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# RTG seminar

The Thursday morning seminar (10:15-11:45 in WSC-N-U-3.05) will be the “Research Training Group Seminar” where members of the RTG (PhD students, post-docs,…) present their results. Sometimes, we also have speakers from other places. Depending on the number of speakers and on the proposed topic, a speaker could use one or two sessions.

 Termin Vortragende*r Titel on-site / online 14.4.2022 Andreas Nickel Some topological dynamical systems of number-theoretic origin on-site 21.4.2022 Joachim Hilgert (Paderborn) Quantum-Classical correspondences on-site 12.5.2022 Nicolas Dupré Model categories and pro-$p$ Iwahori-Hecke modules I on-site 19.5.2022 Nicolas Dupré Model categories and pro-$p$ Iwahori-Hecke modules II on-site 2.6.2022 Xucheng Zhang Characterization of open substacks that admit good moduli spaces on-site 9.6.2022 Jonas Franzel Local Theta Correspondence and Torus Periods canceled 23.6.2022 Jarod Alper Tannaka duality for algebraic stacks on-site 30.6.2022 Jarod Alper Equivariant Artin algebraization and local structure theorems on-site 7.7.2022 Jarod Alper Existence of moduli spaces on-site 14.7.2022 Jarod Alper Applications to the moduli of vector bundles on a curve on-site

## Xucheng Zhang: Characterization of open substacks that admit good moduli spaces, June 2, 2022

For an algebraic stack arising from a moduli problem in algebraic geometry, usually one can find some open substack that admits a (proper) good moduli space, via introducing suitable stability criteria with the help of educated-guessing. However, it would be also interesting to find all open substacks of the algebraic stack that admit proper good moduli spaces. In this talk we provide two examples where all such open substacks can be characterized:

1. Moduli stack of rank 2 vector bundles over a curve.

2. Quotient stack by $\mathbb G_m$.

A major ingredient of the proof is the recent work of Jarod Alper, Daniel Halpern-Leistner and Jochen Heinloth on the existence of good moduli spaces for algebraic stacks.