Possible topics include but are not restricted to the following:

+ Proof theory for systems of arithmetic and analysis;

+ Reflection principles;

+ Turing--Feferman recursive progressions;

+ Provability logics and algebras;

+ Polymodal provability logic GLP, its fragments and extensions;

+ Conservation results for fragments of arithmetic and analysis;

+ Ordinal notation systems;

+ Provably recursive functions;

+ Combinatorial principles and independence results;

+ Topological and set-theoretic semantics of modal logic;