**Professor:** Kirill Zaynullin

**E-mail:** kirill@uottawa.ca (put ‘FLAG’ in the subject).

**Lectures: 11:00-13:00 on 2.02, 5.02, 6.02, 19.02, 20.02, 26.02, 1.03**

**Course material:** The course will be based on* *the lecture notes. See the reference section of the notes for additional reading material.

**Content of the course:** This course is a general introduction to the theory of algebraic cycles and motives of twisted flag varieties.

Part1

We first recall basic concepts related to root systems, (lectures 1-2)

Chevalley groups, linear algebraic groups, and the associated projective homogeneous varieties (lectures 2-3)

Part 2

We then discuss twisted flag varieties — our main object of study, e.g., generalized Severi-Brauer varieties, anisotropic quadrics, and twisted flag varieties (lecture 4)

As the next step, we introduce their Chow groups, and the associated category of Grothendieck-Chow motives (lecture 5)

Part 3

We provide several classical examples of motivic decompositions of twisted flag varieties (lecture 6)

At the end of our course, we intend to demonstrate how a modern Schubert calculus technique (e.g. nil-Hecke modules) can be applied to obtain new/different proofs of motivic decompositions (lectures 7)

**Final exam: **There will be a home-taken written final exam. It will consist of exercises posted in the lecture notes.

The exam will be collected online before the due time March 11.