant will integrate the research activities of this core part of the faculty into a unified training program involving postdoctoral faculty, graduate students, and undergraduates from UW and elsewhere. The eight faculty members involved in the grant cover the entire spectrum of number theory and algebraic geometry, from automorphic forms to arithmetic geometry to interfaces with mathematical physics and theoretical computer science. The team will run a collaborative undergraduate research laboratory in which undergraduates work together with graduate students in the focus areas with the goal of producing publishable research and easing the transition to graduate school. For US undergraduates outside our program who are admitted to UW for Ph.D. study, we will offer a Summer Enhancement Program, in order to prepare the students for qualifiying exams as quickly as possible so that their research can begin without delay. Once the research is underway, we will provide teaching relief to these students with RTG fellowships. In addition, we will run annual graduate student conferences, focusing on number theory and algebraic geometry in alternate years, where students from UW and other schools will get up to speed with currrent developments in all aspects of this rapidly changing subject in a collaborative environment, and gain professional skills in lecturing and presentation. Taken together, these programs will enable us to enhance our already strong record of producing very strong Ph.D. graduates in number theory and algebraic geometry. We will also offer new postdoctoral fellowships, aimed at bringing top new Ph.D.s in the focus areas to Wisconsin to serve as a critical bridge between senior faculty and students, and allowing us to continue our tradition of energetic mentorship of postdocs, and research collaboration between postdocs and graduate students.
Number theory -- the study of numbers, their patterns, their properties -- is one of the oldest branches of mathematics, in which we still wrestle with some of the problems that vexed the Greeks. Algebraic geometry -- the study of equations and the shapes traced out by their graphs -- is much younger, but still goes back centuries to the time of Rene Descartes. But with the revolutionary work of Alexander Grothendieck and his collaborators in the 1960s, a magnficent unity between these two seemingly unrelated subjects was exposed. This new paradigm has become so central to modern mathematics that the boundary between number theory and algebraic geometry has been almost entirely erased. The University of Wisconsin is a center of cutting-edge research in this new hybrid subject. The RTG will allow us to leverage our research strength to create a completely integrated training program for new researchers in the area, starting at the undergraduate level and continuing all the way up to young Ph.D.s in the pre-tenure phase of their career
