An equivalence of graded hypersurface singularities of infinite type A and D

Abstract: The one-dimensional hypersurface singularities of countably infinite Cohen–Macaulay type are precisely those of infinite type A and D. They are the infinite analogues of simple plane curve singularities, which have finite Cohen–Macaulay type and are classified by the finite ADE diagrams. From a cluster theoretic perspective, it is natural to study these, and related, singularities with a specific grading. This was pioneered in work by Jensen, King and Su for the finite rank case. We explain how to translate this idea to the infinite rank case, and conclude with a surprising observation: Under this grading, we find a stable equivalence of graded Cohen–Macaulay modules for the hypersurface singularities of infinite types A and D. This talk is based on two WINART projects, the first joint with August, Cheung, Faber and Schroll and the second joint with Cummings, Kirkman, Letz, Rock and Špenko.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Comments: https://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09

Meeting ID: 918 7552 8987 Password: LAGOON

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