Cambridge, England, June 2007

 

Nahum Zobin

Professor of Mathematics

Department of Mathematics
College of William and Mary
Williamsburg, Virginia 23187-8793

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), 12:00 – 1:20 pm, usually at Jones 131.

 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.

Whitney Problem page

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. Jordan Decomposition, 1. Geometric Approach, Russian Journal of Mathematical Physics, vol. 6. # 1, (1999), 113-123.jordgeom.pdf

4. Jordan Decomposition, 2. Analytic Approach, Russian Journal of Mathematical Physics, vol. 6,  # 2, (1999), 235-243.jordanal.pdf

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, Berlin -- New York, (2002), 213--240, (with J. Brandman, J. Fowler, B.Lins, I. Spitkovsky).survbirk.pdf

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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Other Interesting Web Sites:

  1. W&M LION On-line Library Catalog.
  2. The W&M Grants Web
  3. MathSciNET
  4. Zentralblatt für Mathematik
  5. Math Information
  6. Mathematics Journals Online
  7. The Math Forum
  8. netlib home page - contains freely available soft ware, documents, and databases of interest to the numerical, scientific computing, and other communities.