AGNES Summer School

Inspired by the highly successful Arizona Winter School in Arithmetic Geometry, this summer school will feature three mini-courses on different aspects of moduli of higher-dimensional varieties. A key component of the school will be afternoon working sessions, where participants will work together in groups on problems, ranging from exercises to open-ended examples and research problems, relating to the topics of the lectures.

This summer school is designed for graduate students who have completed a yearlong course covering the foundations of algebraic geometry (e.g., Hartshorne's Algebraic Geometry) and are working in the field.

Mini-courses

Dori Bejleri: Moduli of stable (log) varieties

Moduli of stable (log) varieties or are the generalization of the Deligne-Mumford-Knudsen space of (pointed) stable curves to higher dimensions. They provide the natural compactification for moduli spaces of (log) general type varieties. After introducing stable (log) varieties, we will discuss some of the tools and techniques that are used to study these moduli spaces with an emphasis on explicit examples.

Video of Lecture 1

Video of Lecture 2

Video of Lecture 3

Video of Lecture 4

Kristin DeVleming: K-moduli spaces and K-stability of Fano varieties

The "right" stability notion to impose to construct well-behaved moduli spaces of Fano varieties and log Fano pairs turns out to be K-stability, a notion with origins in differential geometry. We will discuss algebraic definitions of K-stability along with several tools to determine whether or not a given variety is K-(semi)stable. We will also discuss constructions of K-moduli spaces in general along with wall crossing for K-moduli spaces of log Fano pairs, and provide many examples along the way.

Video of Lecture 1

Video of Lecture 2

Video of Lecture 3

Video of Lecture 4

James McKernan: Introduction to MMP and moduli

We will introduce some of the techniques of birational geometry necessary to construct moduli spaces of higher dimensional varieties.

Video of Lecture 1

Video of Lecture 2

Working session advisors

Nathan Chen (Harvard)

Giovanni Inchiostro (Washington)

Lena Ji (Michigan)

Justin Lacini (Kansas)

Yuchen Liu (Northwestern)

Julie Rana (Lawrence)

*REGISTRATION IS NOW CLOSED*

Instructions for recommenders: All applicants must arrange to have a paragraph of recommendation sent in by their advisor to Lori_Nascimento@brown.edu by June 1, 2022. This paragraph should (a) confirm that the applicant has the background in algebraic geometry and has started working on a thesis problem with them, and (b) describe how attending this conference will have a positive impact on the applicant.

If you have comments or feedback that you would like to see the organizers address during or after the week of the conference, you can submit it here: Anonymous feedback form

Practical Information

COVID-19 Requirements: All visitors and guests must comply with Brown's current COVID-19 guidelines, which can be found on the University’s COVID-19 Community Response page. AGNES Summer School participants are considered short term visitors and are required to complete the University's Vaccination Attestation, which will be emailed to you once you have registered to attend.

Hotel Accommodations: We encourage participants to share hotel accommodations when possible. If you need accommodations for your stay, please indicate this and your preferred roommate in the registration form. We will make the reservation for you and forward you the confirmation.

Transportation: Other than driving, there are several ways to come to campus.

• RIPTA (RI Bus lines) - located at Kennedy Plaza in downtown Providence

• Peter Pan - 2 locations in Providence

• Amtrak and Massachusetts Bay Transit Authority (MBTA) - located at the Providence Train Station

• T.F. Green Airport - located in Warwick, RI, just a 15 minute drive from campus.

• Logan Airport - located in Boston, MA. Approximately 1.5 hours from campus.
  

Parking:

• Parking Lots - Visitors may find parking in Lot 68 Upper, also called the Power Street Parking Garage, located at 111 Power Street (2 blocks away from the conference location). The lot entrance is located at the intersection of Power and Thayer Streets (View Map). This lot contains two pay stations, which are located at the front and rear of the garage. Parking in this lot is $3/hour or $15/day. *Please make sure to leave your parking pass on your dashboard.

• Street Parking - Visitors may find metered parking on the streets in and around campus. These meters take both cash and cards. Metered spaces allow for a maximum of 2 hours. *Please pay close attention to on-street signs marked for Brown Permit Parking. These spaces require a Brown employee daytime parking permit between 8am-12pm.

• ADA Visitor Parking - Brown maintains visitor spaces that meet ADA standards for accessibility in Lot 65, which is located on the south side of Benevolent Street between Thayer and Brook Streets. Any valid state ADA placard may be used in any ADA space in the lot to park for FREE.
  

Travel Reimbursement: If you are requesting reimbursement for travel, you must fill out the Supplier and Individual Payee Registration Form. Without this, Brown will not be able to process your reimbursement request. After your travel is complete, please send all original, itemized receipts to the conference administrator, Lori Nascimento.

When making your travel arrangements please be aware that Brown will only reimburse payments for coach seating. Reimbursement requests must be submitted within 60 days from the date of your trip. (Brown considers expense requests that are over 60 days to be income, which would be reported on your W-2 form.)

Due to IRS/Homeland Security requirements, Brown requires us to verify that foreign nationals have the appropriate visa to allow for travel reimbursement. Please click here for more information on what documentation you will need to provide in order to process your reimbursement.

Conference administrator: Lori Nascimento (Brown University)

Funding provided by the National Science Foundation and Brown University.

Conference organizers: Dan Abramovich, Melody Chan, Brendan Hassett, Eric Larson and Isabel Vogt

We are committed to creating a safe, professional, and welcoming environment at the AGNES Summer School that benefits from the diversity and experiences of all its participants. Brown University's "Code of Conduct", "Discrimination and Workplace Harassment Policy", "Sexual and Gender-based Misconduct Policy", and "Title IX Policy" apply to all summer school participants and staff. Participants with concerns or requests for assistance on a discrimination or harassment issue should contact one of the organizers or the conference administrator Lori Nascimento.