Complex Geometry and Complex Analysis - University of Houston
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Complex Geometry and Complex Analysis

The members of the Complex Geometry and Complex Analysis group conduct research in the areas of  Complex Geometry and Several Complex Variables, Algebraic Geometry, Complex Analysis, Differential Geometry, Diophantine Geometry, and Number Theory etc. The group consists of  faculty members Gordon Heier, Shanyu Ji and Min Ru, as well as seven current graduate students. It runs the Seminar on Complex Geometry and Complex Analysis and regularly offers graduate and undergraduate courses on topics in the above areas.

Members of Complex Geometry and Complex Analysis group

Dr. Gordon Heier
Research Faculty

Ph.D. (Dr. rer. nat.), Bochum University (Germany), 2002
M.S. (Dipl.-Math.), Bochum University (Germany), 1999

Dr. Heier's research interests lie at the intersection of algebraic geometry, differential geometry and diophantine geometry. Concrete topics are: linear systems and multiplier ideal sheaves, Shafarevich Conjecture-type problems, integral points and entire curves on projective varieties and the interplay of the curvature and geometry of projective varieties.

Homepage and CV:
Research and Publications:

Selected recent publications:
- G. Heier, S. S. Y. Lu, B. Wong. Kaehler manifolds of semi-negative holomorphic sectional curvature. J. Differential Geom., 2015 (in press).
- G. Heier. Uniformly effective boundedness of Shafarevich Conjecture-type. J. Reine Angew. Math., 674:99--111, 2013.
- G. Heier, M. Ru. On essentially large divisors. Asian J. Math., 16(3):387--408, 2012.
- G. Heier. Existence of Kaehler-Einstein metrics and multiplier ideal sheaves on del Pezzo surfaces. Math. Z., 264(4):727--743, 2010.


Dr. Shanyu Ji
Research Faculty

Ph.D., Johns Hopkins, 1988

Dr. Shanyu Ji's research interests is in complex analysis, complex geometry, and on CR geometry. In particular, he is interested in the problems on proper mappings between complex balls with different dimension.

Homepage and CV:
Research and Publications:

Selected publications:
- X. Huang, S. Ji and W. Yin, The third gap for proper holomorphic maps between balls , Math. Ann. 358, No. 1-2, 115-142 (2014).
- X. Huang and S. Ji, Mapping Bn into B^{2n-1}, Invent Math, 145(2001), 219-250.
- S.-S. Chern and S. Ji, On the Riemann mapping theorem, Annals. of Math., 144(1996), 421-439.


Dr. Min Ru
Research Faculty

Ph.D., University of Notre Dame, 1990

Dr. Min Ru is a professor at the University of Houston. Before joining UH, he was Benjamin Pierce Assistant Professor at Harvard University. His research interests include Complex and algebraic geometry, Diophantine approximation and Differential geometry (minimal surfaces). He has published over 60 research papers  and has been the recipient of the UH Award for Excellence in Research and Scholarship. He serves on the editorial boards of the Houston Journal of Mathematics. He also has been the recipient of about 10 (combined) NSF and NSA grants.

Homepage and CV:
Research and Publications:

Selected publications:
- Min Ru, Holomorphic curves into algebraic varieties, Annals of Mathematics, 169(2009), 255-267.
- Min Ru & P. Vojta, Schmidt's subspace theorem with moving targets, Inventiones Mathematicae, Vol. 127 (1997), 51-65.
- Min Ru & P.M. Wong, Integral points of P^n - {2n + 1 hyperplanes in general position}, Inventiones Mathematicae, Vol. 106, (1991), 195-216.



Graduate Students:

Current Graduate Students:

    • Alvarez, Angelynn (Advisor: Gordon Heier),
    • Chaturvedi, Ananya (Advisor: Gordon Heier)
    • Hussein, Saud (Advisor: Min Ru)
    • Liao, Hungzen (Advisors: Min Ru and Gordon Heier)
    • Mills, Charles (Advisor: Min Ru)
    • Park, Jungim (Advisor: Min Ru)
    • Ugur, Gul (Advisor: Min Ru)

Former Graduate Students (with Ph.D. degree):

    • 2003: Eunjeong Yi (Advisor: Min Ru). Thesis:  Nevanlinanna theory and iteration of rational maps.
      Current job: Associate Professor, Texas A & M University at Galveston.
    • 2006: Xu, Dekang (Advisor: S. Ji).  First job: CGGVeritas, Houston.
    • 2007: Liu, Y (Advisor: Min  Ru). First job: dGB-USA Earth Science.
    • 2008: Dulock, Matthew (Advisor: Min Ru). Uniqueness theorem for holomorphic curves into Abelian variety. First job: Post-doc at the Fields Institute. Current job: University of North Texas.
    • 2011: Sogome, Suraizou (Advisor: Min Ru).
      Thesis: Non-Intergrated Defect Relation for Meromorphic Maps of Complete Kahler Manifolds Encountering Divisors. 
      First job: HHC, Northwest College.
    • 2014: Andrews, Jared (Advisor Shanyu Ji). Thesis: A New Gap Theorem Result For Proper Holomorphic Mappings Between Complex Balls.
      First job: Data Scientist at Havas Edge, San Diego.
    • 2014: Lee, Brandon (Advisor: Shanyu Ji).
      Thesis: Pseudoconformal Curvature and the Embeddability of a CR Hypersurface.
      First job: Clements high school, Sugar Land.