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This volume contains the proceedings of the ICM 2018 satellite school and workshop $K$-theory conference in Argentina. The school was held from July 16-20, 2018, in La Plata, Argentina, and the workshop was held from July 23-27, 2018, in Buenos Aires, Argentina.
The volume showcases current developments in $K$-theory and related areas, including motives, homological algebra, index theory, operator algebras, and their applications and connections. Papers cover topics such as $K$-theory of group rings, Witt groups of real algebraic varieties, coarse homology theories, topological cyclic homology, negative $K$-groups of monoid algebras, Milnor $K$-theory and regulators, noncommutative motives, the classification of $C^*$-algebras via Kasparov's $K$-theory, the comparison between full and reduced $C^*$-crossed products, and a proof of Bott periodicity using almost commuting matrices.
K-theory in Algebra, Analysis and Topology
P. Bressler, A. Gorokhovsky, R. Nest, and B. Tsygan, Comparison of spaces associated to DGLA via higher holonomy
U. Bunke, A. Engel, D. Kasprowski, and C. Winges, Equivariant coarse homotopy theory and coarse algebraic K-homology
A. Buss, S. Echterhoff, and R. Willett, Injectivity, crossed products, and amenable group actions
L. Hesselholt and T. Nikolaus, Algebraic $K$-theory of planar cuspidal curves
D. Juan-Pineda, On $NK_0$ of the group of quaternions
M. Karoubi and C. Weibel, The Witt group of real surfaces
A. Krishna and H. P. Sarwar, Negative $K$-theory and Chow group of monoid algebras
S. T. Melo, The principal-symbol index map for an algebra of pseudodifferential operators
R. Meyer, A more general method to classify up to equivariant KK-equivalence II: Computing obstruction classes
A. Neeman, Grothendieck duality made simple
J. Park, Calculus of absolute Kahler forms and Milnor $K$-theory
G. Tabuada, Noncommutative counterparts of celebrated conjectures
R. Willett, Bott periodicity and almost commuting matrices.