Summer Programs on Commutative Algebra and Its Interactions with Algebraic Geometry and on p-adic L-functions and Eigenvarieties

University Of Notre Dame, Notre Dame IN

Investigators

Abstract

The Center for Mathematics at the University of Notre Dame will run a 2019 program on Commutative Algebra and Its Interactions with Algebraic Geometry and a 2020 program on p-adic L-functions and Eigenvarieties. In 2019, the program will consist of an undergraduate summer school from May 28 to June 1, a graduate level summer school from June 3 to June 14, and an international research conference from June 16 to June 21. In 2020, the program will consist of a one week undergraduate summer school, a one week graduate level summer school, and a one week conference. The purpose of the programs is to introduce students at various levels to important ideas in commutative algebra and in number theory, which are both active and central areas of mathematics with many connections to other areas of mathematics and to science. The goal of the undergraduate week is to expose undergraduates to fundamental ideas they would not normally see until graduate school. We will introduce material through a combination of lectures and active learning sessions, with the aim of inspiring students to take advanced courses or reading courses when they return to university. The graduate summer schools are geared towards graduate students in the field, and will be followed by a conference which will present current research on topics developed in the earlier weeks. The goal is to inspire graduate students to explore connections between different areas of mathematics, beyond the level they may see in their own graduate program. We also hope to bring together graduate students and postdocs from different institutions so they can develop productive professional relationships. We note that many students from previous Center for Mathematics at Notre Dame programs have gone on to get a Ph.D. in mathematics. The goal of the program Commutative Algebra and Its Interactions with Algebraic Geometry is to educate undergraduates and to bring together researchers interested in the area. The first week will introduce useful techniques and examples amenable to calculation. The graduate summer school will introduce cutting edge topics and computational tools using the Macaulay2 program, and the conference will emphasize exciting new research developments. The topics for the 2020 program on p-adic L-functions and Eigenvarieties are not completely set, but will include an interactive program for students, and advanced topics such as the Iwasawa main conjecture, the exceptional zero conjecture, and eigenvarieties. The program website is available at www3.nd.edu/~cmnd/programs/https://centerformath.nd.edu/scientific-events-and-programs/ 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.