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for this workshop

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, Jeremy Miller, Mona Merling, and Jenny Wilson

This workshop, sponsored by AIM and the NSF, 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:

  • Scissors congruence K-theory
  • Resolutions of Steinberg modules
  • (Co)algebraic structures of Steinberg modules and scissors congruence spectra
  • Connections with more classical forms of K-theory

This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

Space and funding is available for a few more participants. If you would like to participate, please apply by filling out the on-line form no later than February 15, 2024. Applications are open to all, and we especially encourage women, underrepresented minorities, junior mathematicians, and researchers from primarily undergraduate institutions to apply.

Before submitting an application, please read the description of the AIM style of workshop.

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