Intrinsic Moduli Theory Seminar

This seminar has two parts. The first develops the theory of good moduli spaces and culminates in the existence theorem of Alper, Halpern-Leistner, and Heinloth (AHLH), which characterizes when an algebraic stack admits a good moduli space.

The second introduces Halpern-Leistner’s intrinsic theory of stability and GIT (also known as beyond GIT, or BGIT) using filtrations, numerical invariants, and Θ-stratifications. Combined with the first part, this culminates in the main theorem of intrinsic moduli theory.

This is a joint seminar bringing together algebraic geometers from the University of Melbourne (UniMelb) and the Australian National University (ANU).

When: Mondays, 4pm - 5pm (17 August to 2 November 2026) Where: Zoom (details by email)

Part I

Good Moduli Spaces: Existence and Local Structure

  1. Good Moduli Spaces

    Alper §7.5

    Adam MonteleoneUniMelb

  2. Luna’s Fundamental Lemma

    Alper §7.5

    Tianqi FengUniMelb

  3. Coherent Completeness and Tannaka Duality

    Alper §7.6

    Oliver LiUniMelb

  4. Local Structure Theorems

    Alper §7.7

    Fei PengUniMelb

  5. Θ- and S-completeness

    Alper §7.9

    Gufang ZhaoUniMelb

  6. Reductivity and Unpunctured Inertia

    Alper §7.10

    Nicolas VilchesANU

  7. Existence of Good Moduli Spaces

    Alper §7.10

    Anand DeopurkarANU

Part II

The Intrinsic Approach to Stability and GIT

  1. The Stacks Filt and Grad, and Θ-Stratifications

    Halpern-Leistner §16.2, §17.1

    Sveta MakarovaANU

  2. Degenerations and Numerical Invariants

    Halpern-Leistner §17.2

    Adam MonteleoneUniMelb

  3. Harder-Narasimhan Filtrations, Specialization, and Boundedness

    Halpern-Leistner §17.3

    Sveta MakarovaANU

  4. The Intrinsic GIT Theorem

    Halpern-Leistner §18.1

    Adam MonteleoneUniMelb

  5. Applications

    Halpern-Leistner §18.2, §18.3

    Sveta MakarovaANU

References