# The Topology Seminar

## Autumn 2007

**21st November: 14:15 - 16:00****, ****734, Sentralbygg II.**

Boris Kruglikov and Valentin Lychagin (University of Tromsų): Homological Methods in Compatibility Study of PDEs, Differential Syzygies and Applications

**Abstract:** *We discuss formal theory of differential equations. Compatibility and integrability issues are related to Spencer cohomology groups and we explain how to compute them and the corresponding curvature tensors. Moreover we make use of the commutative algebra and algebraic geometry for effective calculations of these objects. We briefly discuss application of the technique for solving some classical problems in differential geometry: linearization of webs, counting Abelian relations, existence of projective vector fields etc.*

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**14th November: 14:15 - 16:00****, ****734, Sentralbygg II.**

Gerd Laures (University of Bochum): Commutative Ring Structure for Quinn Spectra

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**7th November: 14:15 - 16:00****, ****734, Sentralbygg II.**

Urs Schreiber and Konrad Waldorf (University of Hamburg): Generalized Parallel Transport

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**30th October: 14:15 - 16:00****, ****734, Sentralbygg II.**

Lars Sydnes: Symplectic Geometry IV: Poisson Manifolds II

**Abstract:** *We look at the local structure of Poisson manifolds (Weinstein coordinates), the symplectic foliation, and the canonical Poisson structure of the cotangent bundle.*

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**24th October: 14:15 - 16:00****, ****734, Sentralbygg II.**

Andrew Stacey: The Structure of Unstable Operations (part B)

**Abstract:** *I shall continue with the description of the structure on the set of unstable operations of a suitable generalised cohomology theory.*

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**23rd October: 14:15 - 16:00****, ****734, Sentralbygg II.**

Lars Sydnes: Symplectic Geometry IV: Poisson Manifolds

**Abstract:** *We introduce Poisson manifolds with an emphasis on the relationship between symplectic manifolds and Poisson manifolds.*

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**17th October: 14:15 - 16:00****, ****734, Sentralbygg II.**

Andrew Stacey: The Structure of Unstable Operations

**Abstract:** *In this talk I shall give an algebraic description of the structure on the set of unstable operations of a suitable generalised cohomology theory. The aim is to give a description in terms of generators and relations that can be used to examine the properties of these operations in concrete terms.
This is based on joint work with Sarah Whitehouse of Sheffield University.*

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**10th October: 14:15 - 16:00****, ****734, Sentralbygg II.**

Andrew Stacey: Generalised Bundles

**Abstract:** *We shall take a general stroll through the various ideas of "spaces over a base"; starting with the most general form and ending up with the idea of a "generalised bundle", taking in "fibrations" and "fibre bundles" on the way.*

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**3rd October: 14:15 - 16:00****, ****734, Sentralbygg II.**

Tore Kro: The Homotopy Type of the Cobordism Category - part III

**Abstract:** *We will complete the proof of the main theorem of GMTW.*

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**2nd October: 14:15 - 16:00****, ****734, Sentralbygg II.**

Mahdi K. Salehani: Symplectic Geometry III

**Abstract:** *First, some examples of Lagrangian submanifolds of the cotangent bundle will be given and then the method of Generating Functions as a method for producing symplectomorphisms will be introduced.*

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**25th September: 14.15 - 16:00****, ****734, Sentralbygg II.**

Lars Sydnes: Symplectic Geometry II

**Abstract:** *The canonical symplectic form on cotangent bundles. Lagrangian submanifolds.*

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**19th September: 14:15 - 16:00****, ****734, Sentralbygg II.**

Tore Kro and Marius Thaule: The Homotopy Type of the Cobordism Category - part II

**Abstract:** *In the first half we will finsih describing the embedded cobordism category.
The second half will be on the sheaf model for the embedded cobordism category as well as the infinite loop space of MTO(d).*

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**18th September: 14:15 - 16:00****, ****734, Sentralbygg II.**

Lars Sydnes: Symplectic Geometry I

**Abstract:** *This is meant to be the beginning of a series of lectures giving a gentle introduction to symplectic geometry. Today we cover symplectic vector spaces and the local structure of symplectic manifolds.*

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**11th September: 14:15 - 16:00****, ****734, Sentralbygg II.**

Marius Thaule: The Homotopy Type of the Cobordism Category

**Abstract:** *I will describe work done by Galatius-Madsen-Tillmann-Weiss relating to the Mumford conjecture. In particular I will describe the cobordism category defined in their paper.*

The article is available through arXiv:math/0605249.

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**## Seminars given last semester