Degenerations of polarized Hodge structures

Reading Seminar


  Fall 2018


Thursdays 1-2 PM
(Tuesdays 3-4 PM)

MATH 350


   
  Zheng, Jonathan, and Yano are leading a reading seminar roughly following Kato and Usui's Classifying spaces of degenerating polarized Hodge structures.

Schedule of talks:

 Thursday September 13
 Zheng, Jonathan, and Yano
 Organization and Jonathan's brief introduction to log structures
 Thursday September 20
 Zheng
 Review of pure Hodge structures, and Kato Usui's Chapter 1
 Thursday September 27
 Zheng  Review of pure Hodge structures, and Kato Usui's Chapter 1, continued: degenerations of Hodge structures
 Tuesday October 2
 Yu  A longer introduction to log structures
 Thursday October 4  Yu
 Intro to log structures continued
 Thursday October 11  Yu
 Log structures continued
 Thursday October 24
 Yano
 Log geometry and toric varieties
  Thursday November 1
 Sebastian
 Log smooth maps
 Thursday November 8  Sebastian
 Log smooth maps continued
 Thursday November 15
 Jonathan  Kato--Nakayama spaces
 Tuesday November 27
 Jonathan 
 K-U Chapter 2.1-2, Kato--Nakayama spaces continued
 Thursday November 29
 Jonathan
 K-U Chapter 2.3-4, Local systems on Kato--Nakayama spaces, and polarized log Hodge structures
 Tuesday December 4
 Jonathan
 K-U Chapter 2.3-4, Local systems on Kato--Nakayama spaces, and polarized log Hodge structures continued
 Thursday December 6
 Jonathan
 K-U Chapter 2.5, Nilpotent orbits and period maps
 Tuesday December 11
 Yano and Zheng
 Review of classical degeneration of Hodge structures, in connection with K-U polarized log Hodge structures
 Thursday December 13
 Zheng
 Classical degenerations of Hodge structures, continued: Clemens--Schmid and degenerations of curves
 Tuesday December 18
 Yano
 Classical degenerations of Hodge structures, continued: Mumford et al. toroidal compactifications of arithmetic quotients

This seminar will continue in the spring.


References:
  1. Kato and Usui's Classifying spaces of degenerating polarized Hodge structures.
  2. Peters and Steenbrink's Mixed Hodge structures.
  3. Griffiths et al. Topics in transcendental algebraic geometry.
  4. Kazuya Kato, Logarithmic structures of Fontaine--Illusie
  5. Dan Abramovich et al., Logarithmic geometry and moduli (arXiv)
  6. Danny Gillam, Log geometry
  7. Arthur Ogus, Lectures on logarithmic algebraic geometry
  8. Volker Pahnke, Uniformizing log-abelian varieties



This webpage is yet another example of a shameless (indirect) copying of a webpage of Pasha Belorousski's at the University of Michigan.