Schedule（July 1－12,2007）

Speakers & Titles

Peter Abramenko:

Title is "Buildings and finiteness properties of groups".

Abstract:
As an interesting feature of group (co)homology, two fundamental finiteness conditions occurring in combinatorial group theory, namely F_1 := finitely generated and F_2 := finitely presented, can naturally be generalized to a sequence F_n of finiteness conditions. Continuing Ken Brown's lectures, I will present methods how to derive finiteness properties of groups which act "nicely" on "appropriate" spaces. These methods will then be applied to some important classes of groups, in particular S-arithmetic groups, where the corresponding spaces often involve (Bruhat-Tits) buildings.
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Ken Brown:

The title of the lecture series is "Cohomology of groups".

The lectures will give an introduction to the cohomology of groups, with emphasis on infinite groups and finiteness properties. The computational techniques, including discrete Morse theory, will be discussed.
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Tom Farrell:
"Topological Rigidity (from splitting to flowing) and applications"

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Dan Grayson：

The title of the lecture series is "Algebraic K-theory", which includes as follows:
1. Constructing spaces combinatorially
2. Definitions and theorems of higher K-theory
3. Higher K-theory of fields
4. Finite generation of K-groups
5. Weight filtrations
6. Motivic cohomology
I intend to start gently. In the first talk I will carefully define simplicial sets and geometric realizations, and state a few preliminary theorems. Soule and I have discussed it, and we feel his first talk should occur after my second talk. Although it may not appear so at first glance, the last two talks are connected to each other by the motivic spectral sequence. The middle two talks are separate topics, and I may end up squeezing them into less than an hour if I fell the other topics deserve more time, or depending on what Soule ends up preparing about finite generation.
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Zongzhu Lin:
The title of talk is "Support varieties of finite groups and Lie algebras".
Depends on the time, I can talk about finite generation theorems of cohomology rings for finite group spaces and their cohomological varieties as well as the support varieties for finitely generated modules in general and relating the support varieties of finite groups of Lie types to that of their Lie algebras as specific problems and the current work in this direction.

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Wolfgang Lueck:

The main title of the six talks is “Isomorphism Conjectures in K- and L-theory”.
1. The role of lower and middle K-theory in topology
Here I would talk about finiteness obstructions and the h-cobordim theorem and explain
their meaning and why they lead to the definition of K_0(ZG) and Wh(G).
2. The Isomorphism Conjectures in the torsionfree case
In the case of torsionfree groups the conjectures are easy to formulate and one can already discuss many applications. One can also see how ideas from group homology enter.
3. Classifying spaces for families
Here I would only treat this notion independent of the Conjectures. This is also interesting for geometric group theory itself.
4. Equivariant homology theories same as under 3.
5. The Isomorphism Conjectures for arbitrary groups
Here I would formulate the conjectures in general and give some applications. Maybe I would give a status report.
6. Methods of proof and outlook

Prof. Wolfgang Lueck has prepared his lectures for the summer school
and has posted them on his home page. Please see:
http://www.math.uni-muenster.de/u/lueck/org/staff/publications.html#sl
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Hourong Qin and Guoping Tang:

The title of Qin's talk is:
Iwasawa Theory For K_{2n}O_F

唐国平教授讲群的上同调和K0-群，K1-群的基本内容。秦厚荣教授讲Galois上同调和K2-群，他打算讲的内容中，有关the cohomology of groups部分，准备涉及与 number fields 的K_2 群有关的Galois cohomology。

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C.Soule:
The title for the talks is:
"Higher K-theory of algebraic integers and the cohomology of arithmetic groups".

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Arthur Bartels:

1) Controlled topology and the assembly map

We discuss how controlled topology can be used to construct assembly
maps. In particular, we give a construction of the assembly map
appearing in the Farrell-Jones conjecture as a forget-control map.
This interpretation is important, because it enables us to apply
geometric methods to the Farrell-Jones conjecture.

2) The Farrell-Jones conjecture in algebraic K-theory for hyperbolic groups

In joint work with Wolfgang Lueck and Holger Reich we proved the
Farrell-Jones conjecture in algebraic K-theory for hyperbolic groups
(in the sense of Gromov). We will discuss this result and its proof.

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Feng Luo (Rutgers and Zhejiang U)：

The title of the talk in the conference is:
Automorphisms of the complex of curves on a surface

Abstract: The complex of curves on a surface is the simplical complex whose vertices are homotopy
classes of essential simple loops in the surface and whose simplexes are represented by disjoint essential simple loops. The complex of curves was introduced by Harvey in 1978. It is known that any automorphism of the complex of curves is induced by a self-homeomorphism of the surface. We will give a sketch of the proof this theorem and discuss some applications.

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Lizhen Ji：

The title of the talk in the conference is:

The large scale geometry and topology of linear groups, mapping class groups and outer automorphisms of free groups.

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David Rosenthal:

Continuously Controlled Algebra and Finite Asymptotic Dimension