The next meeting of the Mathematical Foundations of Informatics seminar will be held on June 27th, 2023, at 2 p.m. in Room 278 of the Institute of Mathematics and Informatics. A talk on: The Erdős Box Problem and the Combinatorial Nullstellensatz will be delivered by Dr. Alexey Gordeev, guest researcher. Abstract. The Erdős box problem can be formulated as follows: how many points of {1,2,…,n}^m can we take so that for every m-dimensional box (hyperrectangle with sides parallel to coordinate axes) at least one of its vertices is not taken? When m is fixed and n increases, an order of growth of this number is known only in the case m=2. I will talk about Alon’s Combinatorial Nullstellensatz and its connection with the Erdős [...]

The next meeting of the Mathematical Foundations of Informatics seminar will be held on May 10, 2023, at 3 p.m. (UTC+2) in Room 503 of the Institute of Mathematics and Informatics. A talk on: Ternary self-dual codes, Hadamard matrices and related designs will be delivered by Prof. Vladimir D. Tonchev, Michigan Technological University, Houghton, USA. Abstract.

The next meeting of the Mathematical Foundations of Informatics seminar will be held on March 9, 2023, at 3 p.m. (UTC+2) in Room 503 of the Institute of Mathematics and Informatics. A talk on Introduction to the dimer model on the plane: scaling limit and conformal invariance will be delivered by Dr. Mikhail Basok, visiting researcher under the PIKOM program. Abstract: Dimer model is a classical model in planar statistical physics. Given a finite graph, the model is described as a probability distribution on the set of dimer covers (=perfect matchings) of the graph. In the case when the graph is planar each dimer cover is described with the so-called height function, which is a certain function on the faces of the graph. In this [...]

The next meeting of the Mathematical Foundations of Mathematics Seminar will be held on July 5th, 2022, at 2:00 pm (UTC+3) in the Conference Room of IMI-BAS. Prof. Alexander Barg from the University of Maryland will deliver a lecture on Remarks on the 1st linear programming bound for binary codes Abstract: The "linear programming bound" on the rate of binary codes (1977) is a fundamental result in coding theory that continues to attract attention to this day, with new proofs appearing every now and then. I will discuss 2 proofs from about 2006-08, appearing in arXiv:cs/0512025 (Barg-Nogin) and arXiv:math/0702425 (Navon and Samorodnitsky). Both proofs are based on Fourier analytic arguments on the Boolean cube and exhibit interesting parallels and differences (none of them actually [...]