**NABUTOVSKY, A.** (Professor)

Department of Mathematics

University of Toronto

Toronto, ON M5S 3G3

Tel: (416) 978-3321

Fax: (416) 978-4107

alex@math.utoronto.ca

**esearch:**
Global Riemannian Geometry, quantitative and algorithmic aspects of Topology
of Manifolds.

- Alexander Nabutovsky and Regina Rotman Linear bounds for lengths of geodesic segments on Riemannian 2-spheres, submitted for publication.
- Yevgeny Liokumovich, Alexander Nabutovsky, Regina Rotman Contracting the boundary of a Riemannian $2$-disc, submitted for publication.
- Alexander Nabutovsky and Regina Rotman Length of geodesics and quantitative Morse theory on loops spaces, accepted for publication in Geom. Funct. Anal. (GAFA)
- Alexander Nabutovsky and Regina Rotman Linear bounds for lengths of geodesic loops on Riemannian 2-spheres, J. of Differential Geom. 89(2011), 217-232.
- Alexander Nabutovsky and Regina Rotman Lengths of simple periodic geodesics on two-dimensional Riemannian spheres, J. of Topology and Analysis, 3(2011), 423-432.
- Alexander Nabutovsky Morse landscapes of Riemannian functionals and related problems, Proceedings of ICM-2010, vol. 2, 862-881, Hindustan Book Agency, New Delhi, 2010.
- Alexander Nabutovsky Effective universal coverings and local minima of the length functional on loop spaces, Geom. Funct. Anal. (GAFA) 20(2010), 545-570.
- Alexander Nabutovsky and Regina Rotman Short geodesic segments between two points on a closed Riemannian manifold, Geom. Funct. Anal (GAFA) 19(2009), 498-519.
- Alexander Nabutovsky and Regina Rotman Length of geodesics on a two-dimensional sphere, American J. Math. 131(2009), 545-569.
- Alexander Nabutovsky and Regina Rotman The length of the second shortest geodesic, Comment. Math. Helv. 84(2009), 747-755.
- Alexander Nabutovsky and Regina Rotman Shapes of geodesic nets, Geometry and Topology 11(2007), 1225-1254.
- Alexander Nabutovsky and Shmuel Weinberger Betti numbers of finitely presented groups and very rapidly growing functions, Topology 46(2007), 211-233.
- Alexander Nabutovsky and Regina Rotman Lengths of geodesics between two fixed points on a Riemannian manifold, ERA of the AMS, 13(2007), 13-20.
- Alexander Nabutovsky Combinatorics of the space of Riemannian structures and logic phenomena of Euclidean Quanum Gravity, in ``Perspectives in Riemannian Geometry", ed. by V. Apostolov et al., CRM Proceedings and Lecture Notes, vol. 40, 223-248, AMS, Providence, RI, 2006..
- Alexander Nabutovsky and Regina Rotman Curvature-free upper bounds for the smallest area of a minimal surface, Geom. Funct. Anal. (GAFA), 16:2(2006), 453-475..
- Alexander Nabutovsky and Regina Rotman The minimal length of a non-trivial geodesic net on a closed Riemannian manifold with non-trivial second homology group, Geom. Dedicata 113(2005), 243-254.
- Alexander Nabutovsky and Regina Rotman Volume, diameter and the minimal mass of a stationary 1-cycle, Geom. Funct. Anal. (GAFA), 14(2004), 748-790. .
- Alexander Nabutovsky and Regina Rotman Upper bounds for the length of the shortest closed geodesic and quantitative Hurewicz theorem, J. of the Europ.Math.Soc.(JEMS) 5(2003), 203-244.
- Alexander Nabutovsky and Regina Rotman The minimal area of an embedded minimal 2-sphere in a manifold diffeomorphic to S^3, IMRN 2003(2003), 39, 2121-2129..
- Alexander Nabutovsky and Shmuel Weinberger The fractal nature of Riem/Diff I, Geom. Dedicata 101(2003), 1-54..
- Alexander Nabutovsky and Regina Rotman The length of the shortest closed geodesic on a two-dimensional sphere, IMRN, 23(2002), 1211-1222.
- Alexander Nabutovsky and Shmuel Weinberger Variational problems for Riemannian functionals and arithmetic groups, Publications d'IHES, 92(2000), 5-62.
- Alexander Nabutovsky and Shmuel Weinberger Algorithmic aspects of homeomorphism problems, Contemp. Math. 231(1999), 245-250.
- Alexander Nabutovsky and Shmuel Weinberger Algorithmic unsolvability of the triviality problem for multidimensional knots, Comm. Math Helv. 71(1996), 423-434.
- Alexander Nabutovsky Disconnectedness of sublevel sets of some Riemannian functionals, GAFA 6(4)(1996), 703-725.
- Alexander Nabutovsky Geometry of the space of triangulations of a compact manifold, Comm.Math.Phys. 181(1996), 303-330.
- Alexander Nabutovsky Fundamental group and contractible closed geodesics, Comm. Pure Appl. Math. 49(12)(1996), 1257-1270.
- Alexander Nabutovsky Einstein structures: existence versus uniqueness, GAFA 5(1)(1995), 76-91.
- Alexander Nabutovsky Non-recursive functions, knots "with thick ropes" and self-clenching "thick" hyperspheres, Comm. Pure Appl. Math. 48(1995), 381-428.
- Alexander Nabutovsky and Radel Ben-Av Non-computability arising in dynamical triangulation model of four-dimensional quantum gravity, Comm. Math. Phys. 157(1993), 1, 93-08.
- Alexander Nabutovsky Number of solutions with a norm bounded by a given constant of a semilinear elliptic PDE with a generic right-hand side, Trans. Amer. Math. Soc. 332(1992), 135-166.
- Alexander Nabutovsky Smoothing of real algebraic hypersurfaces by rigid isotopies, Ann. Inst. Fourier(Grenoble), 41(1991), 11-25.
- Alexander Nabutovsky Isotopies and non-recursive functions in real algebraic geometry, in Real Analytic and Algebraic Geometry, Springer Lecture Notes in Mathematics 1420, Springer, 1990, 194-205.
- Alexander Nabutovsky Non-recursive functions in real algebraic geometry, Bull. Amer. Math. Soc. 20(1989), 61-65.
- A. Nabutovsky Irrationality of limits of quickly convergent algebraic number sequences, Proc. Amer. Math. Soc. 102(1988), 473-479.