Group on combinatorial and applied algebra

People:

Roman S. Avdeev

Big Data and Information Retrieval School: Associate Professor

 

Ivan Arzhantsev

Professor, Dean of Faculty of Computer Science

 

Sergey Gayfullin

Joint Department with Yandex: Associate Professor

 

Alexey Zobnin

Joint Department with Yandex: Associate Professor

Polina Kotenkova

Joint Department with Yandex: Associate Professor

 

Dmitri Piontkovski

Department of Mathematics: Professor

 

Dmitry Trushin

Big Data and Information Retrieval School: Associate Professor

 

Stanislav N. Fedotov

Joint Department with Yandex: Associate Professor

 

Research interests:

1. Algebraic transformation groups and invariant theory;
2. Combinatorial methods in algebraic geometry;
3. Toric varieties and convex geometry;
4. Automorphisms of algebraic varieties and locally nilpotent derivations;
5. Lie groups, Lie algebras, algebraic groups and their representations;
6. Representations of quivers and associative algebras;
7. Operad theory;
8. Differential algebra;
9. Groebner bases and symbolic computations;
10. Applications in coding theory and crypthography.

Publications of group members:

• Roman Avdeev. Strongly solvable spherical subgroups and their combinatorial invariants. Selecta Math., New Series 21 (2015), no. 3, 931-993
• R.S.Avdeev and A.V.Petukhov. spherical actions on flag varieties. Sb. Math. 205 (2014), no. 9, 1223-1263
• R.S.Avdeev. Normalizers of solvable spherical subgroups. Math. Notes 94 (2013), no. 1, 20-31
• Ivan Arzhantsev and Sergey Gaifullin. The automorphism group of a rigid affine variety. Mathematische Nachrichten 290 (2017), no. 5-6, 662-671
• Ivan Arzhantsev and Elena Romaskevich. Additive actions on toric varieties. Proceedings of the American Mathematical Society 145 (2017), no. 5, 1865-1879
• Ivan Arzhantsev. On rigidity of factorial trinomial hypersurfaces. International Journal of Algebra and Computation 26 (2016), no. 5, 1061-1070
• Ivan Arzhantsev, Ulrich Derenthal, Juergen Hausen, and Antonio Laface. Cox rings. Cambridge Studies in Advanced Mathematics, No. 144, Cambridge University Press, 2015, 530 pages
• Ivan Arzhantsev and Polina Kotenkova. Equivariant embeddings of commutative linear algebraic groups of corank one. Documenta Mathematica 20 (2015), 1039-1053
• Ivan Arzhantsev, Alexander Perepechko, and Hendrik Süß. Infinite transitivity on universal torsors. Journal of the London Mathematical Society 89 (2014), no. 3, 762-778
• Ivan Arzhantsev, Juergen Hausen, Elaine Herppich, and Alvaro Liendo. The automorphism group of a variety with torus action of complexity one. Moscow Mathematical Journal 14 (2014), no. 3, 429-471
• Ivan Arzhantsev and Andrey Popovskiy. Additive actions on projective hypersurfaces. In: Automorphisms in Birational and Affine Geometry, Levico Terme, Italy, October 2012, Springer Proceedings in Mathematics & Statistics 79, Springer, 2014, 17-33
• Ivan Arzhantsev, Hubert Flenner, Shulim Kaliman, Frank Kutzschebauch, and Mikhail Zaidenberg. Flexible varieties and automorphism groups. Duke Mathematical Journal 162 (2013), no. 4, 767-823
• Ivan Arzhantsev, Devrim Celik, and Juergen Hausen. Factorial algebraic group actions and categorical quotients. Journal of Algebra 387 (2013), 87-98
• Ivan Arzhantsev and Ivan Bazhov. On orbits of the automorphism group on an affine toric variety. Central European Journal of Mathematics 11 (2013), no. 10, 1713-1724
• Alexander Gaifullin and Sergey Gaifullin. Defornations of period lattices of flexible polyhedral surfaces. Discrete and Computatinal Geometry 51 (2014), no.3, 650-665
• A.I.Zobnin and M.A.Limonov. Algorithm for checking triviality of "mixed'' ideals in the ring of differential polynomials. Program. Comput. Softw. 41 (2015), no. 2, 84-39
• Alexey Zobnin. Anti-Frobenius algebras and associated Yang-baxter equation. Mat. Model. 26 (2014), № 11, 51-56
• Polina Kotenkova. On restriction of roots on affine T-varieties, Beiträge zur Algebra und Geometrie 55 (2014), no. 2, 621-634
• Dmitri Piontkovski and Anton Khoroshkin, On generating series of finitely presented operads, Journal of Algebra 426 (2015), 377-429
• Stanislav Fedotov. Framed moduli and Grassmannians of submodules. Transactions of the American Mathematical Society 365 (2013), no.8, 4153-4179
• Adina Cohen, Michael Temkin, and Dmitri Trushin. Morphisms of Berkovich curves and the different function. Adv. Math. 303 (2016), 800–858
• I.Soloveychik, D.Trushin. Gaussian and robust Kronecker product covariance estimation: existence and uniqueness. J. Multivariate Anal. 149 (2016), 92–113
• Ilya Soloveychik, Dmitry Trushin, and Ami Wiesel. Group symmetric robust covariance estimation. IEEE Trans. Signal Process. 64 (2016), no. 1, 244–257
• Benjamin Antieau, Alexey Ovchinnikov, Dmitry Trushin. Galois theory of difference equations with periodic parameters. Comm. Algebra 42 (2014), no. 9, 3902–3943
• Russell Miller, Alexey Ovchinnikov, and Dmitry Trushin. Computing constraint sets for differential fields. J. Algebra 407 (2014), 316–357  

Grants:

• RSF-DFG 16-41-01013 "Geometry and representation theory at the interface of Lie algebras and quivers", grant holder E.B.Feigin, 2016-2018
• RFBR 16-01-00818 "Algebraic groups, spherical varieties, and equivariant Poisson geometry", grant holder E.B.Vinberg, 2016–2018

Student Term / Thesis Papers:

• Maxim Kaledin, «Toric Ideals and Groebner Bases in Integer Programming». Faculty of Computer Science, 2017, advisor I.V.Arzhantsev
• Daria Kuvshinova, graduation thesis “Separation indices of low rank irreducible root systems”, 2017, advisor R.S.Avdeev