Students' reading seminar
Most people are other people. Their thoughts are someone else's opinions,
their lives a mimicry, their passions a quotation. (Oscar Wilde)
Most people are other people. Their thoughts are someone else's opinions,
their lives a mimicry, their passions a quotation. (Oscar Wilde)
The purpose of the seminars is to learn topics somewhat out of the curriculum of bachelor's studies (mostly in probabilistic and extremal combinatorics) and to learn explaining mathematics to others. Seminar is open to students of any stage and one can join at any moment.
We typically we will meet at the CS Institute (Ústav informatiky, Pod Vodárenskou věží 2; directions)
At the CS Institute, the seminar takes place in room 410 or 419 (third floor).
Default time of the seminar is Friday, 11:30-12:30
--- End of seminar in the spring semester ---
May 24: 10:00 Artem will present an upper bound for hypergraph Ramsey number [7, hypergraph Ramsey numbers]
May 17 10:00 Anna will talk about clique dynamics (her thesis presentation) and then finish the Kruskal-Katona theorem
May 10 10:00 Anna will continue the Kruskal-Katona theorem (for about an hour), Sofiia will talk about hypergraph Ramsey theorem
April 26 10:00 Matas will talk about the Kruskal-Katona theorem on shadows of hypergraphs [4, Chapter 5] thresholds of monotone properties (part 4.2 of Zhao [3])
April 19: no seminar (Spring School)
April 12 10:00, cancelled
April 5 March 22, 11:30, Vova will present 3.1 (Dominating set in graphs) and 3.2 (Heilbronn triangle problem) of Zhao [5]
March 29: no seminar (Good Friday)
March 22, 11:30, Jan Hladký will introduce graph limits
March 15, 10:00, Tim will present Part 2.6 (Crossing numbers) of Zhao [5]
March 8, 11:30, Matas will present Part 2.5 (Unbalancing lights) of Zhao [5]
March 1, 10:00, Sofiia will present proofs of Dirac's theorem and Ore's theorem
[ Break due to university exam session ]
Friday January 5, 11:30-12:30, Matas will talk about subgraph counts in G(n,p)
Friday December 15, 11:30-12:30, Tim will finish §3 (Sperner systems) from Bollobás [4]
Friday December 8, 11:30-12:30, Mariia will start §4 (Littlewood-Offord problem) from Bollobás [4]
Friday December 1, 11:30-12:30, Tim will present most of §3 (Sperner systems) from Bollobás [4]
Friday November 24, 11:30-12:30, Mariia will finish §2 from Bollobás [4]
Monday November 13, 13:00-14:00, Vova will present Section 2.1 in Janson-Luczak-Rucinski [6] (Chernoff inequality)
Monday November 6, 13:00-14:00, Mariia will present beginning of §2 from Bollobás [4]
Monday October 30, 13:00-14:00, Mariia will present beginning of §2 from Bollobás [4] (cancelled)
Monday October 23, 13:00-14:00, Vova will present Part 2.4 (Sampling) of Zhao [5]
Friday May 26, 14:00-15:00 Tomas presented two proof of Turán's theorem, in particular covering 2.3 from Zhao [5].
Friday May 19, 14:00-15:00 Vova will present sections 2.1-2.3 2.1 and 2.2 from Zhao's notes [5]
Friday May 12, 14:00-15:30
Friday May 5, no seminar
Friday April 28, 14:00-15:00 Honza V. will talk about the Lovász Local Lemma
Friday April 21, 14:00-15:00 Honza V.
Friday April 14, 14:00-15:00 Mariia will present existence of graphs with high girth and large chromatic number
Friday April 7, no seminar
Friday March 31, 15:00-16:00, Matas presented upper bound on m(k) (Zhao 1.3) and deduced lower bound on choosability of K_{n,n}
Friday March 24, 14:00-15:00, Vova will present Sperner's theorem (Zhao's notes, section 1.2.1 and extension Zhao's assignement A4)
Friday March 17, 14:00-15:00, Mariia will present Erdős-Ko-Rado theorem and the upper bound for m(k)
Friday March 10, 14:00-15:00, Matas will present the chapter (or part of it) 2 of Matoušek-Vondrák
The probabilistic method:
J. Matoušek, J. Vondrák, The Probabilistic Method
N. Alon, J. Spencer, The Probabilistic Method
Y. Zhao's course Probabilistic Method in Combinatorics at MITOpenCourseWare: lecture notes and assignements
B. Bollobás, Combinatorics: Set Systems, Hypergraphs, Families of Vectors and Combinatorial Probability
Y. Zhao's course 18.226 Probabilistic Methods in Combinatorics on his website: lecture notes
S. Janson, T. Luczak, A. Rucinski. Random graphs. John Wiley & Sons, 2011.
T. Szabó, Extremal Combinatorics and its Methods, lecture notes
Papers to present (suggested by M. Tyomkyn):
Torsten Mütze. A book proof of the middle levels theorem
Tung Nguyen, Alex Scott, Paul Seymour. A note on the Gyárfás-Sumner conjecture
Matt DeVos, Jessica McDonald, Kathryn Nurse. Another proof of Seymour's 6-flow theorem
Thomas Richthammer. Bunkbed conjecture for complete bipartite graphs and related classes of graphs