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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)
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.
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.

NCTS support Algebraic Geometry in East Asia Seminar officially, please check the link below for more information.



Generalized Canonical Models of Foliated Surfaces Abstract: By work of McQuillan and Brunella, it is known that foliated surfaces of general ty...
Stokes Matrices, Surfaces, and Points on Spheres Abstract: Moduli spaces of points on n-spheres carry natural actions of braid groups. For n=0...
On the Four-dimensional Minimal Model Program for Singularities and Families in Positive Characteristic Abstract: I will discuss new developments on the four-dimensional Minimal Model Program in po...
Some Algebraic Surfaces with Canonical Map of Degree 10, 12, 14 Abstract: Surfaces of general type with canonical map of degree d bigger than 8 have boun...
2021 NCTS Workshop and Course on Higher Dimensional Algebraic Geometry Aim & Scope: Higher dimensional algebraic geometry has been an active and exciting resear...
Miranda Chih-Ning Cheng
Korteweg-de Vries Institute for Mathematics and Institute of Physics, University of Amsterdam
March 11 - December 31, 2020
Hsueh-Yung Lin
Kavli Institute for The Physics and Mathematics of The Universe
April 28, 2020 - January 6, 2021


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