RESEARCH INTERESTS
My research interests are algebra, universal algebra and topology. In particular I am interested in binary algebraic structures related to the solutions of the Yang-Baxter equation, as quandles and skew braces.
Published papers
Acri E., B.M., Skew of size p^2q I: abelian type, Algebra Colloquium Vol.29 (2), (2022).
B. M., Connected quandles of size pq and 4p, Osaka journal of Mathematics 59 (1), 145-175, (2022)
Acri E., B.M., Skew of size p^2q II: non-abelian type, Journal of algebra and its applications, Vol. 21, No. 3 (2022).
B. M., Medial and semimedial left-quasigroups, Journal of Algebra and Its Applications Vol. 21, No. 02, 2250021 (2022).
B. M., Fioravanti S., Mal'cev classes of left quasigroups and quandles, Quasigroups and related systems, vol.29 No. 2 (2021).
Bianco G., B. M., On connected quandles of prime power order, Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry volume 62, 555–586 (2021).
B. M., Stanovský D., Commutator theory for racks and quandles, Journal of the Mathematical Society of Japan, Vol. 73, No. 1, 41-75 (2021).
B. M., Crans A., Nasybullov T., Whitney G., Quandles with orbit series conditions, Journal of Algebra 567, 284-309 (2021).
B. M., Kynion M., Stanovský D., Vojtěchovský P., Latin Involutive solutions to the Yang-Baxter equation, Journal of Algebra, Volume 565 (1), Pages 128-159 (2021).
Acri E., B. M., Skew Braces of size pq, Communications in Algebra, Volume 48, Issue 5, 1872-1881 (2020).
B. M., Principal and doubly homogeneous quandles, Monatshefte für Mathematik 191, 691–717 (2020).
B. M., Dikranjan D., Generalized Heisenberg groups and self-duality, Questions and answers in general topology 37 Number 2, 89-108 (2019).
B. M., A. Crans, G. Whitney, On the structure of Hom quandles, Journal of Pure and Applied Algebra, Volume 223, Issue 11, 5017-5029 (2019).
B. M., Vojtěchovský P., Simply connected latin quandles, Journal of Knot Theory and its Ramifications, Volume No.27, Issue No. 11 (2018).
Accepted for publications
B.M., Jedlička P., Central nilpotency of skew braces accepted by Journal of Algebra and its applications.
B.M., Superconnected left quasigroups and involutory quandles, accepted by Communications in Algebra.
B. M., Stanovský D., A universal algebraic approach to quandle covering, accepted by Journal of knots and its ramifications
Submitted
B.M., Dikranjan D., Toller, D., Groups with cofinite Zariski topology and potential density.
B. M., Cattabriga A., Horvat E., Knot quandle decomposition along a torus.
B.M., Cattabriga A., On the axioms of Singquandles.
Preprints
In progress
B. M., Cattabriga A., On oriented singquandles and related algebraic structures.
B.M., Two Galois connections for left quasigroups.
B.M., A conjecture on superconnected quandles.