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