Period Domains, Algebraic Cycles, and Arithmetic

Summer School, 10-13 June 2013, UBC (Vancouver)

Suggested texts:

For students attending the summer school, it will be useful to know something of period maps and period domains, Hodge structures and variations thereof, normal functions, basic representation theory of Lie groups, and the concept of a Mumford-Tate group. Here are some notes which cover these basics:

J. Carlson, "Period domains and period mappings"

E. Cattani, "Introduction to variations of Hodge structure"

P. Griffiths, talk on "Mumford-Tate groups and Mumford-Tate domains"

A. Knapp, "Structure theory of semisimple Lie groups"

M. Kerr and G. Pearlstein, section 1 of "An exponential history of functions with logarithmic growth"; alternatively V.B-C of Kerr's Hodge Theory notes

Summer School Schedule: mouse over titles to view descriptions.

Monday, June 10

Speaker	Time	Topic
	9:00-9:30	Welcome/info
E. Izadi	9:30-10:20	Mixed Hodge structures
	10:20-11:00	coffee
J. Lewis	11:00-11:50	Normal functions and the Hodge conjecture
	11:50-1:20	lunch
R. Laza	1:20-2:10	Classical period domains, I
C. Robles	2:20-3:10	Mumford-Tate groups and domains, I
	3:10-3:30	coffee
J. Lewis	3:30-4:20	Algebraic cycles and regulator maps

Tuesday, June 11

Speaker	Time	Topic	Notes
D. Arapura	9:00-9:50	D-modules and Hodge modules, I	(pdf)
	9:50-10:10	coffee
G. Pearlstein	10:10-11:00	Degenerations of Hodge structure, I
R. Laza	11:10-12:00	Classical period domains, II
	12:00-1:20	lunch
C. Robles	1:20-2:10	Mumford-Tate Groups and Domains, II
M. Kerr	2:20-3:10	Arithmetic of period maps, I	(pdf)
	3:10-3:30	coffee
W. Goldring	3:30-4:20	Automorphic representations and cohomology, I

Wednesday, June 12

Speaker	Time	Topic	Notes
G. Pearlstein	9:00-9:50	Degenerations of Hodge structure, II
	9:50-10:10	coffee
P. Brosnan	10:10-11:00	Admissible normal functions, I
D. Arapura	11:10-12:00	D-modules and Hodge modules, II	see above
	12:00-1:20	lunch
R. Laza	1:20-2:10	Classical period domains, III
C. Robles	2:20-3:10	Mumford-Tate Groups and Domains, III
	3:10-3:30	coffee
W. Goldring	3:30-4:20	Automorphic representations and cohomology, II

Thursday, June 13

Speaker	Time	Topic	Notes
P. Brosnan	9:00-9:50	Admissible normal functions, II
	9:50-10:10	coffee
M. Kerr	10:10-11:00	Arithmetic of period maps, II	(pdf)
R. Hain	11:10-12:00	Hodge theory and iterated integrals	(pdf) (pdf2) (pdf3)
	12:00-1:20	lunch
B. Moonen	1:20-2:10	Galois representations
W. Goldring	2:20-3:10	Automorphic representations and cohomology, III
	3:10-3:30	coffee
S. Zucker	3:30-4:20	The Borel-Serre compactifications