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2024 TIMS Program in Geometry
Every Monday, Sep. 2 - Oct. 28, 2024
Room 201, Astronomy Mathematics Bldg., NTU

Program

In this lecture series, we will explore several geometric structures on Riemannian, Kaehler and Sasakian manifolds. Topics will include :
• Sasakian manifolds and Sasakian structures
• Foliation singularities and transverse K-Polystable
• The twisted Sasaki-Ricci flow
• Geometrization problem on Sasakian 5-manifolds and analytic MMP
• Geometry and topology of Sasaki-Ricci solitons
• Yau-Tian Donaldson conjecture
• Stability thresholds and canonical metrics
• The uniformization conjecture on complete noncompact Sasakian manifolds
The goal of this lecture series is to provide several analytic methods for existence problems of canonical metrics in Sasakian manifolds.

Speaker : Shu-Cheng Chang (NTU) 

Date : Every Monday, Sep. 2 - Oct. 28, 2024

Time : 14:00 - 15:30 (Lecture); 16:00 - 17:00 (Discussions and Invited talks)

Prerequisites :
   Preliminary knowledge of the Kaehler-Ricci flow and Mori program will be very helpful.

References :
(A) Riemannian, Sasakian and Algebraic geometry :
  1. C. P. Boyer and K. Galicki, Sasaki geometry. Oxford Mathematical Monographs. Oxford University Press, Oxford, 2008.
  2. David E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Progress in Mathematics,  Volume 203, 2001.
  3. Kenji Matsuki, An introduction to Mori program, Springer-Verlag New York, lnc. 2002.
  4. J. Kollar, Einstein metrics on five-dimensional Seifert bundles, J. Geom. Anal. 15 (2005), no. 3, 445--476.
(B) The Kaehler-Ricci flow and Sasaki-Ricci flow :
  1. H. Cao, The Kaehler-Ricci flow on Fano manifolds, Lecture Notes Math. 2086, Springer 2013.
  2. J. Song and B. Weinkove, Introduction to the Kähler-Ricci flow, Lecture Notes Math. 2086, Springer 2013.
  3. V. Tosatti, Kawa lecture notes on the Kähler-Ricci flow, Ann. Fac. Sci. Toulouse Math. 27 (2018), no.2, 285-376.
  4. K. Smoczyk, G. Wang and Y. Zhang, The Sasaki-Ricci flow, Internat. J. Math. 21 (2010), no. 7, 951--969.                 

Organizers : Shu-Cheng Chang (NTU) and Chin-Lung Wang (TIMS & NTU)