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(Zeno) Zheng Huang
Department of Mathematics
CUNY - Staten Island 
1S-208
Staten Island, NY 10314
Tel: 918-582-3625(O)   

        Current status


Assistant Professor in the Mathematics Department at College of Staten Island, the City University of New York. Previously, I spent Fall 2007 at MSRI, Berkeley, on an MSRI research fellowship; I was an assistant professor at the University of Michigan, from 2004 to 2007, and before that, I was a visiting assistant professor at the University of Oklahoma, from 2003 to 2004, immediately after I graduated from Rice University with a PhD in 2003.  

 Research interests

Much of my research has been focusing on Riemann surfaces and their moduli spaces, especially on Teichmuller space. This is a space of complex (or conformal) structures on a (compact) Riemann surface, and the theory of Teichmuller space has played a central role in many aspects of modern mathematics.

I also study differential geometry (Riemannian and Kahlerian) and geometric analysis. The theory of harmonic maps is an important part of my research.

I try to learn more algebraic geometry as well, especially the connection to Teichmuller theory.

      
           Seminars         

         1. Tuesdays: Geometry seminar at Princeton.
          2. Fridays: Teichmuller seminar at the Graduate Center

       Math resources on the web

        1. Rice library webpage
        2. MSRI webpage
        3. Webpages of AMS , SIAM and IMA
        4. Mathematics www virtual library
        5. Mathematical Reviews on the web: MathSciNet
      6. A Gallery of Minimal Surfaces
      7. Mathematical Problems by David Hilbert

          Complete List of Publications

8. Huang Z.: in preparation, 2007       

7. Huang Z.: Average curvatures of Weil-Petersson geodesics in Teichmuller space,math.DG/0703775, submitted, 2007

We aim to investigate the shape of a Weil-petersson geodesic, by looking at a surface bundle over a Weil-Petersson geodesic in Teichmuller space as a three manifold. We obtain results on all three basis curvatures and show that the total curvatures over the surface are zero in transverse directions, and so is the curvature in the fiber direction (after normalization).  

6. Huang Z.: The Weil-Petersson geometry on the thick part of the moduli space of Riemann surfaces , PDF Proc. Amer. Math. Soc., No. 135 (2007) 3309-3316       

We show that, in the thick region, the Weil-Petersson sectional curvatures of the moduli space are bounded independent of the genus of the underlying surface.  

5. Huang Z.: Calclulus Variation and the $L^2$-Bergman metric on Teichmuller space, math.DG/0506569 submitted, 2005

I was finally able to type it up to this paper. We show the second variation of a chosen family of harmonic maps between canonical metrics on a Riemann surface yields the $L^2$-Bergman metric on Teichmuller space globally.  

4. Huang Z.: Asymptotics of the Gaussian Curvatures of the Canonical Metric on the Surface, math.DG/0604579, submitted, 2005       

In this short note, we study the Gaussian curvatures of the canonical metric on a Riemann surface under deformation. We find the Gaussian curvatures have no lower bound, nor negative upper bound (even in the case of nonhyperelliptic surfaces) near the compactification divisor of the moduli space.  

3. Huang Z.: On Asymptotic Weil-Petersson Geometry of Teichmueller space of Riemann surfaces, Asian J. Math., vol. 11, no.3, 459-484 (2007) PDF.

This is a work extended from my thesis on the geometry of Teichmuller space. We provide pointwise estimates on the Weil-Petersson sectional curvatures, anywhere in Teichmuller space. More precise way to state the main theorem is: we obtain the extremely hyperbolic directions (holomorphic sectional curvatures in the order of the hyperbolic systole) and we find asymptotically flat directions with lower bounds in the order of O(systole). Recently, Wolpert improved the lower bounds for asymptotically flat directions to O(sys^2).

2. Huang Z.: Asymptotic flatness of the Weil-Petersson metric on Teichmueller space, Geom. Dedi., Vol. 110, No. 1, 81-102, (2005) PDF.

