Job Title: Professor Emeritus, University of Bath

E-mail Address: masnnvATbath.ac.uk

Some recent papers and preprints:

1. Complexity of computations with Pfaffian and Noetherian functions, PDF
by A. Gabrielov and N. Vorobjov, in: Normal Forms, Bifurcations and Finiteness Problems in Differential Equations, 211-250, Kluwer, 2004.

2. Betti numbers of semialgebraic and sub-Pfaffian sets, PDF
by A. Gabrielov, N. Vorobjov, and T. Zell, J. London Math. Soc., 69, part 1, 2004, 27-43.

3. Betti numbers of semialgebraic sets defined by quantifier-free formulae, PDF
by A. Gabrielov and N. Vorobjov, Discrete Comput. Geom., 33, 3, 2005, 395-401.

4. On the number of homotopy types of fibres of a definable map, PDF
by S. Basu and N. Vorobjov, J. London Math. Soc., 76, part 3, 2007, 757-776,

5. Bounds on sizes of finite bisimulations of Pfaffian dynamical systems, PDF
by M. Korovina and N. Vorobjov, Theory Comput. Systems, 43, 2008, 498-515.

6. Approximation of definable sets by compact families, and upper bounds on homotopy and homology, PDF
by A. Gabrielov and N. Vorobjov, J. London Math. Soc., 80, 2, 2009, 35-54.

7. Semi-monotone sets, PDF
by S. Basu, A. Gabrielov, and N. Vorobjov, J. European Math. Soc., 15, 2, 2013, 635-657. DOI 10.4171/JEMS/369

8. Monotone functions and maps, PDF
by S. Basu, A. Gabrielov, and N. Vorobjov, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas (RACSAM),
107, 1, 2013, 5-33. DOI 10.1007/s13398-012-0076-4

9. A Helly-type theorem for semi-monotone sets and monotone maps, arXiv
by S. Basu, A. Gabrielov, and N. Vorobjov, Discrete and Computational Geometry, 50, 4, 2013, 857-864. DOI 10.1007/s00454-013-9540-y

10. Toric cubes are closed balls, arXiv
by S. Basu, A. Gabrielov, and N. Vorobjov, arXiv:1202.5572.v1 [math.AG] 24 Feb 2012 (this paper is now Section 6 in [8]).

11. Triangulations of monotone families I: two-dimensional families, arXiv
by S. Basu, A. Gabrielov, and N. Vorobjov, Proc. London Math. Soc., 111, 5, 2015, 1013-1051. DOI 10.1112/plms/pdv052

12. On topological lower bounds for algebraic computation trees, PDF
by A. Gabrielov and N. Vorobjov, Foundations of Computational Mathematics, 17, 1, 2017, 61-72. DOI 10.1007/s10208-015-9283-7
View-only version via Springer Nature Sharing

13. Topological lower bounds for arithmetic networks, arXiv
by A. Gabrielov and N. Vorobjov, Computational Complexity, 26, 3, 2017, 687-715. DOI 10.1007/s00037-016-0145-8
View-only version via Springer Nature Sharing

14. On irreducible components of real exponential hypersurfaces, arXiv
by C. Riener and N. Vorobjov, Arnold Mathematical Journal, 3, 3, 2017, 423-443. DOI 10.1007/s40598-017-0073-y
View-only version via Springer Nature Sharing

15. Upper bounds on Betti numbers of tropical prevarieties, arXiv
by D. Grigoriev and N. Vorobjov, Arnold Mathematical Journal, 4, 1, 2018, 127-136. DOI 10.1007/s40598-018-0086-1
View-only version via Springer Nature Sharing

16. Complexity of deciding whether a tropical linear prevariety is a tropical variety, arXiv
by D. Grigoriev and N. Vorobjov, Appl. Algebra Engrg. Comm. Comput., 32, 2, 2021, 157-174. DOI 10.1007/s00200-019-00407-w
Online First
Extended abstract in: CASC 2018, LNCS 11077, 187-196. DOI 10.1007/978-3 -319-99639-4_13
2021 AAECC Best Paper Award

17. Effective cylindrical cell decompositions for restricted sub-Pfaffian sets, arXiv
by G. Binyamini and N. Vorobjov, International Mathematics Research Notices, 2022, 5, 3493-3510. DOI 10.1093/imrn/rnaa285
Article

18. Lecture notes on complexity of quantifier elimination over the reals, arXiv
by N. Vorobjov, arXiv:2112.00456 [math.HO]

List of publications

Non-technical lectures

N N Vorobiev (1925-1995)

A. A. Markov

N. A Shanin

[University of Bath]