Homepage for Naichung Conan Leung

Associate Professor of Mathematics
Office: Vincent Hall 355
Phone: 612-624-5224
Email: LEUNG@MATH.UMN.EDU
Address: School of Mathematics, University of Minnesota, MN 55455                        Last update: April 30, 2004
During the Spring semester of 2004, I am teaching:
(1) Math 8271, Lie groups & Lie algebras;
(2) Math 1271, Lecture 50, Calculus I.
My office hours are 1:25 pm - 2:15 pm, MWF.


I orgainize the weekly Differential Geometry and Geometric Analysis seminars : Every Thursday from 2:20 pm to 3:20 pm in room 570, Vincent Hall.

I am an editor of the New York Journal of Mathematics.


Future conferences/workshops that I (co-)organize :   
-- Symplectic Geometry/Topology seminars in the University of Minnesota, April 30 - May 3, 2004.
(Speakers: X.X. Chen, T. Coates, R. Gompf, N.C. Leung, J. Li, T.J. Li, Y.G. Oh, Y.B. Ruan).

-- Mirror Symmetry conference, July 9 - 13, 2004, in the National Center for Theoretical Sciences in Taiwan.
(Speakers: J. Bryan, R. Donagi, M. Gross, S. Gukov, S. Hosono, A. Kovalev, K.F. Liu, J. Loftin, Z.Q. Lu, B. Siebert, N.C. Leung, S.T. Yau, I. Zharkov and more).  

-- The second Yamabe Symposium in UMN, Septermber 17 - 19, 2004.
(Speakers: R. Bryant, K.F. Liu, D.H. Phong, Y.B. Ruan, I.M. Singer, K. Uhlenbeck, S.T. Yau).     

-- Differential Geometry Program for year 2004 - 2005 in the National Center for Theoretical Sciences in Taiwan.

-- Symplectic Geometry and Physics program, Reunion conference in Lake Arrowhead, May 22 - 26, 2005, by the Institute of Pure and Applied Mathematics.

 

  
   My Research statement (updated 10/2002); Curiculum Vita (updated 10/2002)


   Papers and preprints:
G_2-flops, triality for TQFT and exact triangle for Floer homology
In preparation.



Counting elliptic curves on K3 surfaces
(with Junho Lee)
Preprint
Yau-Zaslow formula for non-primitive classes in K3 surfaces
(with Junho Lee)
math.SG/0404537
Instantons and branes on manifolds with vector cross products
(with Jao-Hyouk Lee)
math.DG/0402044
Intersection theory of coassociative submanifolds in G_2 manifolds
and Seiberg-Witten invarinats  (with Xiaowei Wang)
math.DG/0401419 .
Almost toric symplectic four-manifolds
(with Margaret Symington)
math.SG/0312165
Topological Quantum Field Theory for
Calabi-Yau threefolds and G_2 manifolds		 Abstract ,
ps , pdf 		Adv. Theor. Math. Phys.. (2002)
Vol. 6, 575-589.
Riemannian geometry over different normed division algebra Abstract ,
ps , pdf 		Journal of Differential Geometry
61 (2002), no. 2, 289-333.
Geometric aspects of mirror symmetry,
with SYZ for Rigid CY manifolds		 Abstract ,
ps , pdf 		To appear in the 
proceedings of ICCM 2001.
Geometric structures on G2 and Spin(7)-manifolds 
(with Jae-Hyouk Lee)		 Abstract ,
ps , pdf .		 Preprint
A general Plucker formula Abstract ,
ps , pdf 		Preprint
Lagrangian submanifolds in hyperkahler manifolds and 
Legendre transformation		 Abstract ,
ps , pdf 		Journal of Differential Geometry (2002)
61, 107-145.
Mirror symmetry without corrections Abstract , 
ps , PDF 		To appear in
Comm. Analysis and Geometry
ADE-bundles over rational surfaces, 
configuration of lines and rulings		 Abstract , 
ps , PDF 		Preprint
The signature of a toric variety
(with Victor Reiner).		 Abstract , 
ps , DVI .		 Duke Math. Journal (2002)
Vol. 111, no. 2, 253-286.
Harmonic maps and the topology of 
conformally compact Einstein manifolds (with Tom Wan)		 Abstract ,
ps , pdf 		Math. Res. Lett., (2001),
vol. 8, no. 5-6, 801-812.
G-Bundles on Abelian surfaces, Hyperkahler manifolds and 
Stringy Hodge numbers (with Jim Bryan and Ron Donagi).		 Abstract , 
ps , PDF 		Turkish J. Math. 25 (2001), 
no. 1, 195--236
Multiple covers and the integrality conjecture for rational curves in
CY threefolds (with Jim Bryan and Sheldon Katz).		 Abstract , 
ps , PDF 		J. Algebraic Geometry 10 (2001), 
no. 3, 549--568. 
From Special-Lagrangian to Hermitian-Yang-Mills via 
Fourier-Mukai Transform (with S.-T. Yau, Eric Zaslow).		 Abstract , 
ps , PDF 		Adv. Theor. Math. Phys.. (2000),
Vol. 4, No. 6, 1319-1341.
The enumerative geometry of K3 surfaces and modular forms 
(with Jim Bryan).		 Abstract , 
ps , PDF 		Journal Amer. Math. Soc. (2000),
13, 371-410. 
Non-Abelian Seiberg-Witten equations on Einstein manifolds. Abstract ,
ps , DVI 		Journal fur die reine und angewandte Mathematik.
Vol. 519 (2000) 17-29.
Counting curves on irrational surfaces (with Jim Bryan). Abstract ,
ps, PDF 		Survey of Differential Geometry, 
Vol. V. (1999) 313-339.
Generating functions for the number of curves on Abelian surfaces (with Jim Bryan). Abstract , 
ps , PDF 		Duke Math. Journal
Vol. 99, No.2 (1999)  311-328.
Degeneration of Kahler Einstein metrics on complete Kahler manifolds (with Peng Lu). ps , DVI Comm. Analysis and Geometry
Vol.7,  No.2 (1999), 431-449.
Branes and toric geometry (with Cumrun Vafa). Abstract
ps , DVI 		Advance Theor. Math. Phys. 
No. 2 (1998) 91-118.
Bando Futaki invariants and Kahler Einstein metric. Abstract ,
ps , DVI  		Comm. Analysis and Geometry
Vol. 6, No. 4 (1998) 799-808.
Symplectic structures on gauge theory. Abstract ,
ps , DVI 		Comm. Mathematical Physics
193 (1998) 47-67.
Einstein type metrics and stability on vector bundles. Abstract ,
ps , DVI 		Journal of Differential Geometry
Vol. 45 no.3, (1997) 514-546.
Seiberg Witten invariants and uniformizations. Abstract ,
ps , DVI 		Mathematische Annalen
306 (1996) 31-46.
Thesis, Differential geometric and symplectic
interpretations of stability in the sense of Gieseker		 Abstract ,
ps , DVI 		M.I.T. thesis.






