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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.
 

 

 
Events
2019/01/04
Feynman Diagrams and Singularities of Configuration Polynomials Abstract: A Feynman diagram is a graph with some extra decorations. It contains in condensed ...
2018/12/21
Demailly's Conjecture on Waldschmidt Constants for Sufficiently Many Points in P^n Abstract: Let be a set of general points in the projective space  over an alg...
2019/07/29
MSRI-NCTS Joint Summer School on Toric Varieties Description Toric varieties are algebraic varieties defined by combinatorial data, and there ...
2019/02/18
Taiwan Mathematics School: Algebraic Surfaces 1.Background and purpose: In this course, we are going to give an introduction to the theory...
 
 
Visitors
Paolo Cascini
Imperial College London & NCTS
p.cascini[AT]imperial.ac.uk
December 7 - 18, 2018
 
Chen Jiang
University of Tokyo
chen.jiang[AT]ipmu.jp
December 23 - 30, 2018
 
Zhi Jiang
Fudan University
zhijiang[AT]fudan.edu.cn
January 10 - 20, 2019
 
Bernhard Müuhlherr
Justus-Liebig-Universität Gießen
Bernhard.Muehlherr[AT]math.uni-giessen.de
March 1 - 22, 2019
 
Arick Shao
Queen Mary University of London
a.shao[AT]qmul.ac.uk
December 10 - 23, 2018
 
Richard M. Weiss
Tufts University
rweiss[AT]tufts.edu
March 1 - 22, 2019
 

 

 
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