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Topics in noncommutative geometry : Third Luis Santalo Winter School-CIMPA Research School, Topics in Noncommutative Geometry, Universidad de Buenos Aires, Buenos Aires, Argentina,...
Providence, RI : Cambridge, MA : American Mathematical Society ; Clay Mathematics Institute, 2012“…Luis Santaló Winter School-CIMPA Research School Topics in Noncommutative Geometry Buenos Aires, Argentina…”
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$K$-theory -- $K$-theory and operator algebras -- Kasparov theory ($KK$-theory)
$K$-theory -- Topological $K$-theory -- Equivariant $K$-theory
$K$-theory -- Topological $K$-theory -- Twisted $K$-theory; differential $K$-theory
Algebraic geometry -- Foundations -- Noncommutative algebraic geometry
Category theory; homological algebra -- Categories with structure -- Operads
Commutative algebra
Differential geometry -- Symplectic geometry, contact geometry -- Deformation quantization, star products
Functional analysis -- Selfadjoint operator algebras ($C *$-algebras, von Neumann ($W *$-) algebras, etc.) -- Noncommutative dynamical systems
Global analysis, analysis on manifolds -- Infinite-dimensional manifolds -- Noncommutative geometry (a la Connes)
Group theory and generalizations -- Special aspects of infinite or finite groups -- Word problems, other decision problems, connections with logic and automata
Quantum theory -- Groups and algebras in quantum theory -- Noncommutative geometry