Tatiana Ivanova

Ph.D., Mathematics, Algebra, Moscow State University, Russia, 1979
M.A., Mathematics, Algebra, Sofia University, Bulgaria
Fulbright Research Scholar at Massachusetts Institute of Technology (MIT), USA, 1994-95

I am on a reasearch sabbatical leave for AY 2018-19 and will be visiting
(i) Max-Plank Institute for Mathematics in the Sciences, Leipzig, Germany, September 2018 -January, 2019, and 
(ii) Max-Plank Institute for Mathematics, Bonn, Germany, February-June, 2019

Teaching Interest at AUBG:  
Introduction to Abstract Algebra; Calculus III - Multivariate Calculus and Geometry; Advanced Linear Algebra; Topics in Abstract Algebra; Galois Theory; Introduction to Lie Algebras; Ideals, Varieties and Algorithms; Representation Theory;

Graduate courses taught in Research Universities: 
Combinatorial Methods in Non-commutative Algebra; Algebra;  Set-Theoretic solutions of the Yang-Baxter equation and related algebraic objects.

Research Interest
Non-commutative algebra and applications for quantum groups, non-commutative geometry, symbolic computation

Topics of study include
Set-theoretic solutions of the Yang-Baxter equation and related algebraic objects;  braided groups;   Artin-Schelter regular algebras; quadratic algebras; the study of concrete algebras, groups, monoids, presented via generators and relations; rewriting systems;  computational aspects of non-commutative algebra, non-commutative Groebner bases

Some Recent Publications

Tatiana Gateva-Ivanova,  (2018) . Set-theoretic solutions of the Yang-Baxter equation, Braces and Symmetric groups.  Advances in Mathematics  338  (2018), 649—701. https://doi.org/10.1016/j.aim.2018.09.005
Tatiana Gateva-Ivanova,  (2018) . A combinatorial approach to noninvolutive set-theoretic solutions of the Yang-Baxter equation,  arXiv preprint arXiv:1808.03938 (2018). https://arxiv.org/abs/1808.03938
Cedó, F., Tatiana Gateva-Ivanova and Agata Smoktunowicz  (2018).   Braces and symmetric groups with special conditions. J. Pure and Applied Algebra, 222, (2018)  3877-3890. https://doi.org/10.1016/j.jpaa.2018.02.012
Cedó, F. , Tatiana Gateva-Ivanova and Agata Smoktunowicz .  (2017). On the Yang–Baxter equation and left nilpotent left braces.  Journal of Pure and Applied Algebra, 221 (4), 751–756. https://doi.org/10.1016/j.jpaa.2016.07.014
Tatiana Gateva-Ivanova, & Gunnar Fløystad. (2014). Monomial algebras defined by Lyndon words. Journal of Algebra, 403, 470–496.  https://doi.org/10.1016/j.jalgebra.2014.01.012
Tatiana Gateva-Ivanova, & Peter Cameron.  (2012).  Multipermutation Solutions of the Yang-Baxter Equation. Communications in Mathematical Physics, 309 (3), 583–621. https://doi.org/10.1007/s00220-011-1394-7
Tatiana Gateva-Ivanova. (2012). Quadratic algebras, Yang-Baxter equation, and Artin-Schelter regularity. Advances in Mathematics, 230 (4–6), 2152–2175. https://doi.org/10.1016/j.aim.2012.04.016


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