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Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Probability and Statistics, Game Theory,    Geometry and Topology

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

MPI f. Mathematik, Bonn

Algebraic K-theory is an object that sits at the centre of large parts of algebra, geometry, and topology because of its universal role as a receptacle to count other mathematical objects with signs. However, since its invention, a phenomenon often called the Eilenberg swindle - which says that the algebraic K-theory of a category which is too large must necessarily be zero - has been accepted as a fundamental limit to the theory. Recently, Alexander Efimov introduced a construction called continuous K-theory which allows one to make sense of algebraic K-theory of certain large categories known as dualisable categories in a nontrivial way, thus surmounting the problem of the aforementioned Eilenberg swindle. These dualisable categories encompass geometrically interesting and previously inaccessible examples such as sheaves on locally compact Hausdorff spaces. This new direction in K-theory has seen many recent advancements such as the rigidity of non-commutative motives by Efimov and the polynomial functoriality of continuous K-theory by Akhil Mathew and collaborators.

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

SFB 1085 Higher Invariants at the Faculty of Mathematics at the Universität Regensburg

Analysis,    Courses and Events for Math Students and Early Career Researchers

Goethe University Frankfurt

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)