A. Bak *(coordinator),*

R. Hazrat*,
*

G. Minian,

A. Mundkur,

G. Tang.

CO is experienced in the theory of quadratic and Hermitian forms over arbitrary form rings , including its K-Theory, especially stability and prestability questions. The notions of global action and category with dimension were invented by CO. There is also experience in model categories for various homotopy theories. The generalized Milnor conjecture was coauthord by a member of CO.

**CR1. Bangor University**

R. Brown,

M. Lawson,

C. Wensley,

T. Porter
*(local coordinator),*

E. Moore.

CR1 is experienced in algebraic topology, algebraic homotopy theory, and category theory. Simplicial techniques are one of its specialties and one of its members is the founder of the theory of crossed algebras and the nonabelian tensor product. This complements well CO and supports CR3.

**CR2. Bar-Ilan University**

B. Kunyavskii,

E. Plotkin,

G. Soifer
*(local coordinator),*

R. Shklya*,*

A. Vaknin.

CR2 is experienced in Chevalley
groups over rings and their representation theory, their structure, and
stability questions for their K_{1 }and K_{2 }groups. There
is also experience in the K-theory of triangulated categories. This fits
well to the competencies in CO and CR5 and contrasts those in CR1.

**CR3. Georgian Academy
of Sciences, Razmadze Mathematical Institute**

G. Donadze,

H. Inassaridze
*(local coordin*ator),

N. Inassaridze,

T. Kandelaki,

E. Khmaladze,

A. Patchkoria.

E. Khmaladze,

A. Patchkoria.

CR3 is experienced in nonabelian homotopical and
homological algebra, nonabelian derived functors, nonabelian homology
theories, algebraic K-theory, topological K-theory,
C^*-algebras, generalized operator algebras. Simplicial methods
are also well understood. This complemets
well CO and supports CR1.

**CR4. Moscow State
University**

V. Artamonov,

V. Mikhalev *(local coordinator)*,

A. Mikhalev,

P. Solovyev.

CR4 is experienced in quantum
spaces and their K-theory. algebraic topology, operator algebras, topological
K-theory, Hermitian K-theory, Lie algebras and conformal algebras. This
complements and extend capabilities of all previous teams.

**CR5. Russian Academy
of Sciences, Steklov Math Institute (POMI)**

S. Joukhovitsky,

A. Nenashev,

A. Scorichenko,

A. Suslin *(local coordinator),*

S. Yagunov,

O. Pushin.

CR5 is world class in K-theory
and motivic methods and its application in algebraic geometry. Their methods
contributed to the solution of the Milnor conjecture.

**CR6. St. Petersburg
State University**

E. Dybkova,

V. Khalin,

K. Pimenov,

N. Vavilov *(local coordinator)*

CR6 is experienced in the representation theory, geometry, and structure of Chevalley groups over rings as well as in questions of stability for their K-groups. There is also experience concerning problems of their generation. This extends competencies in CO, CR2, CR4, CR5 and CR7 and complements those in CR1 and CR3.

**CR7. St. Petersburg
Electrotechnical University**

A. Korotkevich*,*

V. Petrov*,*

A. Sivatsky,

A. Stepanov
*(local
coordinator).*

CR7
is experienced in structural and word length questions concerning classical-like
groups over rings, as well various questions concerning stable rank for
rings and its application to stability questions in K-theory.