Jie Wu's Home Page

Department of Mathematics National University of Singapore Block S17 (SOC1), 06-02 10, Lower Kent Ridge Road Singapore 119076
matwuj@nus.edu.sg
Office: S-14 04-07
Telephone: +65 6516-4940 (Office) Fax:+65 6779 5452

RESEARCH INTERESTS: Algebraic Topology and Group Representation Theory.
A chart of my research interests: This may just give basic information what we intend to do.
My Mathematical Ancestry: Well you can see who is my academic grand-grand-grand father.
Research of Jie Wu This is a brief introduction to my research
PUBLICATIONS and SELECTED TALKS: You may download some of our papers from here.
Curriculum Vitae  

What is homotopy theory

In this section, I explain some questions/concepts in homotopy theory without assuming that you know any mathematics. Hopefully, you have a glance at homotopy theory through reading these files. If you have any comments/questions, please e-mail me.
  • Multiplications on spheres.
  • From calculus to topology.
  • What are homotopy groups?
  • Homotopy Groups: Talked at NUS Summer School, 9:30-10:30, May 25, 2006. This is an introductory talk on homotopy groups.
  • Braid Groups: Talked at International Summer School on Geometric Topology in Dalian, July 19-28, 2006 (5-hour lectures).
  • Milnor's Report on Poincare Conjecture
  • Topology and Poincare Conjecture, Mathematics Enrichment Camp 2006, National University of Singapore, 11:30-12:30, December 14, 2006
  • By identifying the sides of a rectangle as shown in the left, you will get the Klein bottle as shown in the right.

    Remember to identify the left and the right sides of the rectangle in the same direction, but to identify the top and bottom sides in  reverse direction.

    Take a piece of paper and try to make the Klein Bottle. If you are a superman lived in 4-dimensional space, then you can easily make it.


    Research Problems

    In this section, I propose some research problems. Many of these problems have some connections between homotopy theory and other areas. If you are not in the area of homotopy theory, you may think about these problems from your views. Some of these problems may deal with very hard problems in homotopy theory such as homotopy groups and long standing conjectures.
    1. a problem on combinatorial groups.
    2. a problem on Lie(n) and symmetric group algebras.
    3. a problem on Stiefel manifolds. This question has been solved recently except one special case.
    4. Foulkes Conjecture in representation theory and its relations to homotopy theory.
    5. a problem on Brunnian braids.
    6. Exponent problem in homotopy theory.
    7. a problem on braid group actions.
    8. a problem on modules over general linear groups.

    Tables on Homotopy Groups

  • A table of the homotopy groups of spheres: From Toda's book "Composition methods in homotopy groups of spheres".
  • A table of the homotopy groups of the suspensions of the projective plane.
  • A table of orders of Whitehead products Provided by Juno Mukai.

  • Topology in Singapore

  • The second East Asia Conference will hold in the Institute of Mathematical Sciences of NUS during 15-19 December, 2008.
  • Together with a workshop on homotopy, braids and mapping class groups, 4-14 December, 2008.

  • Ph. D. Students


  • ZHANG, Wenbin, 2007 --
  • CHEN, Weidong, 2007 --
  • GAO, Man, 2007 --
  • LIU, Minghui, 2007 --
  • YUAN, Zihong, 2009 --

  • Post-doctoral Researchers and Visiting Scholars

  • GRBIC, Jelena, July 2005 -- January 2006
  • MA, Kai, August 2008 -- July 2009
  • BEBEN, Piotr, March 2009 --

  • Lecture Notes

  • Lecture Notes on algebraic topology.
  • Lecture Notes on Calculus II.

  • Current Course Information

    MA5210, Differentiable Manifolds, Spring 2010

    Coming Courses


  • Previous Courses

  • Math 141, Calculus II for Natural Sciences, Fall 97, University of Pennsylvania.
  • Math 170, Ideas in Mathematics, Fall 97, University of Pennsylvania.
  • Math 141, Calculus II for Natural Sciences, Spring 98, University of Pennsylvania.
  • Math 150, Calculus I for Social Sciences, Fall 98, University of Pennsylvania.
  • Math 141, Calculus II for Natural Sciences, Spring 99, University of Pennsylvania.
  • Math 240, Calculus III for Natural Sciences, Spring 99, University of Pennsylvania.
  • MA 3111, Complex Analysis I, Fall 99.
  • MA 4215, Introduction to Algebraic Topology, Spring 2000.
  • MA 2108, Advanced Calculus II, Summer 2000.
  • MA 4215, Introduction to Algebraic Topology, Spring 2001.
  • MA 2108, Advanced Calculus II, Fall 2001.
  • MA 2108, Advanced Calculus II, Spring 2002.
  • MA 2108, Advanced Calculus II, Fall 2002.
  • MA 2108, Advanced Calculus II, Spring 2003.
  • MA 2108, Advanced Calculus II, Fall 2003.
  • MA 5210, Differentiable Manifolds Spring 2004.
  • MA 2108 and MA 2108S, Advanced Calculus II Fall 2004.
  • MA 2108, Advanced Calculus II, Fall 2005.
  • MA 5209, Algebraic Topology, Spring 2006.
  • MA 5209, Algebraic Topology, Fall 2006.
  • MA 2108, Mathematical Analysis I, Spring 2007
  • MA 2108, Mathematical Analysis I, Fall 2007
  • MA 5210, Differentiable Manifolds, Spring 2008.
  • MA5209, Algebraic Topology, Fall 2008
  • MA5237, Homotopy Theory, Fall 2008
  • MA5210, Differentiable Manifolds, Spring 2009
  • MA 6211 Topics in Geometry and Topology I, Fall 2009.

  • Some links

  • Victor Wu's Home Page
  • hopf: Algebraic Topology.
  • q-alg: Quantum Algebra and Topology (Including Knot Theory).
  • hep-th: High Energy Physics - Theory (since 8/91).
  • alg-geom: Algebraic Geometry.
  • XXX ARCHIVE: E-Print.
  • AMS.



  • 易经

    Asia in 1892


    From 16 November, 2007: