UIUC Dept. of Mathematics Seminar Calendar

      July 2009             August 2009           September 2009   
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           1  2  3  4                      1          1  2  3  4  5
  5  6  7  8  9 10 11    2  3  4  5  6  7  8    6  7  8  9 10 11 12
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                        30 31

Tuesday, September 22, 2009

Differential Geometry Seminar
1:00 pm in 243 Altgeld Hall, Tuesday, September 22, 2009

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Submitted by ekerman.

Isidora Milin (UIUC Math)
Orderability of Contactomorphism Groups of Lens Spaces
Abstract: A contact isotopy of a contact manifold is "positive" if during it, each point of the manifold moves in a positively transverse direction to the contact hyperplane distribution. The question of whether this notion induces a partial order on the universal cover of the identity component of the contactomorphism group - whether the contact manifold is "orderable" - turns out to be sensitive to the topology of the contact manifold, and is related to nonsqueezing phenomena in contact geometry, as studied by Eliashberg, Kim and Polterovich. I will begin by explaining this relation, and then describe a version of contact homology for domains that enables us to detect relevant contact nonsqueezings. This will be illustrated by standard contact sphere (not orderable) and lens spaces (orderable).

Friday, October 9, 2009

Tuesday, October 27, 2009

Differential Geometry Seminar
1:00 pm in 243 Altgeld Hall, Tuesday, October 27, 2009

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Rebecca Goldin (George Mason University)
Full Orbifold K-theory of Abelian Symplectic Quotients
Abstract: We will begin with a review of one way in which orbifolds arise, which is via the symplectic of a Hamiltonian T-space, where T is an abelian Lie group. Our goal is to describe the full orbifold K-theory for this class of spaces. Toward that purpose, we introduce the *inertial K-theory* of a Hamiltonian T-space M and show that it surjects as a ring onto the full orbifold K-theory of the symplectic quotient, denoted M//T (at a regular value). This research essentially involves two ingredients: The fact (due to M. Harada and G. Landweber) that equivariant K-theory of M maps surjectivity onto the K-theory of M//T, and the invention of a fancy product on the inertial K-theory of M, so that it surjects onto the full orbifold K-theory of M//T. These ideas are based on a similar (though rational) story in cohomology which we will also discuss. This is joint work with T. Holm, M. Harada, and T. Kimura.

Tuesday, November 3, 2009

Thursday, November 19, 2009

Thursday, December 10, 2009

Thursday, December 17, 2009

Group Theory/Differential Geometry Seminar
1:00 pm in 347 Altgeld Hall, Thursday, December 17, 2009

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Jason Deblois (UIC Math)
Geometry, topology, and rank gradient of hyperbolic manifolds
Abstract: The rank of a finitely generated group is the minimal cardinality of a generating set. Despite the seemingly fundamental nature of this invariant, and the ease with which it may be computed for basic examples such as free or abelian groups, until recently rank has been difficult to determine for broader classes of groups, such as the fundamental groups of hyperbolic 3-manifolds. Recent work of several authors corrects this situation to some degree by relating the geometry of a manifold to the rank of its fundamental group. I will describe some questions about rank gradient, which measures how rank grows among finite-degree covers of a fixed manifold, focusing in particular on groups that split, and guess at some answers.

Monday, March 1, 2010

Tuesday, March 9, 2010