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30 Geometry and Topology
Geometry and Topology Speaker: Alexandra Pettet (Michigan) "Dynamics of Out(F): twisting out fully irreducible automorphisms" Time: 15:30 - 16:30 Room: MC 107 The outer automorphism group Out(F) of a free group F of finite rank shares
many properties with the mapping class group of a surface, however the
techniques for studying these groups are generally quite different.
Analogues of the pseudo-Anosov elements of the mapping class group are the
so-called fully irreducible automorphisms, which exhibit north-south
dynamics on Culler-Vogtmann's Outer Space. We will explain a method for
constructing these automorphisms and suggest why this construction should be
useful. This is joint work with Matt Clay (University of Oklahoma).
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31 Geometry and Topology
Geometry and Topology Speaker: Jean-Francois Lafont (Ohio State University) "Hyperbolic groups act on high-dimensional spheres" Time: 12:30 - 13:30 Room: MC 107 I'll show that every torsion-free delta-hyperbolic group
supports a non-trivial topological action on a high-dimensional ball.
Aside from a bad limit set in the boundary of the ball, this action is
well-behaved. This was joint work with Tom Farrell. Analysis Seminar
Analysis Seminar Speaker: Eduardo Gonzalez (University of Massachusetts Boston) "Compactness of the moduli space of symplectic vortices and gauged- Gromov Witten invariants" Time: 15:30 - 16:30 Room: MC 108 Let X be a symplectic manifold and G a Lie group acting in a Hamiltonian fashion with a moment map f. Let P denote a principal G-bundle over a surface with area form V. A pair (A,u) of a connection A on P and a section u of the associated bundle P(X):=P imes_G X is a gauged pseudo-holomorphic map if it satisfies the A-twisted Cauchy-Rieman equation. The space of vortices is the quotient of gauged pseudo-holomorphic map by Aut(P). We will give a brief introduction to moduli spaces of curves arising from Gromov-Witten theory, including some Fredholm theory. We will show that under some good choices this moduli space can be compactified and get an orbifold structure. This is work in progress with A. Ott, C. Woodward and F. Ziltiner. |
1 Coffee
Coffee Speaker: (Western) "Coffee will be served" Time: 15:00 - 15:30 Room: MC 109A Colloquium
Colloquium Speaker: Eduardo Gonzales (University of Massachusetts Boston) "Symplectic Vortices and Equivariant Gromov-Witten Theory" Time: 15:30 - 16:30 Room: MC 108 Gromov-Witten theory for projective varieties has been the subject
of intense research since its intruduction. Many important results in the
area (eg. Givental's mirror theorem) were proven using equivariant
localization techniques from topology, using natural group actions. For a
symplectic manifold X, GW invariants are defined using moduli spaces
pseudoholomophic maps u:Σ o X from a Riemann surface Σ to
X. Suppose that a compact Lie group is acting on X in a Hamiltonian way.
After an introduction to the general theory, I will introduce the "space of
vortices" which are pairs (A,u) of a connection over a principal bundle
P, and a section u:Σ satisfying certain "gauged" equations. Using
these spaces one can define gauged Gromov-Witten invariants, which are an
equivariant version of Gromov-Witten invariants. This theory depends on a
choice of area form on Σ as well as Σ. I will describe joint
work with C. Woodward regarding the dependency on the area form, as well as
joint work with Ott, Ziltener and Woodward on punctured surfaces. I will
also give relations with other equivariant theories and I will discuss a
conjecture related to the Gromov-Witten theory of symplectic quotients. |
2 Colloquium
Colloquium Speaker: Jean-Francois Lafont (Ohio State University) "Introduction to simplicial volume" Time: 15:30 - 16:30 Room: MC 108 Simplicial volume is an invariant of closed manifolds that
measures how efficiently the manifold can be "triangulated over the
reals". I will discuss various geometric and topological consequences that
result from positivity of the simplicial volume. Finally, I will end by
giving an indication of the proof (joint with Ben Schmidt) that locally
symmetric spaces of non-compact type have positive simplicial volume. |
3 Algebra Seminar
Algebra Seminar Speaker: Richard Kane (Western) "Cobordism and BP theory plus K-theory continued" Time: 15:30 - 16:30 Room: MC 106 Generalized cohomology theories have been studied continuously since the late 1950's. My lecture of several weeks ago was devoted to a brief survey of topological K-theory, the first generalized cohomology theory to be developed and utilized. The present lecture will begin by discussing another family of generalized cohomology theories which have also been extensively studied - cobordism theory and its associated theories, notably Brown-Peterson theory
and Morava K-theory. This work includes major contributions by Thom, Novikov and Quillen. A major theme of this discussion will be the algebra of cohomology operations associated with each of these theories. As we will see, topological K-theory can also be fitted into the framework of this family of cohomology theories. In addition we will return to K-theory and discuss both operations and Adams operations. However these operations will turn out out be rather distinct from the ones considered for cobordism and BP theory. |
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6 Geometry and Topology
Geometry and Topology Speaker: Rick Jardine (Western) "Pointed torsors and Galois groups" Time: 15:30 - 16:30 Room: MC 107 Suppose that H is an algebraic group which is defined over a field k,
and let L be the algebraic closure of k. The canonical stalk for the
etale topology on k induces a simplicial set map from the classifying
space B(H-tors) of the groupoid of H-torsors (aka. principal
H-bundles) to the space BH(L). The homotopy fibres of this map are
groupoids of pointed torsors, suitably defined. These fibres can be
analyzed with cocycle techniques: their path components are
representations of the absolute Galois groupoid in H, and each path
component is contractible. The arguments for these results are simple,
and applications will be displayed.
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7 Coffee
Coffee Speaker: (Western) "Coffee will be served" Time: 15:00 - 15:30 Room: MC 109A Colloquium
Colloquium Speaker: C. Denson Hill (Stony Brook University) "Einstein's equations and embedding 3-dimensional CR manifolds" Time: 15:30 - 16:30 Room: MC 108 We discuss several theorems concerning the connection
between the local CR embeddability of 3-dim CR manifolds,
and the existence of algebraically special Maxwell and
gravitational fields in an associated 4-dim spacetime. |
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16 Analysis Seminar
Analysis Seminar Speaker: Remus Floricel (University of Regina) "Purification of E_0-semigroups" Time: 15:30 - 16:30 Room: MC 108 |
17 Stable Homotopy
Stable Homotopy Speaker: David Barnes (Western) "(Equivariant) Orthogonal Spectra" Time: 14:00 - 15:00 Room: MC 106 Algebra Seminar
Algebra Seminar Speaker: Lila Kari (Western) "The undecidability of the infinite ribbon problem: implications for computing by self-assembly" Time: 15:30 - 16:30 Room: MC 106 Self-assembly, the process by which objects autonomously come together to form complex structures, is omnipresent in the physical world and has recently become of interest due to advances in nanotechnology. A systematic study of self-assembly as a mathematical process has been initiated by L. Adleman and E. Winfree. The components are modelled as
square tiles on the infinite two-dimensional plane. Each side of a tile is covered by a ``glue'', and two adjacent tiles stick iff they have matching glues on their abutting edges. Tiles that stick to each other may form various two-dimensional structures or may cover the entire plane. We prove that it is undecidable whether an arbitrary finite set of tiles can be used to assemble an infinite ribbon. While the problem can be shown undecidable by existing techniques if the ribbon must start with a given ``seed'' tile, our result settles the ``unseeded'' case, an open problem known as the ``unlimited infinite snake problem''. |
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