Introduction to Modular Forms, Summer Term 2022Dr hab. Masha VlasenkoModular forms belong to the most advanced tools of modern arithmetic. First examples were discovered back in XIX century. These are holomorphic functions on the complex plane that, quoting Barry Mazur, "satisfy so many internal symmetries that their mere existence seem like accidents". Such functions appear to be useful in combinatorics (e.g. for studying properties of partition functions), number theory (to prove Fermat's Last Theorem) and other areas of mathematics and theoretical physics (e.g. Monstrous moonshine, sphere packing in higher dimensions, quantum field theory). Modular or, more generally, automorphic forms are key objects in the Langlands Program, a metahypothesis that shapes current development of arithmetic algebraic geometry. Our course is a handy introduction to this theory. During problem sessions students will work on key examples and learn to apply modular forms to various questions. Here is a presentation of this course in Polish. Time: Tuesday, 14:15-16:00 (lecture) 16:15-18:00 (tutorial) starting from March 1 Spring break: April 14-19 Venue: 5870, Faculty of Mathematics of the University of Warsaw, Banacha 2 Assessment: 40 % continuous assessment (tutorial work and written homework), 60 % final exam + extra points for solving the projects. Final exam: Friday, June 24 from 2 to 6 pm in room 2100 at Banacha 2 |