|October 3, 2013|
|Hermitian symmetric domains and moduli of Hodge Structures — Sean Howe|
We will explore the connection between Hermitian symmetric domains and moduli of Hodge Structures. For example, the upper half plane is a connected component of the parameter space for complex structures on R^2 (via sending a point to the complex structure J with i-eigenspace spanned by [, 1]), and it is also a Hermitian symmetric domain with the standard metric.
If instead of the complex structure we consider the equivalent Hodge structure, then we can view the upper half plane as a parameter space for a certain type of Hodge structure closely related to elliptic curves. In general, parameter spaces for Hodge Structures that “look like” they come from algebraic varieties will have Hermitian symmetric domains as their connected components; this is the result we will try to understand. In the talk I will define most of the notions above.
|November 14, 2013|
|The topology of hyperplane complements — Jenny Wilson|
|This will be an expository talk on some old and new results on hyperplane complements. For a finite real reflection group W, let A denote the set of its (complexified) reflecting hyperplanes, and M their complement in C^n. I will survey results by Fox–Neuwirth, Arnold, Brieskorn, Deligne, Orlik–Solomon, and Lehrer–Solomon on the topology of M, addressing questions such as: What is the fundamental group of M, and when is M a K(pi, 1) space? What is the cohomology of M, and how is it encoded by the combinatorics of the hyperplane arrangement? What is H*(M) as a representation of W? Recent progress has been made on a conjecture of Lehrer and Solomon related to this last question.||Talk notes.|
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