Professor of Mathematics

Department of Mathematics

Tel: (757)
221-2024 (office)

(757) 221-1873 (Dept)

Fax: (757) 221-7400 (Dept)

E-mail: nxzobi@wm.edu

**Office: Jones Hall, 118.**

Research Interests:

__Analysis: Function Theory,
especially spaces of smooth functions and extension theorems;
Operator Theory, especially ____Jordan____ decomposition and interpolation of operators,
Nuclear Spaces.__

__Mathematical Physics: Quantization,
Functional Integrals, Noncommutative Quantum Gauge
Field Theory, Representations and Theta
Functions, Chaotic dynamical systems __

__Geometry: Convex geometry and Coxeter groups__

__Algebra: Polynomial automorphisms
of affine spaces, ____Newton____ Polyhedra__

__Applied Mathematics: Problems of Plasma
Physics, Hydrodynamics of Non-Newtonian fluids, Medical Imaging__

**SEMINARS.**

I am coordinating an interdepartmental
MATHEMATICAL PHYSICS SEMINAR which
brings together faculty and students from various departments. We meet every
Wednesday (including summer breaks),

The
seminar continuously works since 2000, we have studied such topics as
Hamiltonian and Lagrangian formalisms, Symplectic geometry, Group representations, Chaotic dynamical systems, Introduction to Algebraic
Topology, Newton Polyhedra, Quantum Field Theory.

If you wish to be included into the seminars
mailing list and receive announcements about our meetings, please send me your
email address at nxzobi@wm.edu.

There were other seminars which we conducted
in recent years:

SEMINAR on ALGEBRO-GEOMETRIC METHODS IN
NONLINEAR EQUATIONS was working in 2002
-- 2004. We studied such topics as Solitons, Theta
Functions, Inverse Scattering Methods.

NONCOMMUTATIVE GEOMETRY SEMINAR was working
in 2001 -- 2003. We mostly studied the works of Alain Connes
and applications of these ideas to noncommutative
quantum gauge field theories.

CV, list of publications, etc. cvfmt.pdf

RECENT PAPERS (since 1998)

1. Whitney's problem on extendability of functions
and an intrinsic metric, Advances in Mathematics, vol. 133, # 1, (1998),
96-132. ext.pdf

2. Szego extremal problems,
Amer. Math. Soc. Transl., 2, vol. 184, (1998),
253-263.(reprints available)

3.

4.

5. Extension of smooth functions from finitely connected planar domains,
Journal of Geometric Analysis, vol. 9, # 3, (1999), 489-509.(reprints
available)

6. Some remarks on quasi-equivalence of bases in
Frechet spaces, Linear Algebra and Applications, vol.
307, #1-3, (2000), 47-67.quasi.pdf

7. Geometric structure of $B_{2,2}$-orbihedra and interpolation of operators, Linear and Multilin. Algebra, vol. 48, (2000), 67--91, (with V. Zobin) (reprints available)

8. Linear preservers of isomorphic types of lattices of invariant operator
ranges, Proc. of Amer. Math. Soc., vol.
129, (2001), 2981-- 2986,(with L. Rodman).operng.pdf

9. On eigenvalues and boundary curvature of
the numerical range, Linear Algebra and Applications, vol. 322,
#1-3, (2001), 129--140, (with L. Caston, M. Savova, I. Spitkovsky).numerng.pdf

10. Birkhoff's Theorem and convex hulls of Coxeter groups, Linear Algebra and Applications, vol. 347,
(2002), 219--231, (with N. McCarthy, D. Ogilvie, I. Spitkovsky).birfi.pdf

11. Convex hulls of Coxeter groups, in "Function Spaces, Interpolation Theory and
Related Topics", Walter de Gruyter,

12. Noncommutative gauge theory without Lorentz violation, Phys. Rev. D, vol. 66, (2002),
075001-8 (with C. Carlson, C. Carone).ncft.pdf

13. Convex geometry of Coxeter-invariant polytopes, Contemp.
Math., vol. 321, (2003), 153--180, (with N. McCarthy, D. Ogilvie,
V. Zobin).coxpoly.pdf

14. Finite reflection groups and linear preserver problems, Rocky
Mountains Journal of Mathematics, 34 (2004), 225-252 (with C.K. Li, I. Spitkovsky).lsz.pdf

15. $C^1$ extension of
functions and stabilization of Glaeser refinements, Revista Math. Iberoamericana,
23:2 (2007), 635-669,(with B. Klartag)
whitney\glaeserrefinements.pdf.

**Teaching.**

**Fall 2008:**

**Math 412-01 Introduction to Number Theory (TR ****3:30**** -- ****4:50
pm****, Small 109), see syllabus **

**Math 112-03 Calculus 2 (TR ****12:30****
-- ****1:50 pm****, Jones
131), see syllabus and a list of homework assignments**

**Office hours: TR ****5:00 – 6:00 pm****,
and by appointment**

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