Ping Wong Ng
Assistant Professor

Contact:
Office: 404 Maxim Doucet
Phone: 337-482-5272
E-mail: png@louisiana.edu
Home page: http://www.ucs.louisiana.edu/~pwn1677

Degrees:
Ph.D.: 2000, University of California at Los Angeles
M.S.: 1997, University of California at Los Angeles
B.S. 1995 Simon Fraser University

Statement:
Well, to me, mathematics is a creative endeavour and I'm (like everybody else!) generally interested in just about anything. (So if you have an interesting (and doable) research problem, please do knock on my door!) However, since you insist(!) here are three recent things:

(1) C*-algebras, K-theory, representation theory. This is a subject which I have (for the past long while) focussed a great deal of attention on. Much of my attention has been arrested by the Elliott program for classifying simple nuclear C*-algebras using K-theory invariants. For the past 5 years, I have spent a great deal of time working on several hard problems in the real rank zero case. In addition, much of my other work in absorbing extensions is also directed towards a better understanding of structure and classification.

(2) ``Big" topological groups. I have in the past couple of years developed an interest in abstract harmonic analysis on ``big" (i.e., nonlocally compact) topological groups. My work here is greatly motivated by that of Bekka, Giordano and Pestov (I collaborate with the latter two). Some examples of properties that I study are amenability, property T and structure (e.g. simplicity).

Nonlocally compact groups often exhibit interesting phenomenon that is not present in the locally compact case. For instance, no locally compact group can have the property of extreme amenability (a type of ``superamenability"). But there are many nonlocally compact groups coming from operator algebras that have this property.

(3) Frame theory. I very recently went to a conference in Texas A & M and developed an interest in frame theory. Frame theory is a branch of functional analysis connected with signal processing. (Roughly speaking, a frame is a generalization of an orthonormal basis (for a Hilbert space) but redundancy is allowed.) I am currently working on a project (jointly with some people at the University of Cincinnati) concerning C*-algebra theory (pure mathematics) problems motivated by results by Larson et al on the existence of frames satisfying certain conditions. This is an interesting field which (though with origins in applied mathematics) exhibit much interesting pure mathematics (though the applied math is also interesting!).

Selected research publications:

• The multiplier algebra of a nuclear quasidiagonal C*-algebra, Bulletin of the London Mathematical Society, 40 (2008), 827-837.
• The automorphism group of a tracially AI-algebra (with E. Ruiz), Communications in Mathematical Physis, 280 (2008), 427-444.
• Extending maps in K-theory (with E. Ruiz), International Journal of Pure and Applied Mathematics, 41 (2007), 419-442.
• Nonregular ideals in M(A \otimes K) (with D. Kucerovsky), Houston Journal of Mathematics, 33 (2007), 1117-1131.
• Stability of a \sigma_P-unital continuous field algebra (with B. Burgstaller), Journal of Functional Analysis, 248 (2007), 303-316.
• AF-skeletons and the corona factorization property for simple real rank zero C*-algebras (with D. Kucerovsky), Canadian Mathematical Bulletin, 50 (2007), 227-233.
• A note on subhomogeneous C*-algebras (with W. Winter), C. R. Math. Acad. Sci. Soc. R. Can. (Mathematical reports of the Academy of Science of the Royal Society of Canada), 28 (2006), 91-96.
• S-regularity and the corona factorization property (with Dan Kucerovsky), Mathematica Scandinavica, 99 (2006), 204-216.
• The corona factorization property, Contemporary Mathematics (AMS) 414 (2006), 97-111.
• Amenability of the sequence of unitary groups associated to a C*-algebra, Indiana U. Math. J., 55 (2006), 1389-1400.
• AFD multiplier algebras, International J. of Math., 17 (2006), 1091-1102.
• Simple real rank zero algebras with locally Hausdorff spectrum, Proc. Amer. Math. Soc., 134 (2006), 2223-2228 (electronic).
• The corona factorization property and approximate unitary equivalence (with Dan Kucerovsky), Houston J. Math. 32 (2006), 531-550 (electronic).
• An abstract Pimsner-Popa-Voiculescu theorem (with Dan Kucerovsky), J. Operator Theory 55 (2006), 169-183.
• Infinite stable rank for a continuous field algebra with fibres K (with Dan Kucerovsky), J. Operator Theory 54 (2005), 377-386.
• Decomposition rank and absorbing extensions of type I algebras (with Dan Kucerovsky), J. Funct. Anal. 221 (2005), 25-36.
• On the stable rank of algebras of operator fields over metric spaces (with Takahiro Sudo), J. Funct. Anal. 220 (2005), 228-236.
• On the stable rank of algebras of operator fields over an N-cube (with Takahiro Sudo), Bull. London Math. Soc. 36 (2004), 358-364.
• A characterization of completely 1-complemented subspaces of noncommutative L₁-spaces (with Narutaka Ozawa), Pacific J. Math. 205 (2002), 171-195.