Some talks by Ching-Li Chai
Work on these articles have been supported by the National Science
Foundation since 1990, including the following grants:
DMS09-01163, DSM04-00482, DMS01-00441, DMS98-00609, DSM95-02186.
p-divisible groups and a foliation of moduli spaces of abelian varieties,
Harvard-MIT Algebraic Geometry Seminar, November 26, 2019.
p-divisible groups: foliation of moduli spaces revisited
Plenary lecture, ICCM Annual Meeting, December 27, 2018.
- Moduli of abelian
varieties, Graduate Colloquium, University of Pennsylvania,
March 15, 2017.
- Siegel modular varieties
and Hecke symmetry, Colloquium, Lehigh University, Bethlehem,
September 21, 2016.
- A tour
of Fermat's world, preceptorial lecture, March 14, 2016.
- Moduli of abelian varieties:
symmetry and rigidity, Colloquium, Univervisty of Michigan,
Ann Arbor, December 1st, 2015.
- Sustained p-divisible
groups. Slides of a talk at the Conference on Arithmetic Algebrai
Geometry on the occasion of the 60th birthday of Gerd Falting.
- A scheme-theoretic definition
of leaves and Serre-Tate coordinates. Hand-written notes of a lecture
on April 14, 2014, in the conference "Application of automorphic forms
in number theory and combinatorics", in honor of Wen-Ching Winnie Li,
April 12-15, Baton Rouge, Louisiana.
- Leaves and local Hecke symmetry.
Slides of a lecture given on July 15 in ICCM 2013, Taipei.
- Algebraic interpretation of
modular forms. Notes for a talk at TIMS, National Taiwan University, Taipei,
October 31, 2012. Contents: modular forms as global sections of powers
of the Hodge line bundle on modular curves, Shimura's nearly holomorphic
modular forms as global sections of symmetric powers of the relative
first de Rham cohomology, modular interpretation of some Eisenstein series,
including the non-holomorphic weight 2 Eisenstein series and also
Hecke's weight one forms.
- How to compute the Lubin-Tate
action print version of a talk on September 12, 2012, NCTS, Hsinchu;
- Geometry and numbers
print version of a talk on June 06, 2012 at National Chiao Tung University;
- Hecke symmetry, rigidity
and the Lubin-Tate action print version of a talk at the June 2012 conference
"p-adic modular forms and arithmetic, a conference in honor of Haruzo Hida on
his 60th birthday"; slides
- CM liftings
print version of a talk at the June 2011 NCTS International Conference
on Galois representations, automorphic forms and Shimura varieties;
- CM liftings
print version of a colloquium at University of Minnesota, April 29, 2010.
- CM lifting of
abelian varieties .dvi file of slides for a talk at Princeton
University, March 26, 2008=.
Slides for a colloquium talk at Utrecht University, May 15, 2008.
- Numbers: Fun and
Challenge Slides for Leung Yeung Lam Memorial Lecture,
Chinese University of Hong Kong, August 10, 2007.
Notes for the talk.
- Hecke orbits as Shimura
varieties in positive characteristic, .pdf file. Slides
for talk at ICM2006, Madrid, August 25, 2006.
- Hecke Oribts and Canonical
Coordinates, .pdf file. Colloquium talk at Academia
Sinica, Taipei, December 2004.
- Hecke Orbits, .pdf
format. This is a survey talk on the Hecke orbit conjecture for
Siegel modular varieties, in a conference in memory of Armand Borel
in Hangzhou, July 2004.
- The abstract Artin problem for
a global function field, .pdf format
- A possible generalization of
Artin's conjecture for primitive roots, .pdf format
- Fine structures of moduli spaces
in positibe characteristics, .pdf format
- Families of abelian varieties in
positive characteristics, .pdf format, or
Families of abelian varieties in
positive characteristics, .dvi format. This is a survey talk
on the fine structures of modular varieties classifying abelian
varieties with prescribed symmetries, including the Oort foliation
and the Tate-linear subvarities.
- Geometry of Shimura varieties,
This is a survey talk on the geometry of Shimura varieties,
emphasizing the characteristic p aspects.
- Generalized Newton
polygons, .pdf format.
This is a talk on some combinatorial properties
of Newton polygons, generalized to the context of reductive
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