**Department:** Computer Science
**Job Title:** Professor of Theoretical Computer Science

**Telephone:** +44 1225 386104
**Fax:** +44 1225 383493

**E-mail Address:** nnvATcs.bath.ac.uk

**Postal Address:**

- Dept of Computer Science
- University of Bath
- Bath
- BA2 7AY
- United Kingdom

**International workshop Effective Real Analytic Geometry
in honour of Andrei Gabrielov at**
ICMS, Edinburgh

**International seminar Complexity of Symbolic and Numerical Problems
in honour of Dima Grigoriev at**
Schloss Dagstuhl

**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

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. Orthogonal tropical linear prevarieties,
arXiv

by
D. Grigoriev and N. Vorobjov, arXiv:1803.01068 [math.AG] 06 March 2018.

[Department of Computer Science]