Turdibayev Rustam Mirzaliyevich

Dr. Rustam Turdibaev specializes in non-associative algebras. His research focuses primarily on the structural properties and classification of Leibniz, n-Lie, and n-ary Leibniz algebras. His work explores the internal properties of these algebraic structures, including their derivations, automorphisms, and cohomology. Additionally, he investigates the invariants of matrix pairs and their geometric invariant theory quotients using the associated Poisson algebra structures.

PhD in Mathematics — University of Santiago de Compostela, Spain (2013–2016)

Integrated PhD Program in Mathematical Sciences (coursework) — Constructor University (formerly Jacobs University Bremen, Germany) (2011–2013)

M.Sc. in Mathematics — National University of Uzbekistan (2009–2011)

B.Sc. in Mathematics — National University of Uzbekistan (2005–2009)

1. F. Eshmatov, X. García-Martínez, and R. Turdibaev, Noncommutative Poisson structure and invariants of matrices, Advances in Mathematics, 469 (2025), Paper No. 110212, 20 pp arXiv
2. Z. Normatov and R. Turdibaev, Calogero–Moser spaces and the invariants of two matrices of degree 3, Transformation Groups, 30(1) (2025), 393–411 arXiv
3. X. García-Martínez, Z. Normatov, and R. Turdibaev, The ring of invariants of pairs of 3x3 matrices, Journal of Algebra, 603 (2022), 201–212.
4. F. Eshmatov, X. García-Martínez, Z. Normatov, and R. Turdibaev, On the coordinate rings of Calogero–Moser spaces and the invariant commuting variety of a pair of matrices, Results in Mathematics, 80(3) (2025), Paper No. 68, 23 pp arXiv
5. R. Turdibaev, On the coordinate ring of the invariant anti-commuting variety, Linear and Multilinear Algebra, 73(16) (2025), 3667–3681.
6. M. S. Kim and R. Turdibaev, Some theorems on Leibniz n-algebras from the category Un(Lb), Algebra Colloquium, 28(1) (2021), 155–168 arXiv
7. R. Turdibaev, Bipartite graphs and the structure of finite-dimensional semisimple Leibniz algebras, International Electronic Journal of Algebra, 26 (2019), 122–130 arXiv
8. X. García-Martínez, R. Turdibaev, and T. Van der Linden, Do n-Lie algebras have universal enveloping algebras?, Journal of Lie Theory, 28(1) (2018), 43–55 arXiv
9. T. Kurbanbaev and R. Turdibaev, Some Leibniz bimodules of sl2, Journal of Algebra and Its Applications, 19(4) (2020), Paper No. 2050064.
10. Z. Normatov and R. Turdibaev, Poisson algebra structure on the invariants of pairs of matrices of degree three, Journal of Algebra and Its Applications, 22(3) (2023), Paper No. 2350065.

Undergraduate & Graduate Courses:

Foundations and Applications of Geometry • Discrete Mathematics • Engineering Mathematics • Linear Algebra • Calculus • Basic Statistics

Categorical Algebra • Theory of Modules

1. Invariants of Pairs of 4 x 4 Matrices, INdAM workshop "Polynomial Identities and Related Topics" (PI-ART 2025), September 8–12, 2025, Rome, Italy.
2. Invariants of anti-commuting pairs of matrices, Summer Jovens Investigadores em Matemática Days, July 7–11, 2025, University of Coimbra, Portugal.
3. GIT quotients of some matrix pairs, Algebra, Combinatorics and Number Theory Seminar, July 4, 2025, Centro de Matemática da Universidade do Porto, Portugal.
4. Noncommutative Poisson structure and invariants of matrices, Conference on Theoretical and Computational Algebra, June 29 – July 3, 2025, University of Évora, Portugal.
5. Noncommutative Poisson structure and invariants of matrices, Contributed Talk at 9th European Congress of Mathematics (9ECM), July 14 – 19, 2024, Seville, Spain.
6. Defining relations of invariants of two 4 x 4 matrices, Workshop: "Combinatorics in algebraic structures: Invariant theory and its applications", November 30 – December 1, 2023.
7. The ring of invariant polynomials on two matrices of degree 4, Sixth EACA International School on Computer Algebra and its Applications, July 18–21, 2023, CITMAga, Santiago de Compostela, Spain.
8. Poisson structure on the invariants of pairs of matrices, Non-Associative Algebras and Related Topics II, Universidade de Coimbra, 2022, Portugal.
9. Bipartite graphs and the structure of finite-dimensional semisimple Leibniz algebras, Central Asia Joint Meeting in Mathematics & International Doctoral Academic Forum, September 15–20, 2019, Sichuan University, Chengdu, China.
10. On algebraic properties of the human ABO-blood group inheritance pattern, XV Encuentro de Álgebra Computacional y Aplicaciones (EACA 2016), June 22–24, 2016, Logroño, Spain.
11. On algebraic properties of the human ABO-blood group inheritance pattern, Seminario García-Rodeja, May 18, 2016, Santiago de Compostela, Spain.
12. Leibniz cohomology of Leibniz algebras in low degrees, EACA’s Third International School on Computer Algebra and its Applications, January 18–21, 2016, Seville, Spain.

1. Scientific Title: In recognition of my scientific contributions, and following the recommendation of the V. I. Romanovskiy Institute of Mathematics, I was awarded the title of "Senior Scientific Researcher" by the Supreme Attestation Committee of the Republic of Uzbekistan on October 20, 2021.
2. Mathematical Olympiads: I have been deeply involved in university-level competitive mathematics, serving as the Deputy Chairman of the Jury for the first Al-Khorezmi International Mathematical Olympiad for University Students in 2018. I also served as the Team Leader for Uzbekistan at the International Mathematics Olympiad (IMO) in 2019 and 2020, and as Observer-A in 2021, for which I received a distinction from the Ministry of Public Education of Uzbekistan.
3. Mentorship & Research Programs: From 2017 to 2019, I served as a mentor for the International Research Experience for Students (IRES) program in Uzbekistan, hosted by California State University, Fullerton. I guided undergraduate students from institutions including Princeton, Vanderbilt, Rice, and Sonoma State in research on homological algebra, leading to several joint publications.