In this seminar, the participants will present a variety of classical results in the (widely understood) area of discrete mathematics (graph theory, additive number theory, discrete geometry, etc.) that have short elegant proofs. Among other sources, the topics will be selected from the books "The Art of Mathematics: Coffee Time in Memphis" by Bollobás, "Proofs from THE BOOK" by Aigner and Ziegler, and "Thirty-three Miniatures" by Matoušek

The seminar has no prerequisites, but it will be conducted in English.

B. Bollobás, The Art of Mathematics: Coffee Time in Memphis, Cambridge University Press, 2006

M. Aigner, G. Ziegler, Proofs from THE BOOK, 5th edition, Springer, 2014

J. Matoušek, Thirty-three Miniatures. Mathematical and Algorithmic Applications of Linear Algebra, American Mathematical Society, 2010

March 7

Introduction; presentation of topics

March 14

Counting perfect matchings in planar graphs

March 21

Crossing lemma and its applications

April 11

Three theorems in convex geometry

April 25

Bootstrap percolation in the integer grid

May 2

Sperner's theorem and the Littlewood–Offord lemma

May 9

Three lemmas in additive combinatorics

May 16

Shannon capacity of C

_{5}
May 23

Borsuk's conjecture

May 30

The Erdős–Ko–Rado theorem and the chromatic number of the Kneser graph

Jyne 6

Upper bounds on permanents via entropy

June 13

The Kakeya problem over finite fields