Draisma recently proved that finite length polynomial representations of the infinite general linear group GL are topologically GL-noetherian, i.e., the descending chain condition holds for GL-stable closed subsets. The scheme-theoretic variant of this theorem is a major open problem in the area. I will briefly outline the rich history of this problem and provide a negative answer in characteristic two.

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]]>Quivers and their mutations play a fundamental role in the theory of cluster algebras. We focus on the problem of deciding whether two given quivers are mutation equivalent to each other. Our approach is based on introducing an additional structure of a cyclic ordering on the set of vertices of a quiver. This leads to new powerful invariants of quiver mutation. These invariants can be used to show that various quivers are not mutation acyclic, i.e., they are not mutation equivalent to an acyclic quiver. This talk is partially based on joint work with Sergey Fomin [arXiv:2406.03604].

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]]>This is a one day conference that travels around the Midwest; this Fall, we are hosting it in Ann Arbor.

The speakers will be

Chris Eur (Carnegie Mellon University)

Patricia Klein (Texas A&M University)

Matt Larson (Princeton / Institute for Advanced Study)

Jianping Pan (North Carolina State University)

There will also be a poster fair; you can sign up to present a poster!

To register for ALGECOM, please fill out the google poll at

https://forms.gle/BVe3MHfckc8kXTkn9

If you are applying for financial support, please fill out the form before October 1 in order to be considered. However, please do fill out the form if you think you will come, even if you are local and don't need support; it is helpful to us to know who will be coming.

The ALGECOM organizers are

David Speyer (U Michigan)

Peter Tingley (Loyola)

Alex Yong (UIUC)

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