NCTS 2005 Summer School in Algebraic Geometry

	Last updated: June 6, 2005
Time:	August 8–18, 2005, Monday to Thursday, am 9:00–10:30 & am 10:45 to pm 12:15
Organizer:	Chin-Lung Wang
Invited Lecturers:	Andrey Todorov (UC Santa Cruz & Bulgarian Academy of Sciences) Kang Zuo (Mainz, Germany) Jian Zhou (Tsing-Hua University, China) Chin-Lung Wang (National Central University & NCTS)
Place:	Lecture Room B of National Center for Theoretical Sciences 4th floor, The 3rd General Building, National Tsing Hua University
Program:	<< TODOROV, Andrey; >> Moduli of Hyper-Kaehler Manifolds. Large Radius Limit and the SYZ Conjecture. (1) Preliminary material; Variations of Hodge structures of weight two, construction of the Hilbert scheme and the existence of the Teichmuller space. (2) Review of the theory of moduli of Hyper-Kaehler manifolds and the existence of large radius limit in the compactified moduli space. (3) Nef divisors and vanishing theorems. (4) The existence of Lagrangian fibrations of special algebraic HK manifolds. 　 << ZUO, Kang (左康); >> Geometry of Moduli Satcks of Polarized Manifolds. (1) Arakelov inequality over a higher dimension base, characterization of certain type Shimura varieties (joint program with Eckart Viehweg). (2) Geometry and arithmetic of non-rigid families of C-Y3-folds (joint paper with Eckart Viehweg). (3) Intersection-cohomology, algebraic L^2-Higgs cohomology and Chow- Kuenneth decomposition of certain algebraic cycles in universal families over 2-dim Shimura varieties (joint program with Stefen Mueller-Stach). 　 << ZHOU, Jian (周堅); >> Localizations on Moduli Spaces and String Dualities. I will explain how combinatorial objects such as partitions of numbers and summations over graphs arise when one applies localization techniques on various moduli spaces. Applications to some string dualities will also be discussed. (1) Introduction to localization. (2) Localizations on moduli spaces of stable maps. (3) Localizations on relative moduli spaces of stable maps. (4) Localizations on moduli spaces of torsion free sheaves. 　 << WANG, Chin-Lung (王金龍); >> K-equivalence in Birational Geometry. (1) Motivations from 3D minimal model theory. (2) Motivic (cohomological) aspect of K-equivalence relation. (3) Invariance of Complex elliptic genera and the weak decomposition theorem of K-equivalent map. (4) Invariance of quantum product under simple ordinary flops (joint work with Hui-Wen Lin).