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

February 27

Introduction; presentation of topics

March 6

Three theorems in convex geometry

March 13

Counting perfect matchings in planar graphs

March 20

Van der Waerden's permanent conjecture

April 3

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

April 10

Bootstrap percolation in the integer grid

May 1

Borsuk's conjecture

May 15

Shannon capacity of C

_{5}
May 22

Upper bounds on permanents via entropy

May 29

Crossing lemma and its applications

June 5

The Kakeya problem over finite fields