Lecture Notes

Stacks and Moduli, (last updated: July 7, 2025)

For previous versions, click here

Other expository articles

• Evolution of Stacks and Moduli, pdf
• Embracing AI and Formalization: Experimenting with Tomorrow's Mathematical Tools, pdf
  to appear in Bulletin Of The American Mathematical Society.
• Advances in Moduli Theory, pdf.
• A Guide to Organizing a Virtual Conference (with D. Litt and I. Vogt), pdf
  Notices Of The American Mathematical Society, September 2020.
• Artin algebraization and quotient stacks, pdf.
  notes from the summer school Algebraic stacks and related topics in Mainz, Germany (Aug. 31 - Sept. 4, 2015). Much of this material is now incorporated into the manuscript Stacks and Moduli.
• The moduli stack of semistable curves
  Oberwolfach Reports, Report No. 6 (2013), 373-376 (journal version).
• Birational models of M_g
  Oberwolfach Reports, Report No. 30 (2012), 22-25 (journal version).
• Good moduli spaces for Artin stacks
  Oberwolfach Reports, Report No. 26 (2008), 14-16 (journal version).