Scissors congruences, algebraic K-theory and Steinberg modules
July 8 to July 12, 2024
at the
American Institute of Mathematics,
Pasadena, California
organized by
Cary Malkiewich,
Mona Merling,
Jeremy Miller,
and Jenny Wilson
Original Announcement
This workshop will be devoted to connections between scissors congruence K-theory and Steinberg modules. Scissors congruence is the study of when objects such as polyhedra, manifolds, varieties, etc. are equivalent under decomposition into pieces. In the last decade, the introduction of K-theoretic constructions in the study of scissors congruence problems by Campbell and Zakharevich has seen exciting applications and opened new avenues of attack on this problem. Generalizing results for classical scissors congruence groups, Malkiewich showed that scissors congruence groups can be described as group homology with coefficients in Steinberg modules. Steinberg modules are certain representations that are relevant to the study of representations of linear groups, algebraic K-theory, and the cohomology of arithmetic groups. The goal of the workshop is to bring together researchers studying scissors congruence K-theory and as well as Steinberg modules, in order to explore interactions between the two fields.
The main topics for the workshop are:
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Scissors congruence K-theory
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Resolutions of Steinberg modules
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(Co)algebraic structures of Steinberg modules and scissors congruence spectra
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Connections with more classical forms of K-theory
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
A list of open problems.
Workshop videos
