## Schedule

- the coffee breaks are in the
*East Hall Common Room*(on the 2nd floor) - the talks are in the
*East Hall B844*(in the basement) - the group work takes place in the following rooms in
*East Hall*- Johan de Jong
- 2070EH on Monday
- 2058EH on Tuesday–Friday
- Kristin DeVleming
- 2238EH
- Laure Flapan
- 5822EH
- Jason Starr
- 3088EH
- Lenny Taelman
- 3254EH
- Burt Totaro
- 3866EH

- the Tuesday evening session is in the
*East Hall Common Room*.

### Monday, August 7

- 08:30–09:00
- registration
- 09:00–10:00
- welcome
- history and future of the Stacks project (slides)
- 10:00–10:30
- coffee break
- 10:30–12:30
- group work
- 13:30–15:00
- group work
- 15:00–15:30
- coffee break
- 15:30–16:30
- Fantastic stacks and where you do not expect to find them
- Mirko Mauri
- 16:30–18:00
- optional group work

### Tuesday, August 8

- 08:30–09:00
- coffee break
- 09:00–10:00
- Torelli pullbacks and boundary vanishing
- Aaron Pixton
- 10:00–10:30
- coffee break
- 10:30–12:30
- group work
- 13:30–15:00
- group work
- 15:00–15:30
- coffee break
- 15:30–16:30
- crash course on Git (slides)
- 16:30–...
- social event in the Common Room, with food from Ricewood

### Wednesday, August 9

- 08:30–09:00
- coffee break
- 09:00–10:00
- Torsion sheaves on stacky curves
- Lisanne Taams
- 10:00–10:30
- coffee break
- 10:30–12:00
- group work
- 13:30–15:00
- group work
- 15:00–15:30
- coffee break
- 15:30–16:30
- Higher rank Brill-Noether theory for \(\mathbb{P}^2\), and related questions
- Ben Gould
- 16:30–18:00
- optional group work

### Thursday, August 10

- 08:30–09:00
- coffee break
- 09:00–10:00
- Flop connections between minimal models for corank 1 foliations over threefolds
- Pascale Voegtli
- 10:00–10:30
- coffee break
- 10:30–12:00
- group work
- 13:30–15:00
- group work
- 15:00–15:30
- coffee break
- 15:30–16:30
- The period-index conjecture for abelian threefolds
- Alex Perry
- 16:30–18:00
- optional group work

### Friday, August 11

- 08:30–09:00
- coffee break
- 09:00–10:00
- group work
- 10:00–10:30
- coffee break
- 10:30–12:00
- group work
- 13:30–15:00
- final presentations
- 15:00–15:30
- coffee break
- 15:30–17:00
- final presentations
- slides of the group working on Deligne–Illusie

## Abstracts

### Higher rank Brill-Noether theory for \(\mathbb{P}^2\), and related questions

Ben Gould (University of Michigan)

Brill-Noether theory for stable vector bundles is the study of the loci inside moduli spaces of stable bundles where the dimension of cohomology groups jump above their expected values. For surfaces where these moduli spaces and the cohomology of general bundles are well-understood, these jumping loci can be studied precisely. In this talk we will focus on the projective plane \(\mathbb{P}^2\), and summarize recent results on cohomology jumping loci within moduli spaces of stable bundles; this work is joint with Yeqin Liu and Woohyung Lee. Time allowing, we will pose related questions, including extensions of our results to other surfaces, related questions about jumping loci, and other cycles on moduli spaces of sheaves on surfaces.

### Fantastic stacks and where you do not expect to find them

Mirko Mauri (Institute of Science and Technology Austria)

For the present edition of the Stacks Project Workshop, Jason Starr has proposed the topic 'Applications of stacks to "classical" algebraic geometry'. Following this inspiration, I will present two problems about the geometry of Lagrangian fibrations that at first glance have nothing to share with stacks, but whose solution involve them. More specifically, I will show that the fundamental group of the regular locus of an irreducible symplectic variety endowed with a Lagrangian fibration is finite, and that the Hitchin fibration for an arbitrary reductive group is delta-regular. The talk is based on on-going projects with Stefano Filipazzi and Roberto Svaldi, and with Mark de Cataldo, Andres Fernandez Herrero and Roberto Fringuelli.

### The period-index conjecture for abelian threefolds

Alex Perry (University of Michigan)

The period-index conjecture asks for a precise bound on one measure of complexity of a Brauer class (its index) in terms of another (its period). I will discuss joint work with James Hotchkiss which proves this conjecture for Brauer classes on abelian threefolds.

### Torelli pullbacks and boundary vanishing

Aaron Pixton (University of Michigan)

The Torelli map is a morphism from the moduli space of curves to the moduli space of abelian varieties. Canning, Oprea, and Pandharipande recently computed the pullbacks of certain strata classes under this map. I will give a simple formula for these Torelli pullback classes in terms of the double ramification cycle. I will also explain how this construction can be used to produce classes on the moduli space of curves with a special boundary vanishing property.

### Torsion sheaves on stacky curves

Lisanne Taams (Radboud University Nijmegen)

The goal of this talk is to show that the motive of the stack of sheaves on a stacky curve is generated by the motive of the coarse space of the curve. The most challenging case is that of torsion sheaves on stacky curves, which are closely related to representations of cyclic quivers. We highlight some of the geometric constructions that lie at the hart of the proof. If there is time, we will relate this to a graded version of the Grothendieck-Springer resolution.

### Flop connections between minimal models for corank 1 foliations over threefolds

Pascale Voegtli (University College London)

In recent years the understanding of the fundamental biraItional geometry of foliations, especially on 3-folds, has been promoted by several groundbreaking works. Cascini and Spicer have extended most parts of the classical MMP to threefold pairs equipped with a mildly singular corank 1 foliation. In particular, the existence of log-flips has been demonstrated.

The successful establishment of a foliated analogue of the classical MMP in low dimensions naturally raises the question whether classical results being closely related to the MMP do find their natural generalizations to foliated pairs.

One such classical result one might strive to convey to foliations is the well-known theorem of Kawamata from 2007, stating that two minimal models with terminal singularities are related by a sequence of flops.

In the talk, after having introduced the relevant notions, we will sketch a proof of an analogue of Kawamata's theorem for foliated 3-folds. This is recent joint work with Jiao.