Associate Professor Vladimir Ejov

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• Undergraduate and graduate courses in Mathematics and related areas including: Differential Equations, Applied Analysis, Advanced Complex Analysis, Algebraic Topology.

Australian Mathematical Society

Ph.D. 1986, Mathematics, Moscow State University, USSR

• Markov decision processes
• Stochastic algorithms in global optimisation
• Differential and affine geometry
• Several complex variables
• Chern-Moser normal forms
• Cauchy-Riemann (C-R) manifolds, C-R automorphism groups
• Current Grants: Normal forms and Chern-Moser connection in the study of Cauchy-Riemann Manifolds (Australian Research Council Discovery Grant DP0450725 $ 165,000 over 2004-2006), V. Ejov(CI), G. Schmalz(PI), A. Spiro(PI); Singular and analytic perturbations, slow and fast time scales in control theory and viability theory and their applications (ARC Linkage International grant LX0560049 $62,000 over 2005-2007) CIs: V. Ejov J. Filar, V. Gaitsgory, P. Howlett, C. Pearce, international PIs: J. Aubin (University of Paris), K. Avrachenkov (INRIA Sophia Antipolis), H. Frankowska (Ecole Polytechnique), A. Gnedin (Utrecht University), J.-B. Lasserre (LAAS-CNRS, France), M. Quincompoix (University of Bretagne Occidentale), PI P. Saint-Pierre (University of Paris – Dauphine).

Research Monographs:

(with G. Schmalz) "Triviality effect for nil-isotropic automorphisms of real-analytic {CR}-manifolds", Bonner Mathematische Schriften , v. 338 (2001), 1--70.

(with G. Schmalz) Automorphisms and holomorphic mappings of standard CR-manifolds and Siegel domains (in Russian). Progress in Science and Technology. Series on Contemporary Mathematics and its applications. Thematic surveys, VINITI Moscow, v. 32 pp. 2--88, (1996) (Engl. translation in Journ. of Math. Sciences, v. 92:2 (1998), pp. 3712--3763

Selected Journal Publications:

"Triviality of scalar linear type isotropy subgroup by passing to an alternative canonical form of a hypersurfce". Annales Polonici Mathematici, v. LXX, (1998), pp.

(with J. Filar and M. Nguyen) "Hamiltonian Cycles and Singularly Perturbed Markov Chains", Mathematics of Operations Research, v. 29:1 (2004) pp. 114-131,

(with J. Filar and J. Gondzio) "An Interior Point Heuristic for the Hamiltonian Cycle Problem via Markov Decision Processes", Journal of Global Optimization, 29, pp. 315--334 (2004).

(with J. Filar and J. Thredgold) "Geometric interpretation of Hamiltonian Cycles problem via singularly perturbed Markov decision processes", Optimization, 52, pp. 441-458, (2003).

(with G. Schmalz ) "Linearisation of isotropic automorphisms of non-quadratic elliptic CR-manifolds in C4", in: S. Hildebrandt, H. Karcher (eds.) Geometric analysis and non-linear partial differential equations, Springer Verlag, (2002), pp. 89-104.

(with M. Eastwood) "On affine normal forms and a classification of homogeneous surfaces in affine three-space", Geom. Dedic. V. 77 (1999), pp. 11-69.

(with M. Eastwood) "A classification of non-degenearate homogeneous equiaffine hypersurfaces in four complex dimensions" , Asian Journal of Mathematics , v. 5:4 (2001), pp. 721-- 740

(with M. Eastwood) " Homogeneous Hypersurfaces with Isotropy in affine four-space", Trudy of the Steklov Inst. Analytic and geometric problems of complex analysis. Special volume in honour of A.G. Vitushkin, v. 235, (2001), pp. 57--70.

(with G. Schmalz and A. Loboda) "Canonical form of the 4th order polynomial in the normal equation of a real hypersurface in C3" , Russian Math. Notes, (1999), pp. 624--626.

(with G. Schmalz) "Special normal form of a hyperbolic CR-manifold in C4", Annales Polonici Mathematici, v. LXX, (1998), pp. 99--107.

(with A.V. Isaev and G. Schmalz) "Invariants of elliptic and hyperbolic CR-structures of codimension 2", Int. Journ. of Math. (1999), v. 10:1, pp. 1--52

(with G. Schmalz) "A Matrix Poincare formula for Holomorphic automorphisms of quadrics of higher codimension. Real associative quadrics", Journ. of Geom. Analysis, v. 7, (1997), pp. 559--573.

(with G. Schmalz) " X-Starrheit hermitescher Quadriken in allgemeiner Lage", Math. Nachrichten, v. 204 (1999), pp. 41--60.

(with V. Borkar and J. Filar) "Directed graphs, Hamiltonicity and doubly stochastic matrices, Random Structures and Algorithms", 25 (2004), pp. 376—395.

(with G. Schmalz) "Non-linearizable CR-automorphisms, torsion-free elliptic CR-manifolds and second order ODE", Journ. Reine und Angew. Math.,584 (2005) pp. 215—236.

(with M. Eastwood and A. Isaev) "Towards a classification of homogeneous tube domains in C4", J. Diff. Geom. 68:3 (2004), pp. 553-569.

(with A. Isaev) "On the dimension of the stability group for a Levi non-degenerate hypersurface", accepted for publications in Illinois Journal of Math.

(with J. Filar)"Groebner Bases in Asymptotic Analysis of Perturbed Polynomial Programs", accepted for publications in Math. Methods of Operations Research

(with G. Schmalz) "A simple proof of Beloshapka's theorem on the parametrization of the automorphism group of CR-varieties". (Russian) Mat. Zametki 61 (1997), no. 6, 939--942; translation in Math. Notes 61 (1997), no. 5-6, 783--786.

(with G. Schmalz) "Poincaré automorphisms for nondegenerate CR quadrics". Math. Ann. 298 (1994), no. 1, 79--87.

"An example of a real-analytic hypersurface with a nonlinearizable stability group". (Russian) Mat. Zametki 44 (1988), no. 5, 628--635, 701; translation in Math. Notes 44 (1988), no. 5-6, 824--828 (1989)

(with G. Schmalz) Holomorphic automorphisms of quadrics. Math. Zeit. v. 216 (1994) 453--470.

(with V. Borkar and J. Filar) On the Hamiltonicity gap and doubly stochastic matrices, technical report

I am able to provide media comment in the following areas of expertise:

Discipline: Mathematics

• Complex Analysis
• Functional Analysis
• Differential Geometry
• Markov Decision Processes
• Global optimization