Professor of Pure Mathematics 
of the University of Liverpool 
 
Viacheslav Valentinovich Nikulin

Department of Mathematics,
Mathematical Sciences Building,
Peach Street, University of Liverpool
Liverpool L69 7ZL, United Kingdom

Telephone: +44 (0) 151 794 4047 (office)
e-mail: vnikulin@liverpool.ac.uk
vvnikulin@list.ru

Research Interests

Algebraic Geometry, Mirror Symmetry,  Arithmetic of quadratic forms, 
Arithmetic hyperbolic reflection groups, Hyperbolic Kac-Moody Lie algebras. 

Recent publications: 

1. (with C.G.Madonna), Explicit  correspondences of a K3 surface with itself.   Izvestiya: Mathematics 

72 (2008), no. 3. (see also arXiv:math/0605362, 0606239, 0606289). 

2. Finiteness of the number of arithmetic groups generated by reflections in Lobachevsky spaces.  
Izvestia: Mathematics 71 (2007), no. 1, 53-56. (See also arXiv:math/0609256) 

3.  On ground fields of arithmetic hyperbolic reflection groups. In Groups and Symmetries, J. Harnad and 
P. Winternitz (eds.), CRM Proceedings and Lecture Notes, Vol. 47  (2009), 299-326. (See also arXiv:0708:3991)

4. On ground fields of arithemtic hyperbolic reflection groups. II.    Moscow Math. J. 8 (2008), no. 4, 789-812. 
(see also arXiv:0710.0162) 

5.  On ground fields of arithmetic hyperbolic reflection groups. III.  J. London Math. Soc. (2) 79 (2009), no. 3, 
738-756 (See also arXiv:0710.2340) 

6. Self-correspondences of K3 surfaces via moduli of sheaves and arithmetic hyperbolic reflection 
group. Proc. Steklov Mathematical Institute, Vol.  273, 2011, 247-256. (See also arXiv:0810.2945) 

7. The transition constant for arithmetic hyperbolic reflection groups. Izvestia: Mathematics 75:5, 
2011, 971-1005. (See also arXiv:0910.5217) 

8. Elliptic fibrations on K3 surfaces. Preprint 2012, 21 pages. arXiv:1010.3904v4.

http://xxx.lanl.gov/abs/1010.3904 

9. Kahlerian K3 surfaces and Niemeier lattices. Preprint 2013, 88 pages. arXiv:1109.2879v7.

http://xxx.lanl.gov/abs/1109.2879

10. Kahlerian K3 surfaces and Niemeier lattices. I. Izvestiya: Mathematics 77:5, 2013, 954-997 (See also arXiv:1109.2879)

11. Elliptic fibrations on K3 surfaces. Proc. of Edinburgh Math. Soc. Vol. 57, 2014,  253 - 267 (See also arXiv:1010.3904) 

12. Degenerations of Kahlerian K3 surfaces with finite symplectic automorphism groups. Izvestiya: Mathematics 79:4, 

2015, 740-794. (See also arXiv:1403.6061).

13. Degenerations of Kahlerian K3 surfaces with finite symplectic automorphism groups, II. Izvestiya: Mathematics 80:2, 2016, 

81-124. (See also arXiv:1504.00326).

14. (with V.A. Gritsenko) Lorentzian Kac--Moody algebras with Weyl groups of 2-reflections.  Preprint 2016, 73 pages. arXiv:1602.08359v1.  http://xxx.lanl.gov/abs/1602.08359

15. Kahlerian K3 surfaces and Niemeier lattices, II. Advanced Studies in Pure Mathematics. Vol. 69, 2016, Development of Moduli Theory -- Kyoto 2013, pp. 421 -- 471 (See also arXiv:1109.2879v7).

16. Degenerations of Kahlerian K3 surfaces with finite symplectic automorphism groups. III. Preprint 2016, 49 pages. arXiv:1608.04373v1.

http://xxx.lanl.gov/abs/1608.04373

17. (with V.A. Gritsenko) Examples of lattice-polarized K3 surfaces with automorphic discriminant, and Lorentzian Kac--Moody algebras. Preprint 2017, 15 pages. arxiv:1702.07551.  http://xxx.lanl.gov/abs/1702.07551

18. Classification of Picard lattices of K3 surfaces. Preprint 2017, 68 pages. arxiv:1707.05677.  http://xxx.lanl.gov/abs/1707.05677

19. (with V.A. Gritsenko) Lorentzian Kac--Moody algebras with Weyl groups of 2-reflections. Proc. London Math. Soc.

Vol. 116, issue 3, 2018, 485--533 (see also arXiv:1602.08359).

20. Classification of degenerations and Picard lattices of Kahlerian K3 surfaces with small finite symplectic automorphism groups. Preprint 2018, 39 pages. arXiv:1804.00991.  http://xxx.lanl.gov/abs/1804.00991

© vnikulin.com
Department of Mathematics, Mathematical Sciences Building, Peach Street, 
University of Liverpool,  Liverpool L69 7ZL, United Kingdom
Telephone: +44 (0) 151 794 4047 (office)
e-mail: vnikulin@liverpool.ac.ukvvnikulin@list.ru