The next meeting of the Mathematical Foundations of Informatics seminar will be held on February 8, 2024, at 3:00 p.m. in Room 256 of the Institute of Mathematics and Informatics. A talk on: Extremal problems in Euclidean combinatorial geometry will be delivered by Assoc. Prof. Danila Cherkashin. Abstract.  I will talk about several problems in the intersection of extremal combinatorics and Euclidean geometry. Recent results on the Steiner tree problem, Gilbert-Steiner problem, and Nelson-Hadwiger problem will be presented. The seminar will be streamed at  https://meet.jit.si/IMI-MOI-14400

The next meeting of the Mathematical Foundations of Informatics seminar will be held on November 10, 2023, at 2 p.m. in Room 478 of the Institute of Mathematics and Informatics. A talk on: On induced C_4 -free graphs with high average degree will be delivered by Antonio Girao. Abstract. A long-standing conjecture of Thomassen from the 80's states that every graph with sufficiently high average degree contains a subgraph with high girth and still preserving large enough average degree. This conjecture has only been resolved in the early 2000's by Kühn and Osthus in the first non-trivial case i.e. they showed that for every k , there is f(k) such the every graph with average degree at least f(k) contains a subgraph which [...]

The next meeting of the Mathematical Foundations of Informatics seminar will be held on October 31, 2023, at 4 p.m. in Room 578 of the Institute of Mathematics and Informatics. A talk on: On binary codes with distances d and d+2 will be delivered by Dr. Konstantin Vorobev, IMI - BAS. Abstract. In this work, we consider the problem of determining the exact value of A_2(n, {d, d+2}) defined as the maximal cardinality of a binary code of length n with two possible distances d and d+2 . We prove that for fixed even d and n big enough, an optimal code must be a constant-weight code of weight d/2+1 with possibly no more than one additional codeword of a [...]

The next meeting of the Mathematical Foundations of Informatics seminar will be held on August 22, 2023, at 4 p.m. in Room 503 of the Institute of Mathematics and Informatics. A talk on: Data Attribution: Scaling up and Applications to Defending Against Backdoor Attacks will be delivered by Kristian Georgiev, PhD student at MIT under the guidance of Aleksander Mądry. Abstract. The goal of data attribution is to trace model predictions back to training data. Despite a long line of work towards this goal, existing approaches to data attribution tend to force users to choose between computational tractability and efficacy. That is, computationally tractable methods can struggle with accurately attributing model predictions in non-convex settings (e.g., in the context of deep neural networks), while [...]

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 [...]