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Algebraic Geometry
Taiwan has a substantial research group in algebraic geometry and NCTS’s algebraic geometry group is responsible in coordinating and supporting research in this vast area.  Based on members’ expertise, the algebraic geometry group’s current main focuses are as follows:
 
Birational Geometry (Jung-Kai Chen,Jiun-Cheng Chen,Chen-Yu Chi)
The minimal model program attempts to find canonical representatives for birational equivalence class of varieties.  In characteristic zero, the research program follows the foundation outlined by Reid, Shokurov, Kawamata, Kollar, Mori and others.  In positive characteristics, the main focus is the Frobenius morphism and the Serre vanishing theorem and their applications to the minimum model program.
 
Calabi-Yau Varieties, moduli and modularity (Jeng-Daw Yu)
Research on Calabi-Yau manifolds are central in both mathematics and mathematical physics. The algebra-geometric aspects focus on the study of moduli and arithmetic of Calabi-Yau manifolds.  This includes Calabi-Yau threefolds and their relations to string theory and mirror symmetry in mathematical physics and modularity of Calabi-Yau manifolds over Q. 
 
Enumerative Geometry and Gromov-Witten theory (Wan-Keng Cheong)
The recently discovered Gromov-Witten invariants and their variants made solutions to many difficult curve-counting problems possible.  These invariants also give rise to a class of crepant resolution conjectures.  The algebraic group is active in this area.
 
Non-abelian cohomology and related theory (Wu-Yen Chuang,Zhu Eugene Xia)
The algebraic geometry group is active in the moduli spaces of sheaves and Higgs bundles and other related objects and representation varieties over curves and higher dimension varieties.
 
Conferences and Seminars
A major component of NCTS’s responsibility is to promote the exchange of ideas and research collaboration.  The algebraic geometry group routinely organizes conferences both local and international on topics of interest.  One may find these past events from NCTS’s main pages.  
The algebraic group also sponsors weekly regular and student seminars in universities across Taiwan.  The regular seminars focus on recent research advances in topics of importance while the student seminars attempts to introduce research topics and encourages graduate students to give presentations.
 

 

 
 
 
Visitors
Miranda Chih-Ning Cheng
Korteweg-de Vries Institute for Mathematics and Institute of Physics, University of Amsterdam
mcheng[AT]uva.nl
December 20, 2017 - January 20, 2018
 
Yoshinori Gongyo
University of Tokyo
gongyo[AT]ms.u-tokyo.ac.jp
December 28, 2017 - January 4, 2018
 

 

 
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