We proved the sectional curvature of the Weil-Petersson metric on Teichmuller space is not pinched negative in my first paper here. This version is better than the published version because of the improvement of my LaTex typing skill (I was a rookie LaTex user back then!). An argument in one of the lemmas has also been refined.       

1. Huang Z.: Harmonic maps and the geometry of Teichmueller space, thesis, Rice University, 2003              

Selected Invited Talks

2008:
26.   The shape of a Weil-Petersson geodesic, Ahlfors-bers Colloquium, Rutgers University - Newark, May, 2008.
25.   Metrics on Teichmuller space, complex analysis seminar, CUNY, Graduate Center, April, 2008.

2007:
24.   The surface bundle over a Weil-Petersson geodesic, geometry seminar, University of Arizona, Nov., 2007.
23.   On WP, MSRI, Oct., 2007.
22.   The Weil-Petersson geometry of the moduli space, Colloquium, CUNY-Staten Island, March, 2007.
21.   The Weil-Petersson geometry, Colloquium, Central Connecticut State University, Feb., 2007.

2006:
20.   The Asymptotics in the Weil-Petersson geometry of the moduli space of surfaces, University of Illinois, Urbana-Champaign, Nov., 2006.
19.   The Interior geometry of the moduli space of surfaces, University of Connecticut, Oct., 2006.
18.   The canonical metric on a Riemann surface and its induced metric on moduli space, University of Oklahoma, Karcher Colloquium, Aug, 2006.
17.   The Interior geometry of the moduli space of surfaces, Lehigh University, June, 2006.
16.   The Weil-Petersson geometry in the thick part of the moduli space, Fields Institute, Toronto, May, 2006.
15.   Calculus variation and the $L^2$-Bergman metric on the moduli of surfaces, Geometric Analysis Seminar, University of Toledo, Feb., 2006.

2005:
14.   Asymptotic Weil-Petersson geometry, Geometric Analysis Seminar, Michigan State University, September, 2005.
13.  The Canonical Metric on a Riemann Surface and Its Induced Metric on the Moduli Space, Ahlfors-Bers Colloquium, May 2005.
12. Incomplete Riemannian Metrics on Moduli of Curves, IAS/Princeton Complex Geometry Seminar, April, 2005.
11. Asymptotic Weil-Petersson Geometry of Moduli Space of Riemann Surfaces, Geometry Seminar, University of Oregon, March, 2005.

2004:
10.  Geometric Variational Problem and the Geometry of Teichmuller Space, Complex geometry seminar, Johns Hopkins University, October, 2004.
9. Asymptotic Geometry of Moduli Space of Riemann Surfaces, Wesleyan Conference on Hyperbolic geometry and Geometric Analysis, Wesleyan University, October, 2004.        
8.  Asymptotic Weil-Petersson Geometry of Teichmuller Space, Geometry seminar, University of Michigan, Sept., 2004.
7. Variational Aspects of Moduli Space of Riemann Surfaces, AMS/Mexicana Meeting, May, 2004.        
6. Asymptotic Rank of Weil-Petersson-Teichmuller Space, AMS meeting, Phoenix, January, 2004.        

2003:
5. Asymptotic Flatness of Teichmuller Space, Conference on Teichmuller Geometry, U. of Illinois at Chicago, Nov., 2003.  
4. Asymptotic Weil-Petersson Geometry of Teichmuller space, Geometry Seminar, Oklahoma State Univ., October,  2003.  
3. Geometric Variational Problem of 2-dim'l and Harmonic Teichmuller Theory, I, II, Topology Seminar, Univ. of Oklahoma, 2003
 2. Harmonic Maps and Teichmuller Geometry, Geometric Anaysis Seminar, Rice University, 2003        

2002:
1. Asymptotic Flatness of the Weil-Petersson Metric on Teichmueller Space, AMS Meeting, Portland, June, 2002.        
     

 
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