Schedule（July 1－13,2007）

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
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Hourong Qin and Guoping Tang:
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。

Guoping Tang:低阶代数K理论

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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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