Seminar Calendar
for Differential Geometry Seminar events the year of Wednesday, November 4, 2009.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery. 
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Thursday, January 29, 2009

Differential Geometry Seminar
3:00 pm   in Altgeld Hall 347,  Thursday, January 29, 2009
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Submitted by clein.
Chong-Kyu Han (Seoul Nat'l University)
Foliations associated with Pfaffian systems
Abstract: Given a system of smooth 1-forms on a smooth manifold M of dimension m, we give a necessary and sufficient condition for M to be foliated by integral manifolds of dimension n, n ≤ p := m − s, and construct an integrable supersystem by finding additional 1-forms. We also give a necessary and sufficient condition for M to be foliated by reduced submanifolds of dimension n, n ≥ p, and construct an integrable subsystem by finding a system of first integrals. The special case n = p is the Frobenius theorem on involutivity.

Thursday, March 12, 2009

Differential Geometry Seminar
3:00 pm   in 347 Altgeld Hall,  Thursday, March 12, 2009
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Submitted by ekerman.
Jens von Bergmann (Michigan State)
Compactness Results for H-Holomorphic Maps
Abstract: H--holomorphic maps are J--holomorphic maps over the parameter space of harmonic 1--forms on the domain with target space a contact manifold. We show that the space of H--holomorphic maps is compact under the assumption of "bounded periods" and we give counterexamples to show that this assumption is necessary. We show that this assumption is automatically satisfied for certain contact manifolds $ (Z,\alpha)$ and homotopy classes of maps. As an application we show that given any contact structure, there exists a contact form and an open book decomposition supporting the given contact structure so that the pages are H--holomorphic. The compactness result has further applications in the theory of folded holomorphic maps.

Thursday, April 9, 2009

Differential Geometry Seminar
3:00 pm   in 347 Altgeld Hall,  Thursday, April 9, 2009
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Submitted by clein.
Chris Leininger (UIUC Math)
Small dilatation pseudo-Anosovs and 3-manifolds
Abstract: I'll discuss recent joint work with Farb and Margalit in which we prove that all ``small dilatation'' pseudo-Anosov homeomorphisms define only a finite list of mapping tori (up to homeomorphism) after puncturing each of the surfaces at an appropriate set of points.

Thursday, April 16, 2009

Differential Geometry Seminar
3:00 pm   in Altgeld Hall 347,  Thursday, April 16, 2009
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Submitted by clein.
Rupert Venzke (Northwestern)
Minimization of Hyperbolic Volume and Pseudo-Anosov Growth
Abstract: Two standard invariants for a closed fibered orientable hyperbolic 3-manifold are its hyperbolic volume and the pseudo-Anosov growth of a fibering. We investigate the question of minimizing these two quantities among such manifolds having a fiber of specified type. In particular, we analyze a specific sequence of especially low volume manifolds having high genus fibers.

Tuesday, May 19, 2009

Differential Geometry Seminar
2:00 pm   in 341 Altgeld Hall,  Tuesday, May 19, 2009
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Submitted by ekerman.
Alexander Lytchak (Universitat Bonn)
NON-POSITIVELY CURVED SPACES OF FINITE DIMENSION
Abstract: n the talk I would like to discuss some geometric properties of singular spaces with an upper curvature bound that essentially depend on the assumption of finite dimensionality. I will prove some classical geometric results in this setting and explain applications to the structure of convex subsets and to isometric group actions. The talk is based on a joint work with Pierre-Emmanuel Caprace.

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).

Tuesday, October 27, 2009

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

Differential Geometry Seminar
1:00 pm   in 243 Altgeld Hall,  Tuesday, November 3, 2009
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Submitted by clein.
Eriko Hironaka (FSU & Harvard)
Small dilatation mapping classes from the simplest pseudo-Anosov braid
Abstract: By a recent theorem of Farb, Leininger and Margalit, the set of 3-manifolds `realizing' mapping classes with small dilatation (compared to Euler characteristic) is finite. We show that all known minimal dilatation mapping classes for small genus are realized on the complement of Rolfsen's 6_2^2 link in S^3, and discuss the plausibility that minimal dilatation mapping classes for all genus are realized on this manifold.

Thursday, November 19, 2009

Differential Geometry Seminar
3:00 pm   in 347 Altgeld Hall,  Thursday, November 19, 2009
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Submitted by clein.
Ken Bromberg (U. Utah)
The asymptotic dimension of the mapping class group
Abstract: We will show that the mapping class group has finite asymptotic dimension. A key piece of the proof is the construction of a quasi-tree that mapping class acts on. This construction works in a quite general setting for groups that have some aspect of negative curvature. We will describe this construction and explain how it relates to the asymptotic dimension of the mapping class group. This is joint work with K. Fujiwara and M. Bestvina.