I present some of the very fundamental notions in game theory,
with emphasis on their role in the theory of mechanism design and
implementation. Examples include (1) normal-form games: Nash
equilibrium and full implementation, dominant strategy...
Patching methods are usually used to construct global objects
from more local ones. On the other hand, algebraic objects can
sometimes be understood from their local behavior, i.e., they
satisfy a local-global principle. In this talk, we explain...
Quillen's higher K-groups, defined in 1971, paved the way for
motivic cohomology of algebraic varieties. Their definition as
homotopy groups of combinatorially constructed topological spaces
initially seems abstract and inaccessible. In...
