Ivanova, Tatiana

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Ivanova, Tatiana

Email Degree From Ph.D., Mathematics, Algebra, Moscow State University, Russia

Courses

  • Elementary Linear Algebra and Analytical Geometry, MAT 105a
  • Elementary Linear Algebra and Analytical Geometry, MAT 105b
  • Introduction to Abstract Algebra, MAT 205a

Research Interests

  • Non-commutative algebra and applications for quantum groups
  • Non-commutative geometry, symbolic computation
  • 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

Education

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

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.

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. Read more.
  • Tatiana Gateva-Ivanova,  (2018) . A combinatorial approach to noninvolutive set-theoretic solutions of the Yang-Baxter equation,  arXiv preprint arXiv:1808.03938 (2018). Read more.
  • 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. Read more.
  • 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. Read more.
  • Tatiana Gateva-Ivanova, & Gunnar Fløystad. (2014). Monomial algebras defined by Lyndon words. Journal of Algebra, 403, 470–496.  Read more.
  • Tatiana Gateva-Ivanova, & Peter Cameron.  (2012).  Multipermutation Solutions of the Yang-Baxter Equation. Communications in Mathematical Physics, 309 (3), 583–621. Read more.
  • Tatiana Gateva-Ivanova. (2012). Quadratic algebras, Yang-Baxter equation, and Artin-Schelter regularity. Advances in Mathematics, 230 (4–6), 2152–2175. Read more.

Bibliography