Department of Mathematics, HKUST  

  MENG, Guo-Wu   孟國武

  PhD Brown

Office: Room 3484  

Telephone: 7451  

Email: mameng@ust.hk  

URL:
https://www.math.hkust.edu.hk/~mameng   
  Professor

Prof. Meng joined HKUST in Fall 1993. He is a CUSPEA student in class 1986 (from USTC ) and in 1989 he switched to mathematics. His Ph.D. field of research is topology and his thesis advisor is Thomas Goodwillie. Mathematically he is best known as the "Meng" in Meng-Taubes Formula --- a fundamental result in three- and four-dimensional topology which links the modern Seiberg-Witten theory for smooth four-manifolds to the classical Alexander theory for knots, links and three-manifolds. That formula roughly says that each coefficient of the multi-variable Alexander polynomial of a knot, or a link or a three-manifold is exactly the number of solutions (counted with signs) of the static Seiberg-Witten equations for a certain topological setup. In recent years his mathematical exploration is focused on the Kepler problem --- the mathematical model for a solar system with a single planet or an atom with a single electron, depending on whether it is considered classically or quantum mechanically. The goal of this exploration is to find out the mathematical essence of this great problem and to explore the potential implication (of mathematical findings) to fundamental physics. One surprising discovery of this exploration is an intimate relationship between the Kepler problem in classical physics and future light cone in the special theory of relativty.

Teaching

  • MATH4223  Differential Geometry
  • MATH5230  Differential Topology

Research Interests

  • Physics-inspired mathematics

       Selected Publications

Full Publication List [HKUST Scholarly Publications]  

Article   

  1. Magnetized Kepler manifolds and their quantization
    • Author(s): Meng, Guowu
    • Source: Journal of Geometry and Physics, v. 159, January 2021, article number 103891
    • Year: 2021

  2. The Classical Dynamic Symmetry for the Sp(1)-kepler Problems
    • Author(s): Bouarroudj, Sofiane; Meng, Guo Wu
    • Source: Journal of Mathematical Physics. , v.58, (9), September 2017, article number 091702
    • Year: 2017

  3. The classical dynamic symmetry for the U(1)-Kepler problems
    • Author(s): Bouarroudj, Sofiane ; Meng, Guo Wu
    • Source: Journal of Geometry and Physics. , v. 124, January 2018, p. 1-15
    • Year: 2017

  4. On the trajectories of Sp(1)-Kepler problems
    • Author(s): Meng, Guowu
    • Source: Journal of Geometry and Physics. , v. 96, July 2015, p. 123-132
    • Year: 2015

  5. Tulczyjew's approach for particles in gauge fields
    • Author(s): Meng, Guowu
    • Source: Journal of Physics A: Mathematical and Theoretical. , v. 48, (14), April 2015, article number 145201
    • Year: 2015

  6. On the trajectories of O(1)-Kepler problems
    • Author(s): Meng, Guowu
    • Source: Journal of Mathematical Physics. , v. 56, (5), 2015, article number 052901
    • Year: 2015

  7. The Universal Kepler problem
    • Author(s): Meng, Guo Wu
    • Source: Journal of Geometry and Symmetry in Physics. , v. 36, 2014, p. 47-57
    • Year: 2014

  8. Generalized Kepler problems. I. without magnetic charges
    • Author(s): Meng, Guowu
    • Source: Journal of Mathematical Physics. , v. 54, (1), January 2013, article number 012109
    • Year: 2013

  9. On the orbits of magnetized Kepler problems in dimension 2k + 1
    • Author(s): Bai, Z.; Meng, G.; Wang, E.
    • Source: Journal of Geometry and Physics. , v. 73, November 2013, p. 260-269
    • Year: 2013

  10. The Poisson realization of so (2,2k, + 2) on magnetic leaves and generalized MICZ-Kepler problems
    • Author(s): Meng, Guowu
    • Source: Journal of Mathematical Physics. , v. 54, (5), May 2013, article number 052902
    • Year: 2013

  11. The classical magnetized kepler problems in higher odd dimensions
    • Author(s): Meng, G.
    • Source: Journal of Geometry and Symmetry in Physics. , v. 32, January 2013, p. 15-23
    • Year: 2013

  12. Lorentz group and oriented McIntosh-Cisneros-Zwanziger-Kepler orbits
    • Author(s): Meng, Guowu
    • Source: Journal of mathematical physics. , v. 53, (5), May 2012, article number 052901
    • Year: 2012

  13. Generalized MICZ-Kepler problems and unitary highest weight modules
    • Author(s): Meng, Guowu; Zhang, Ruibin
    • Source: Journal of mathematical physics. , v. 52, (4), April 2011, article number 042106
    • Year: 2011

  14. Euclidean Jordan algebras, hidden actions, and J-Kepler problems
    • Author(s): Meng, G.
    • Source: Journal of mathematical physics. , v. 52, (11), 2011, article number 112104
    • Year: 2011

  15. Generalized MICZ-Kepler problems and unitary highest weight modules, II
    • Author(s): Meng, Guowu
    • Source: Journal OF The London Mathematical society-second Series. , v. 81, (Part 3), 2010, JUN, p. 663-678
    • Year: 2010

  16. The U(1)-Kepler Problems
    • Author(s): Meng, G.
    • Source: Journal of Mathematical Physics. , v. 51, (12), 2010, article number 122105
    • Year: 2010

