The course is conducted in English。

This course will introduce students to the problems and methods of extremal combinatorics. The fundamental extremal problem asks how large a structure can be without containing a forbidden substructure. This very flexible problem arises in many different settings and enjoys several applications. A variety of methods have been developed to tackle them, and this course will pay special attention to the probabilistic, linear algebraic and (briefly) topological methods.

The first half of the course will continue from the previous semester’s Graph Theory course, taking a deeper look into Ramsey and Turán Theory. The second half will cover problems from extremal set theory, including the central theorems of Erdős-Ko- Rado and Sperner. Alongside the important results, equal attention will be paid to the development of methods used to prove them.

Successful completion of Graph Theory I (or an equivalent course) Familiarity with linear algebra and (discrete) probability Some knowledge of topology would be a bonus, but is not required

4-6 hours

The course will be self-contained, with notes provided online

Sources for supplemental reading: - “The probabilistic method” (Alon-Spencer) - “Extremal Combinatorics” (Jukna) - “A Course in Combinatorics” (Van Lint-Wilson) - "Graph Theory” (Diestel) - “Linear Algebra Methods in Combinatorics” (Babai-Frankl)