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 and "Proofs from THE BOOK" by Aigner and Ziegler.
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
March 1
Introduction; presentation of topics
March 8
Two problems about tiling rectangles
March 15
Sperner's theorem and the Littlewood–Offord problem
March 22
Bootstrap percolation in the integer lattice
March 29
Borsuk's conjecture
April 12
Three lemmas in additive combinatorics
May 3
The Kakeya problem over finite fields
May 17
The Erdős–Ko–Rado theorem and the chromatic number of the Kneser graph
May 24
Lattice paths and determinants
May 31
Three theorems in discrete convex geometry
June 7
Shannon capacity of C
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