I want to attack outstanding problems concerning

K-theory, L^2-invariants, manifolds and group theory.

Eleven contributions are selected from the eight working groups in the areas of elliptic surfaces and the Mahler measure, analytic number theory, number theory in functions fields and algebraic geometry over finite fields, arithmetic algebraic geometry,

K-theory and algebraic number theory, arithmetic geometry, modular forms, and arithmetic intersection theory.

The analogue of positivity in equivariant

K-theory was (again, abstractly) proven in Anderson et al.

But Nicusor Dan, a mathematician who graduated from the Sorbonne University in Paris, decided to fight back - even if this meant spending less time on his cherished research about polylogarithms and the

K-theory at the Romanian Institute for Mathematics.

Among the topics are the functoriality of Rieffel's generalized fixed-point algebras for proper actions, division algebras and supersymmetry, Riemann-Roch and index formulae in twisted

K-theory, noncommutative Yang-Mills theory for quantum Heisenberg manifolds, distances between matrix algebras that converge to coadjoint orbits, and geometric and topological structures related to M-branes.

We will now use Theorem 6 to compute the

K-theory of [D.

Other more specific themes include: an attempt to clear up the confusion between stocks and flows using a demographic model of living organisms; the importance and dangers of false taxonomies; the importance of identifying pathologies of various systems; how the development of nuclear warheads has rendered obsolete conventional concepts of national defence and war; the

K-theory (Keynes, Kelecki and Kenneth), which focusses on the distribution of national income between profits, interests and wages; the relevance of gap between profit and interest; and many more gems.

In a single room, we have thinkers who helped formulate and refine the Big Bang theory of the universe, the "bootstrap re-sampling technique" of statistics, the algebraic

K-theory of mathematics.

The last objective is to prove the Baum-Connes conjecture for certain limits of hyperbolic groups, using the quantitative

K-theory of Oyono-Oyono and Yu.

Algebraic

K-theory is a field of abstract algebra concerning projective modules over a ring and vector bundles over schemes.

Since increasing tableaux were developed as a K-theoretic analogue of standard Young tableaux, it is tempting also to regard small Schroder paths, polygon dissections, and noncrossing partitions without singletons as

K-theory analogues of Dyck paths, polygon triangulations, and noncrossing matchings, respectively.

Among the topics are D-branes and

K-theory in two-dimensional topological field theory, open strings and Dirichlet branes, metric aspects of Calabi-Yau manifolds, and the mathematics of homological mirror symmetry.