Geometry and Topology

Speaker: Alexandra Pettet (Michigan)

"Dynamics of Out(F): twisting out fully irreducible automorphisms"

Time: 15:30

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).

Geometry and Topology

Speaker: Jean-Francois Lafont (Ohio State University)

"Hyperbolic groups act on high-dimensional spheres"

Time: 12:30

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

Speaker: Eduardo Gonzalez (University of Massachusetts Boston)

"Compactness of the moduli space of symplectic vortices and gauged- Gromov Witten invariants"

Time: 15:30

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.

Coffee

Speaker: (Western)

"Coffee will be served"

Time: 15:00

Room: MC 109A

Colloquium

Speaker: Eduardo Gonzales (University of Massachusetts Boston)

"Symplectic Vortices and Equivariant Gromov-Witten Theory"

Time: 15:30

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.

Colloquium

Speaker: Jean-Francois Lafont (Ohio State University)

"Introduction to simplicial volume"

Time: 15:30

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.

Algebra Seminar

Speaker: Richard Kane (Western)

"Cobordism and BP theory plus K-theory continued"

Time: 15:30

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.

Geometry and Topology

Speaker: Rick Jardine (Western)

"Pointed torsors and Galois groups"

Time: 15:30

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.

Coffee

Speaker: (Western)

"Coffee will be served"

Time: 15:00

Room: MC 109A

Colloquium

Speaker: C. Denson Hill (Stony Brook University)

"Einstein's equations and embedding 3-dimensional CR manifolds"

Time: 15:30

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.

Analysis Seminar

Speaker: Remus Floricel (University of Regina)

"Purification of E_0-semigroups"

Time: 15:30

Room: MC 108

Stable Homotopy

Speaker: David Barnes (Western)

"(Equivariant) Orthogonal Spectra"

Time: 14:00

Room: MC 106

Algebra Seminar

Speaker: Lila Kari (Western)

"The undecidability of the infinite ribbon problem: implications for computing by self-assembly"

Time: 15:30

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''.

Stable Homotopy

Speaker: David Barnes (Western)

"An Introduction to EKMM Spectra I"

Time: 14:00

Room: MC 107

Stable Homotopy

Speaker: David Barnes (Western)

"An Introduction to EKMM Spectra II"

Time: 14:00

Room: MC 108

Analysis Seminar

Speaker: Serge Randriambololona (University of Notre-Dame & Fields Institute)

"An introduction to o-minimal theories"

Time: 15:30

Room: MC 108

Since the late 70s, o-minimal theories have been developed as a generalization of the semi-algebraic setting. In this talk, I will give an historical overview of the main results in o-minimality, say a few words about techniques used to get these results and try to show how they can be useful for studying classical problems. In a second time, I will talk about some of my personal contribution to the subject. Namely, I will discuss the question of the control of o-minimal structures by the function they define in few variables, in the spirit of the Hilbert 13th problem.