Chi-Kwong Fok (aka Alex Fok)

Postdoctoral Fellow
National Center for Theoretical Sciences, Math. Division
National Taiwan University
Taipei, Taiwan, R.O.C.
E-mail: ckfok@ntu.edu.tw
My thesis was successfully defended at Cornell University on July 17, 2014. I have been a postdoctoral fellow
of the National Center for Theoretical Sciences, working in the office located in National Tsing Hua University since August 2014.

Doctoral advisor: Prof. Reyer Sjamaar

Postdoctoral mentor: Prof. Nan-Kuo Ho

Research

Teaching
In Fall 2013 I am an instructor for MATH 1120 Calculus II. For my past teaching experience, click here

Curriculum Vitae

Papers

• Thesis
• The Real K-theory of compact Lie groups   ArXiv link    Slides    Review
  Symmetry, Integrability and Geometry: Methods and Applications, Vol. 10 (2014), 022, 26 pages
• KR-theory of compact Lie groups with group anti-involutions,
  Topology and its Applications, Vol. 197, pp. 50-59, 1 January 2016
• Picard group of isotropic realizations of twisted Poisson manifolds    Slides
  , submitted
• The Real Freed-Hopkins-Teleman theorem, submitted
• Adams operations on classical compact Lie groups, submitted
• Equivariant formality of homogeneous spaces,
  joint with Jeffrey Carlson, preprint
• Equivariant K-theory of compact Lie groups with finite fundamental groups, in preparation

Notes and Slides

• Fun with spheres
  A guest lecture I gave for the Enrichment Programme for Young Mathematical Talents, the Chinese University of Hong Kong
• On the equivariant K-theory of compact simply-connected Lie groups
  In this note we present an alternative proof of Brylinski-Zhang's result on the equivariant K-theory of compact Lie group, in the special case where the Lie group is simply-connected. This proof hinges on a computation of an equivariant index, which is a slight modification of the arguments in Atiyah's paper on the ordinary K-theory of compact Lie groups.
• Examples of Genus 5 Curves
  A very brief note on examples of genus 5 complex algebraic curves, classified by degree and ambient projective space. This originated from a project I did in the course on algebraic curves and surfaces taught by Prof. Michael Stillman.
• Cohomology and K-theory of Compact Lie Groups
  Still a draft with some details missing. Read at your own risk.
• An Invitation to Geometric Quantization
  A talk I gave in Olivetti Club, a graduate student colloquium in the Math Department of Cornell University
• Gromov-Witten Invariant of Grassmannians
  A note written for my presentation in Berstein Seminar in 2009 Fall on quantum Schubert Calculus, following the paper Gromov-Witten Invariants on Grassmannians by Buch, Kresch and Tamvakis
• Cohomology and K-theory of Symplectic Reductions
• Horn's Problem

About me

If I were a Springer-Verlag 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 2-manifolds, 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