The main aim of this school is to introduce young researchers and graduate students to fundamental and advanced tools of homological algebra as applied to non-commutative algebra and number theory, with an emphasis on algebraic, geometric, topological, and numerical methods.
Homological algebra studies algebraic invariants and originated in algebraic topology. Since the 1950s, it has been closely linked to category theory, focusing on functorial invariants. In algebraic number theory, Galois cohomology provides insight into Galois modules and groups. In commutative algebra, homological methods analyze how closely an algebra resembles a polynomial or power series algebra. In representation theory, they yield derived equivalence, generalizing Morita equivalence.
This school explores applications of homological algebra, including surface combinatorics, non-commutative algebras, commutative algebra inspired by modularity lifting, Leavitt path algebras, special values and growth of modular L-functions, and Iwasawa theory in arithmetic.