This award provides funding to help defray the expenses of U.S. participants in the "International Conference on Several Complex Variables and Complex Geometry" that will be held from July 2-13, 2012, in the Institute of Mathematics of the Academia Sinica in Taiwan.
This workshop will highlight recent developments and new research directions in a number of areas that fall under the general heading "several complex variables and complex geometry" (e.g., heat kernels for sub-Laplacians on unit spheres in complex n-space and the Poisson summation formula; equivalence problems for complex manifolds; holomorphic deformation of compact complex manifolds; the Fujita conjecture and related topics; smooth and analytic hypoellipticity for partial differential operators). The program features a slate of mini-courses for graduate student during the week leading up to the main workshop. The conference program also provides ample opportunity for graduate students, postdocs, and other young scientists to present their work.
We used this grant to organize two international workshops at the National Center for Theoretical Sciences in Hisnchu, Taiwan. The first one was "Meet with Professor Ngaiming Mok" which was held at NCTS on June 30, 2104. The second one was "2014 NCTS Workshop on Geometric and Singular Analysis" which was held at NCTS from July 3-4, 2014. These two workshops provided opportunites for researchers and graduate students from USA, Taiwan, Japan, Germany and China to exchange mathematical ideas. We also offered a mini-course on "Singular integrals, Hardy spaces and elliptic boundary value problems" at NCTS. Each person who attended these conferences brought the knowledge gained by our speakers to their own institutes or communities of learning, thus spreading what we taught them to others. During these activites, we started several joint research projects and produced research papers which were published (or accepted for publication) in mathematics journals. These activites also provided opportunites for gradaute students to learn updated research in several complex variables, complex geometry, singular analysis, subRiemannian geometry,... etc. At least one of the students who attended these activities received a full scholarship from University of Maryland at College Park to continue her post graduate study. Several of them were accepetd by Ph.D. programs in Taiwan. We finished several reserach papers and published in renowned research journals. In those papers, we acknowledged NSF for the support. For example: 1. D.C. Chang, S.C. Chang and J. Tie: Calabi-Yau theorem and Hodge-Laplacian heat equation in a closed strictly pseudo convex CR manifold, Journal of Differential Geometry, 97, #3, 395-426, (2014). 2. O. Calin, D.C. Chang and M. Eastwood: Integrability conditions for Heisenberg and Grushin type distributions, Analysis & Mathematical Physics, published online: DOI 10.1007/s13324-014-0073-x, 4, #1-2, 99-114, (2014). 3. D.C. Chang, N. Habal and B.-W. Schulze: The edge algebra structure of the Zaremba problem, J. Pseudo-differential Op. Appl., published online: DOI: 10.1007/s11868-013-0088-7, 5, #1, 69-155, (2014). 4. D.C. Chang and S.Y. Feng: Geometric Analysis on Ornstein-Uhlenbeck Operators with Quadratic Potentials, Journal of Geometric Analysis, Published on line: DOI: 10.1007/s12220-012-9370-9, 24, #3, 1181-1200, (2014). 5. D.C. Chang and J. Xiao: $L^q$-Extensions of $L^p$-Spaces by Fractional Diffusion Equations, published online: DOI: 10.3934/dcds.2015.35.1905, Discrete and Continuous Dynamical System - A, an AIMS's Journals, 35, #5, 1905-1920, (2015). 6. J. Cao, D.C. Chang, D. Yang and S. Yang: Riesz Transform Characterizations of Musielak-Orlicz-Hardy Spaces, to appear Transactions of AMS, (2015).
