AUT - Jiling Cao

Jiling Cao

Associate Professor

Phone: 6421 9999 extn 8433

Email: jiling.cao@aut.ac.nz

Physical Address:
AUT Tower, Level 1,
2 – 14 Wakefield St,
Auckland 1010

Qualifications:

• BSc, Tianjin University, 1986
• MSc, Chinese Academy of Sciences, 1989
• PhD, The University of Auckland, 1999

Memberships and Affiliations:

• Member of the American Mathematical Society
• Member of the New Zealand Mathematical Society
• Reviewer of the Mathematical Reviews, the American Mathematical Society

Teaching Areas:

I have taught undergraduate and postgraduate courses in Mathematics and Applied Mathematics at all levels. In particular, I have taught Calculus, Linear Algebra, Discrete mathematics, Complex Analysis, Engineering Computation, Differential Equations, Topology and Geometry etc.

Currently, I am the course coordinator for Multivariate Calculus, Engineering Computation II, Complex Analysis, Differential Equations.

Research areas:

My main areas of research interest in Mathematics are:Game theory and applications

• General/Analytic Topology
• Mathematical Economics and Financial Modelling
• Non-linear Analysis and Optimization
• Topological Structures and Programming Semantics

Also, I supervise postgraduate students in these areas.

Research Summary:

Previously, I held a JSPS research fellowship from 2000 to 2002 in Ehime University, Japan. During that period, I made a significant progress toward some open problems posed by J. Ginsburg in 1975 on hyperspaces of countable and pseudocompact spaces, see my publication 15 below and the article by J. Ginsburg in Canad. J. Math. 27 (1975), 1392--1399.

From 2002 to 2005, I held a New Zealand Science and Technology research fellowship in the University of Auckland.

Current Research Projects:

Currently, I am involved in a joint Marsden Fund research project, Analytic Topology and its Applications, with Dr Warren Moors from the University of Auckland. This is a three-year research project funded by the Royal Society of New Zealand.

My recent discoveries in Mathematics include: the solution to an open problem of G. Gruenhage and D. Lutzer in 2000 on Volterra spaces, see my publication 4 below and the article by G. Gruenhage and D. Lutzer in Proc. Amer. Math. Soc. 128 (2000) 3115--3124; the solution to a problem of R. McCoy in 1975 on the Vietoris hyerspace of a Baire space, see my publications 2,3 and the article by R. McCoy in Pacific J. Math. 58 (1975) 133--142.

Publications:

J. Cao, D. Gauld, S. Greenwood and A. Mohamad, Games and metrizability of manifolds, New Zealand Journal of Mathematics, to appear.

J. Cao and A. H. Tomita, Baire spaces, Tychonoff topology and the Vietoris topology, Proceedings of the American Mathematical Society 135 (2007), 1565--1573.

J. Cao, S. Garcia-Ferreira and V. Gutev, Baire spaces and Vietoris hyperspaces, Proceedings of the American Mathematical Society 135 (2007), 299--303.

J. Cao and H. J. K. Junnila, When is a Volterra space Baire? Topology and its Applications 154 (2007), 527--532.

J. Cao and S. Greenwood, The ideal generated by $\sigma$-nowhere dense sets, Applied General Topology 7 (2006), 253--264.

J. Cao and J. Rodriguez-Lopez, On hyperspace topologies via distance functionals in quasi-metric spaces, Acta Mathematica Hungarica 112 (2006), 249--268.

J. Cao and W. Morrs, A survey on topological games and their applications in analysis, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 100 (2006), 39--49.

X. Miao, J. Cao and H. Xiong, Banach-Stone theorems and Riesz algebras, Journal of Mathematical Analysis and Applications 313 (2006), 177--183.

J. Cao and W. Moors, Quasicontinuous selections of upper continuous set-valued mappings, Real Analysis Exchange 31 (2005/2006), 63--71.

J. Cao, H. P. Kunzi and I. Reilly, Hausdorff quasi-uniformities inducing the same hypertopologies, Publicationes Mathematicae Debrecen 67 (2005), 27--40.

J. Cao and D. Gauld, Volterra spaces revisited, Journal of the Australian Mathematical Society 79 (2005), 61--76.

J. Cao, Generalized metric properties and kernels of set-valued maps, Topology and its Applications 146/147 (2005), 603--609.

J. Cao, M. Ganster, I. Reilly and M. Steiner, $\delta$-closure, $\theta$-closure and generalized closed sets, Applied General Topology 6 (2005), 79--86.

J. Cao and Z. Piotrowski, Two variations of the Choquet game, Kyungpook Mathematical Journal 44 (2004), 495--504.

J. Cao, T. Nogura and A. H. Tomita, Countable compactness of hyperspaces and Ginsburg's questions, Topology and its Applications 144 (2004), 133--145.

J. Cao and W. Moors, Separate and joint continuity of homomorphisms defined on topological groups, New Zealand Journal of Mathematics 33 (2004), 41--45.

J. Cao and Y. Song, Aquaro number versus absolute star-Lindelöf number, Houston Journal of Mathematics 29 (2003), 925--936.

J. Cao, I. Reilly and H. Xiong, A lattice-valued Banach-Stone theorem, Acta Mathematica Hungarica 98 (2003), 103--110.

J. Cao, M. Ganster, C. Konstadilaki and I. Reilly, On preclosed sets and their generalizations, Houston Journal of Mathematics 28 (2002), 771--780.

J. Cao, Recent progress in some aspects of star covering properties, Kyoto University Research Institute for Mathematical Sciences Kitashirakawa Oiwake-cho, Sakyo-ku Kyoto 1248 (2002), 12--17.

J. Cao, M. Ganster and I. Reilly, On generalized closed sets, Topology and its Applications 123 (2002), 37--46.

J. Cao, W. Moors and I. Reilly, Topological properties defined by games and their applications, Topology and its Applications 123 (2002), 47--55.

J. Cao, M. Ganster and I. Reilly, Recent progress in the theory of generalized closed sets, Mathematics & mathematics education (Bethlehem, 2000), 112--121, World Scientific Publishing Co., River Edge, NJ, 2002.

J. Cao, J. Kim, T. Nogura and Y. Song, Cardinal invariants related to star covering properties, Topology Proceedings 26 (2001/2002), 83--96.

J. Cao, S. Greenwood and I. Reilly, Generalized closed sets: a unified approach, Applied General Topology 2 (2001), 179--189.