Lecturers: Robert Hancock and Jan Volec
Course starts: Mo 16.3. at 9:20
Location: Dejvice campus – FIT, Thákurova 9, 160 00 Prague (Faculty of Information Technology, Czech Technical University)
Room: T9:364 (see Plan of the 3rd floor)
Covered topics: Graham-Pollak Theorem, Polynomial Method, Cap set, Combinatorial Nullstellensatz, Sensitivity Theorem.
References: Lecture notes Algebraic Methods in Combinatorics by Benny Sudakov for his graduate course at ETH. Book Linear Algebra Methods in Combinatorics by Babai and Frankl, and Book Extremal Combinatorics (Part III – The Linear Algebra Method) by Jukna. A draft of the first edition as a PDF.
| Day | Part 1 ‑ Lecture | Part 2 ‑ Exercises |
|---|---|---|
| Mo 16.3. | 9:30-12:30 Jan: Introduction, Basic applications of the Linear Algebra Method (Light-switches, Oddtowns & Eventowns, Fisher's ineq, Sylvester-Gallai) | 14:30-16:00 |
| Tu 17.3. | 9:30-12:30 Robert: The finite field Kakeya Problem, Intro to the Polynomial Method (Frankl-Wilson) | 14:30-16:00 |
| We 18.3. | 9:30-12:30 Jan: Applications of Chevalley-Warning Theorem (Erdős–Ginzburg–Ziv, Berge-Sauer) and Combinatorial Nullstellensatz (Cauchy-Davenport, Permanent lemma) | N/A |
| Th 19.3. | 9:30-12:30 Robert: The Slice Rank and a solution to the Capset Problem, Sunflower-free sets | 14:30-16:00 |
| Fr 20.3. | 9:30-12:30 Jan: Proofs of Chevalley-Warning and Nullstellensatz, Snevily conjecture for prime-ordered fields | 14:30-14:55 Q&A 15:00-16:00 Final Test - solutions: TBU |
We 18.3. 15:15 – Excursion to Technical Museum (Kostelní 42, 170 00 Prague; see Google maps)
Fr 20.3. 17:00-19:00 – Farewell dinner at Rector's office (Jugoslavských partyzánů 3, 160 00 Prague; see Google maps)