  17. The Sp(1)-Kepler problems
    • Author(s): Meng, Guowu
    • Source: Journal of Mathematical Physics. , v. 50, (7), Jul 2009, article number 072107
    • Year: 2009

  18. The Representation Aspect of the Generalized Hydrogen Atoms
    • Author(s): Meng, Guowu
    • Source: Journal of Lie theory. , v. 18, (3), 2008, p. 697-715
    • Year: 2008

  19. A generalization of the Kepler problem
    • Author(s): Meng, G.
    • Source: Physics of atomic nuclei. , v. 71, (5), 2008, MAY, p. 946-950
    • Year: 2008

  20. The O(1)-Kepler problems
    • Author(s): Meng, Guowu
    • Source: Journal of Mathematical Physics. , v. 49, (10), Oct 2008, article number 102111
    • Year: 2008

  21. MICZ-Kepler Problems in all Dimensions
    • Author(s): Meng, Guowu
    • Source: Journal of mathematical physics. , v. 48, (3), 2007, MAR, article number 032105
    • Year: 2007

  22. Dirac and Yang monopoles revisited
    • Author(s): Meng, Guowu
    • Source: Central European Journal of Physics. , v. 5, (4), 2007, DEC, p. 570-575
    • Year: 2007

  23. Legendre transform, Hessian conjecture and tree formula
    • Author(s): Meng, GW
    • Source: Applied mathematics letters. , v. 19, (6), 2006, JUN, p. 503-510
    • Year: 2006

  24. A path integral derivation of χy-genus
    • Author(s): Meng, GW
    • Source: Journal OF PHYSICS a-mathematical and GENERAL. , v. 36, (4), 2003, JAN 31, p. 1083-1086
    • Year: 2003

  25. Geometric construction of the quantum Hall effect in all even dimensions
    • Author(s): Meng, GW
    • Source: Journal OF PHYSICS a-mathematical and GENERAL. , v. 36, (36), 2003, SEP 12, p. 9415-9423
    • Year: 2003

  26. Bracket models for weight systems and the universal Vassiliev invariants
    • Author(s): Meng, GW
    • Source: Topology and its applications. , v. 76, (1), 1997, MAR 11, p. 47-60
    • Year: 1997

  27. SW = Milnor torsion
    • Author(s): Meng, G.; Taubes, C.H.
    • Source: Mathematical Research Letters. , v. 3, (5), 1996, p. 661-674
    • Year: 1996

  28. SW = Milnor Torsion
    • Author(s): Meng, Guowu; Taubes, Clifford Henry
    • Source: Mathematical research letters. , v. 3, (5), 1996, p. 661-674
    • Year: 1996

Conference paper   

  1. Kepler problem and Jordan algebras
    • Author(s): Meng, Guowu
    • Source: Trends in Mathematics, v. 2019, 2019, p. 181-187
    • Year: 2019

  2. Generalized Kepler Problems and Euclidean Jordan Algebras
    • Author(s): Meng, Guowu
    • Source: Proceedings of the Seventeenth International Conference on Geometry, Integrability and Quantization, 2016, p. 72-94
    • Year: 2016

  3. Tulczyjew Mechanics for Particles in Gauge Fields
    • Author(s): Meng, Guowu
    • Source: Banach Center publications. , v. 110, 2016, p. 193-199
    • Year: 2016

  4. On the trajectories of U(1)-Kepler Problems
    • Author(s): Meng, Guowu
    • Source: Proceedings of the Sixteenth International Conference on Geometry, Integrability and Quantization. , Edited by Ivaïlo Mladenov, Andrei Ludu and Akira Yoshioka. Sofia : Avangard Prima, 2015, p. 219-230
    • Year: 2015

  5. Generalized Hydrogen Atoms and Symmetric Domains of the Tube Type
    • Author(s): Meng, G.
    • Source: Symposium on Representation Theory 2009, Okinawa, Japan. , November 17-20 2009
    • Year: 2009

  6. A generalization of Kepler problems
    • Author(s): Meng, G.
    • Source: XIIth International Conference on Symmetry Methods in Physics, Yerevan, Armenia. , July 3-8 2006
    • Year: 2006

  7. Legendre Transform, Hessian Conjecture and Tree Formula
    • Author(s): Meng, G.
    • Source: Affine Algebraic Geometry of the AMS-TMS Joint Meeting, Taichung, Taiwan. , December 14-18 2005
    • Year: 2005

  8. Geometrical construction of the Quantum Hall Effect in all even dimensions
    • Author(s): Meng, Guowu
    • Source: International Conference on Physics Education & Frontier Research, Overseas Chinese Physics Association/Chinese Physical Society/Shanghai Physical Society/Shanghai Jiao Tong University, Shanghai. , Page 98/ June 28 - July 1
    • Year: 2004

  9. Seiberg-Witten invariants and Milnor Torsion
    • Author(s): Meng, G.
    • Source: The First International Congress of Chinese Mathematicians, Proceedings of ICCM, Beijing, China. , December 12-16 1998
    • Year: 1998

  10. Seiberg-Witten invariants and Milnor Torsion
    • Author(s): Meng, G.
    • Source: Conference on topology of 4-manifolds, MSRI, Berkeley, CA, USA. , January 1997
    • Year: 1997

  11. The Stability Theorem for Smooth Concordance Imbeddings
    • Author(s): Meng, G.
    • Source: Conference on Ktheory and homotopy Theory, Oberwolfach, Germany. , November 5-11 1995
    • Year: 1995