The area of the school is number theory, broadly understood - analytic, algebraic, combinatorial, with links to groups and geometry.
All of the our course topics lie at thematic intersections. The course on Galois representations will focus on their connections with modular forms and elliptic curves. The course on arithmetic groups will involve familiarizing students with topics in group theory and modular forms. Equidistribution in a diophantine context will be the main subject of a course. Another lecture series will focus on analysis, combinatorics and discrete geometry. The study of curves over finite fields, and the resulting codes, will allow for an accessible introduction to deep issues in algebraic geometry, with immediate applications. Finally, the course on primes, parity and analysis will combine classical tools and the use of entropy and independence.
The plan is, then, to introduce advanced students to a variety of fields and tools and to notable recent developments.
Arrival date is July 8 and departure date is July 21.