ChiKwong Fok (aka Alex Fok)
Lecturer in Mathematics
Email: alex.fok@auckland.ac.nz
Research Statement
Brief version. Detailed version available upon request.
Teaching
In Fall 2013 I was an instructor for MATH 1120 Calculus II. In Spring 2016 I was an instructor for MATH 1020 Calculus II (微積分二). Letter of compliment on my teaching of this course (Chinese version) (English version).
For my past teaching experience, click here
Curriculum Vitae
Papers
 Thesis
 The Real Ktheory of compact Lie groups
Symmetry, Integrability and Geometry: Methods and Applications, Vol. 10 (2014), 022, 26 pages.
 KRtheory of compact Lie groups with group antiinvolutions,
Topology and its Applications, Vol. 197, pp. 5059, 1 January 2016.
 Picard group of isotropic realizations of twisted Poisson manifolds Slides
Journal of Geometric Mechanics, Vol. 8, No. 2, pp. 179197, June 2016.
 Adams operations on classical compact Lie groups
Proceedings of the American Mathematical Society, Vol. 145, No. 7, pp. 27992813, July 2017.
 Equivariant twisted Real Ktheory of compact Lie groups,
Journal of Geometry and Physics, Vol. 124, pp. 325349, January 2018.
 Equivariant formality of homogeneous spaces, joint with Jeffrey D. Carlson,
Journal of the London Mathematical Society (2), Vol. 97, pp. 470494, 2018.
 Equivariant formality in Ktheory,
New York Journal of Mathematics, Vol. 25, pp. 315327, 2019.
 The ring structure of twisted equivariant KKtheory for noncompact Lie groups, joint with Mathai Varghese, preprint, submitted.
 Ktheory and cohomology rings of the space of commuting elements in SU(2), draft.
 Extended Verlinde algebras for compact Lie groups with nontrivial outer automorphisms, joint with David Baraglia and Mathai Varghese, in preparation
Miscellaneous

If I were a SpringerVerlag Graduate Text in Mathematics, I would be William S. Massey's A Basic Course in Algebraic Topology.
I am intended to serve as a textbook for a course in algebraic topology at the beginning graduate level. The main topics covered are the classification of compact 2manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. These topics are developed systematically, avoiding all unecessary definitions, terminology, and technical machinery. Wherever possible, the geometric motivation behind the various concepts is emphasized.
Which Springer GTM would you be? The Springer GTM Test