Analytic Torsion for Quaternionic manifolds and related topics
(with Sangkug Yi)		 Abstract , 
ps , PDF 		dg-ga/9710022


Conferences/Workshops I organized earlier :
Year 2004

Year 2003
   * The workshop on   'Geometry and Physics on G_2 manifolds' in IPAM in April 2003.

Year 2002
   * The first Yamabe Symposium in UMN, Septermber 20 - 22, 2002. (Photos and Talks online )

Others
    * Weekly Differential Geometry and Geometric Analysis seminars during the Spring semester of 2004.
    * A working seminar on Differetial Geometry which meets on every Tuesday at 3 p.m. during Fall 2003 in VinH 203. Schedule here.


 
Links:
Math departments by country: USA , A-F , G-M , N-Z ,
Math. Institutes: 
US/Canada: MSRI . PIMS . BIRS . IAS . AMS . Clay . Fields .ITP . IPAM
Asia: . NCTS  . IMS  .RIMS  .
Europe: Oberwolfach , IHES . ETH . Newton . MPI  .

Symplectic Topology seminars are organized by Tian Jun Li;

Algebraic Geometry seminars are organized by Ionut Ciocan-Fontanine.


Yahoo , Yahoo mail , New York Times , Minneapolis Weather , Star Tribune .  Singtao . New Math .

        Calender for this academic year in UMN

        Lectures online. 

        If you are visitor, this page contains some useful informations.

        LiE package, Google search, YahooMail .

        Photo site for the Obernai workshop, June 1999.

        My pictures: November 1999 in Toronto , in Niragara Falls
 

I was the organizer for a weekly Geometric Analysis seminar from Fall 1994 till Fall 1999. You can find the previous schedule here .

Courses taught in revious terms: 

Fall  2002, (1) Math 8365 Riemannian Geometry; (2) Math 1271, Lecture 010 , Calculus I; (3) Math 1271, Lecture 060 , Calculus I.
 Spring 2002 Math 8370 Symplectic Geometry (2nd semester)
Fall 2001 MATH 1271 (Calculus I) and MATH 8370 (Symplectic geometry)
Spring 2000 MATH 8302   Manifolds and Topology.
Fall 1999 (i) MATH 1271 Calculus I (sections 22,24,25) and (ii) MATH 8301   Manifolds and Topology.
Spring 1999 (i) MATH 1251 LECTURE 01 One variable Differential & Integration Calculus I
(sections 01-04) and (ii) MATH 8265  Topics in algebraic geometry.
 
 

Disclaimer :The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by the University of Minnesota.