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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. Recently I am working on problems in hyperbolic geometry, or more particularly, the geometry of quasi-Fuchsian space.

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

      
           Seminars         

         I live half way between Princeton and Rutgers, so I attend seminars at these institutions regularly, besides attending CUNY seminars. Seminars at Princeton.
          Seminars at Rutgers.
          Seminars at the CUNY 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

10. Huang Z. (with B. Wang) in preparation, 2009       

9. Huang Z. (with R. Guo, B. Wang) Quasi-Fuchsian 3-manifolds and metrics on Teichmuller spacce, PDF 2009       

We relate the geometry of almost Fuchisan three manifolds to metrics on Teichmuller space: we follow the locus of the normal flow from the minimal surface in Teichmuller space, and obtain upper bounds for Teichmuller distances between points on the locus. Varying the immersions from minimal surfaces into some quasifuchsian manifolds, we estabilish a potential function for the Weil-Petersson metric.  

8. Huang Z. (with B. Wang) Geometric evolution equations and foliations on quasi-Fuchsian three manifolds, PDF, 2009       

For any quasi-Fuchsian manifold which contains an incompressible surface whose principal curvatures are within -1 and 1, using volume preserving mean curvature flow, we show that it admits a (unique) foliation of CMC surfaces. In particular, it admits a unique minimal surface with the same curvature bounds. An upper bound for the convex core volume of such three manifolds is also obtained, in terms of the maximal principal curvature on the minimal surface.  

7. Huang Z.: Average curvatures of Weil-Petersson geodesics in Teichmuller space,preprint, in revision

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.  

6. Huang Z.: The Weil-Petersson geometry on the thick part of the moduli space of Riemann surfaces , PDF PAMS, 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

I was finally able to type it up 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, manuscript        

It was an exercise back in 2002. Will not pursue publication.  

3.5. Huang Z.: Erratum to "On Asymptotic Weil-Petersson Geometry of Teichmueller space of Riemann surfaces" PDF.

The correct statement on the original theorem 1.1 is given.

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 proved the WP sectional curvature has no lower bound by obtaining the extremely hyperbolic directions (holomorphic sectional curvatures in the order of the inverse of the hyperbolic systole) and we find asymptotically flat directions with lower bounds in the order of O(systole). Recently, Wolpert improved this bound 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 only slightly 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

2009:
31.   Undergraduate Lecture Series, CCSU, Nov., 2009.
30.   CUNY-Graduate Center, Nov., 2009.
29.   Complex Geometry Seminar, Rutgers University, Sept., 2009.
28.   NSF Conference on Family of Riemann Surfaces, July, 2009.
27.   Complex Geometry Seminar, Ohio State University, Feb., 2009.

2008:
26.   Ahlfors-bers Colloquium, Rutgers University - Newark, May, 2008.
25.   Complex Analysis Seminar, CUNY, Graduate Center, April, 2008.

2007:
24.   geometry seminar, University of Arizona, Nov., 2007.
23.   MSRI, Oct., 2007.
22.   Colloquium, CUNY-Staten Island, March, 2007.
21.   Colloquium, Central Connecticut State University, Feb., 2007.

2006:
20.   University of Illinois, Urbana-Champaign, Nov., 2006.
19.   University of Connecticut, Oct., 2006.
18.   University of Oklahoma, Karcher Colloquium, Aug, 2006.
17.   Lehigh Geometry Conference, Lehigh University, June, 2006.
16.   Fields Hyperbolic Geometry Workshop, Fields Institute, Toronto, May, 2006.
15.   Geometric Analysis Seminar, University of Toledo, Feb., 2006.

2005:
14.   Geometric Analysis Seminar, Michigan State University, September, 2005.
13.  Ahlfors-Bers Colloquium, Ann Arbor, MI, May 2005.
12. IAS/Princeton Complex Geometry Seminar, April, 2005.
11. Geometry Seminar, University of Oregon, March, 2005.

2004:
10.  Complex geometry seminar, Johns Hopkins University, October, 2004.
9. Wesleyan Conference on Hyperbolic geometry and Geometric Analysis, Wesleyan University, October, 2004.        
8.  Geometry seminar, University of Michigan, Sept., 2004.
7. AMS/Mexicana Meeting, Houston, May, 2004.        
6. AMS meeting, Phoenix, January, 2004.        

2003:
5. Conference on Teichmuller geometry, University of Illinois at Chicago, Nov., 2003.  
4. Geometry Seminar, Oklahoma State Univ., October,  2003.  
3. Topology Seminar, University of Oklahoma, 2003
 2. Geometric Anaysis Seminar, Rice University, 2003        

2002:
1. AMS Meeting, Portland, June, 2002.        
     

 
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