Mathematics Days in Sofia – 2026
Section “Mathematical Logic, Algebra, Number Theory, and Combinatorics”
Participants
Invited Speakers
Ivan Dimitrov, Queen’s University, Canada
- Kalina Mincheva, Tulane University, USA
Contributors
Antun Milas, SUNY-Albany, USA
- Assia Rousseva, Sofia University “St. Kliment Ohridski”, Bulgaria
- Azniv Kasparian, Sofia University “St. Kliment Ohridski”, Bulgaria
Dragan Đokić, University of Belgrade, Serbia
- Elitza Hristova, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
- Erik Paemurru, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
- Georges Tomanov, Institut Camille Jordan, Université Claude Bernard-Lyon 1, France
- Hristo Iliev, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
- Ivan Chipchakov, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
- Ivan Landjev, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
- Lyuba Konova, Sofia University “St. Kliment Ohridski”, Bulgaria
Martin Kassabov, Cornell University, USA
- Nicola Bellumat, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
- Oleg Pikhurko, University of Warwick, UK
- Qëndrim Gashi, University of Maryland, USA
Soowhan Yoon, American University in Bulgaria, Bulgaria
- Tatiana Todorova, Sofia University “St. Kliment Ohridski”, Bulgaria
- Temenoujka Peneva, University of Plovdiv “Paisii Hilendarski”, Bulgaria
- Vasil Zhelinski, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
- Vladimir Mitankin, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
- Wonwoo Kang, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
Program and Abstracts
Interpreting Weyl group elements as inversion sets of positive roots allows for recursive arguments and constructions which remain hidden in the classical approach to Coxeter groups. In this talk I will discuss the notion of an inflation for subsets of positive roots, describe how it applies to Weyl group elements, and will show some applications of this approach.
In this talk, we view the classical Peter-Weyl theorem through the lens of chiral differential operators. As an application, we construct infinitely many minimal Weil-type representations for certain associative algebras, which include the minimal representations of exceptional groups.
We construct a new large family of finitely generated groups with uncountably many values of the following monotone parameters: spectral radius, critical probabilities, and asymptotic entropy. We also present several open problems on other monotone parameters. The construction is quite flexible and is based on limits of marked groups.
This is a joint work with I. Pak.
In this talk I will discuss the status of local-global principles for semi-integral points on orbifold pairs of Markoff type. If time permits, I shall describe how to count Markoff orbifold pairs which satisfy the semi-integral Hasse principle while the corresponding Markoff surface lacks integral points.
This talk is based on a joint work with Justin Uhlemann.
We prove that the rank polynomial of the lattice of order ideals for a loop fence poset is unimodal. This poset arises as the poset of join-irreducibles in the lattice of perfect matchings for loop graphs associated with notched arcs. Equivalently, such polynomials are obtained by specializing all coefficient variables in an F-polynomial to a single variable q. We further establish that the rank polynomial of any tagged arc — whether plain or notched — is not only unimodal but also satisfies a symmetry condition known as almost interlacing. Moreover, we show that unimodality is preserved under certain multiplications of these rank polynomials, and we conjecture that the product of any such rank polynomials remains unimodal.
This is joint work with Kyeongjun Lee and Eunsung Lim.
