(1)(1)(1).jpg)
Mathematisches Institut
Ernst-Abbe-Platz 2
Friedrich-Schiller-Universität Jena
andriyregeta@gmail.com
POSITION
- Since April 2023 I am DFG (Eigene Stelle) fellow at the University of Jena.
- Since October 2019 until March 2023 I was a postdoc at the University of Jena.
- Starting from January 2019 until September 2019 I was a postdoc at the University of Tübingen.
During January - March 2019 I was a visitor in MPI Bonn.
- Starting from October 2017 until December 2018 I was a postdoc at the University of Cologne.
- Starting from April 2016 until September 2017 I was an SNSF (Early Postdoc Mobility) fellow at the University of Grenoble.
- Starting from April 2012 until March 2016 I was a PhD student at the University of Basel.
Conferences which I co-organise:
Regional Workshop in Algebraic Geometry, University of Jena, March 2023 (co-organized with R. Púček).
Workshop on Algebraic Transformation Groups, Monte Verità, Switzerland, May 5 to May 8, 2024
(co-organized with J. Blanc and I. van Santen).
Teaching in the winter semester 2022/2023 (at the University of Jena)
Seminar: The geometry of T-varieties
Teaching in the summer semester 2022 (at the University of Jena)
Lecture: Linear Algebra
Teaching in the winter semester 2021/2022 (at the University of Jena)
Exercise classes: Linear Algebra
Teaching in the summer semester 2021 (at the University of Jena)
Lecture: Introduction to Algebraic Geometry
Teaching in the winter semester 2020/2021 (at the University of Jena)
Exercise classes: Linear Algebra
Teaching in the summer semester 2020 (at the University of Jena)
Lecture: Reflection Groups and Invariant Theory
Earlier I thought other courses at the University of Jena, at the university of Tübingen,
at the university of Cologne and at the University of Basel.
Master student
January-July 2022: Leif Jakob, title: Characterization of smooth Danielewski surfaces by their auto-
morphism groups. Since Fall 2022 L. Jacob is a PhD student under the supervision of Hendrik Süß.
Poster
Automorphism groups without non-algebraic elements, link to the poster (with Perepechko).
Other texts
Lectures on Reflection Groups and Invariant Theory
On the annihilators of rational functions in the Lie algebra of derivations of K[x,y] (with O. Iena and A. Petravchuk)
arXiv:0910.4465 (this text is not and will not be submitted to a peer review journal).
Preprints
1. Group Theoretical Characterizations of Rationality (with C. Urech, and I. van Santen) arXiv:2409.07864
2. The Structure of Algebraic Families of Birational Transformations (with C. Urech and I. van Santen) arXiv:2409.06475
3. The Automorphism groups of zero-dimensional monomial algebras (with R. Díaz, A. Liendo, G. Manzano-Flores),
4. Bracket width of current Lie algebras (with B. Kunyavskii and I. Makedonskyi) arXiv:2404.06045 (submitted).
5. When is the automorphism group of an affine variety linear? (submitted).
Publications
6. Characterization of affine G_m-surfaces of hyperbolic type, arXiv:2202.10761 to appear in J. of Pure and Applied Alg.
https://www.sciencedirect.com/science/article/abs/pii/S0022404924002263
7. On the characterization of affine toric varieties by their automorphism group (with R. Díaz and A. Liendo)
arXiv:2308.08040 to appear in Israel J. Math.
8. Maximal commutative unipotent subgroups and a characterization of affine spherical varieties (with I. van Santen)
9. Automorphism groups of affine varieties without non-algebraic elements (with A. Perepechko) arXiv:2203.08950
Proc. Amer. Math. Soc. 152 (2024), 2377-2383. doi.org/10.1090/proc/16759
(I gave a recorded talk on a very early version of this work at the "Seminar on Algebraic Transformation Groups".)
10. Small G-varieties (with H. Kraft and S. Zimmermann), Canad. J. of Math. (2024) 76(1), 173-215.
(H. Kraft gave a recorded talk on this work at the "Quadratic forms, Linear algebraic groups and Beyond" Seminar).
11. Lie subalgebras of vector fields on affine 2-space and the Jacobian conjecture, to appear in Ann. Inst. Fourier.
12. Bracket width of the Lie algebra of vector fields on a smooth affine curve (with I. Makedonskyi),
Journal of Lie Theory 33 (2023), No. 3, 919--923.
13. Families of commuting automorphisms, and a characterization of the affine space (with S. Cantat and J. Xie)
American Journal of Mathematics 145, no. 2 (2023): 413-434. muse.jhu.edu/article/885815.
14. Characterisation of affine surfaces by their automorphism groups (with A. Liendo and C. Urech) arXiv:1805.03991
Ann. Sc. Norm. Super. di Pisa, 2023: VOL. XXIV, ISSUE 1, 249-289, doi:10.2422/2036-2145.201905_009
(C. Urech gave a recorded talk on an this work at the conference "Algebraic Geometry - Mariusz Koras in memoriam").
15. When is the automorphism group of an affine variety nested? (with A. Perepechko), Transf. Groups, Vol. 28, pp. 401-412 (2023).
(Sasha gave a recorded talk on an this work at the conference Algebraic Geometry - Mariusz Koras in memoriam").
16. Characterisation of n-dimensional normal affine SL_n-varieties, Transform. Groups, Vol. 27, pp. 271–293 (2022).
17. Vector Fields and Automorphism Groups of Danielewski Surfaces (with M. Leuenberger), Int. Math. Res. Not., Vol. 2022,
18. On the characterization of Danielewski surfaces by their automorphism group (with A. Liendo and C. Urech), Transform.
Groups, Vol. 25, No. 4, 2022.
19. Bracket width of simple Lie algebras (with A. Dubouloz and B. Kunyavskii), Doc. Math. 26, 1601-1627 (2021).
(B. Kunyavskii gave a recorded talk on this research work at the conference "Affine Algebraic Groups, Motives and Co-
homological Invariants" in Banff.)
20. Characterizing quasi-affine spherical varieties via the automorphism group (with I. van Santen), Journal de l’École poly-
technique — Mathématiques, Vol. 8 (2021) pp. 379-414.
21. Is the affine space determined by its automorphism group? (with H. Kraft and I. van Santen), Int. Math. Res. Not., Vol. 2021,
Issue 6, pp. 4280–4300.
22. Automorphisms of the Lie algebra of vector fields on affine n-Space (with H. Kraft), J. Eur. Math. Soc, Vol. 19, Issue 5, 2017,
Questions/Problems
1. Does Tits alternative hold for the automorphism/birational transformation groups of affine varieties?
2. Describe/characterize all maximal subgroups of the Cremona group that consists of algebraic elements.
3. Is there an example of an affine variety that has a non-discrete group of automorphisms which does not
contain an algebraic subgroup of positive dimension?
4. Is SAut( A^n) simple? Is Aut(A^n) generated by connected algebraic subgroups?
5. Is there a uniform bound on the derived length of a solvable subgroup of the Cremona group?
Useful Links
Seminars
Seminar on Algebraic Transformation Groups
Conferences in Algebraic Geometry
International Centre for Mathematics in Ukraine