Loading...
Organizing Committee
Bucknell University
UFRO Universidad de La Frontera
Università Statale di Milano
Rijksuniversiteit Groningen
Université de Poitiers
Abstract
This introductory workshop offers a guided entry into the arithmetic, geometry and computation of K3 surfaces. Its aims are to establish a shared foundation for the semester, highlight the central role of K3 surfaces across several areas, and motivate deeper study. The workshop will introduce to the use of symbolic computation systems in algebraic geometry and in particular for computations on K3 surfaces such as giving equations for elliptic fibrations, rational curves, and automorphisms. The workshop will feature three minicourses -on geometry, arithmetic, and computation - together with general talks covering these interconnected topics.
The workshop and in particular the minicourses will be a perfect opportunity for PhD students and postdocs to get acquainted with different aspects and tools for the study of K3 surfaces.
The workshop and in particular the minicourses will be a perfect opportunity for PhD students and postdocs to get acquainted with different aspects and tools for the study of K3 surfaces.
Alessandra Sarti, Université de Poitiers
This opening workshop serves as an introduction for participants in the Fall Semester Program on "Computations on K3 Surfaces and Related Varieties." It is not open to outside applications.
Loading...
Loading participant list in background...
Workshop Schedule
Monday, September 14, 2026
8:30 - 8:50 AM EDT
Check In
11th Floor Collaborative Space
8:50 - 9:00 AM EDT
Welcome
11th Floor Lecture Hall
Brendan Hassett, ICERM/Brown University
9:00 - 9:15 AM EDT
Organizer Welcome
Opening Remarks - 11th Floor Lecture Hall
9:15 - 11:00 AM EDT
Minicourse: K3 surfaces quotients of K3 surfaces
Tutorial - 11th Floor Lecture Hall
Alice Garbagnati, Università Statale di Milano
Abstract
The K3 surfaces are regular surfaces which admit an holomorphic symplectic form. We will consider finite order symplectic automorphisms: the minimal resolution of the quotient of a K3 surface by such an automorphism is another K3 surface.
This creates a relation between families (a priori different) of K3 surfaces, which can be described in terms of lattice polarized K3 surfaces. We will review the classical results for the symplectic involutions and we describe the more recent generalizations for the order 3 automorphisms.
Then, we will concentrate on specific subsets of K3 surfaces admitting symplectic involutions, characterized by the following property: the K3 surface which admits the symplectic automorphism and the one which is the desingularization of its quotient (by the symplectic automorphisms) lie in the same family of K3 surface. This property can be characterized in a lattice theoretically way, but it is not equivalent to be polarized with a prescribed lattice.
11:30 AM - 12:30 PM EDT
Minicourse: Density for rational p0ints on special K3s
Tutorial - 11th Floor Lecture Hall
Brendan Hassett, ICERM/Brown University
12:30 - 2:30 PM EDT
Lunch/Free Time
2:30 - 3:15 PM EDT
Cox rings of Calabi-Yau hypersurfaces in toric Fano varieties
11th Floor Lecture Hall
Michela Artebani, Universidad de Concepción
Abstract
This talk deals with Cox rings of Calabi-Yau varieties X which are general anticanonical hypersurfaces in smooth toric Fano varieties Z. We present two complementary results, formulated in terms of primitive pairs of the anticanonical polytope of Z. The first gives combinatorial conditions ensuring that X is a Mori dream space and provides an explicit presentation of its Cox ring. The second shows that certain relations among primitive pairs force Bir(X) to be infinite, hence X is not a Mori dream space.
As an application, we show that for Calabi-Yau hypersurfaces in dimensions two and three, either the Cox ring is finitely generated or the birational automorphism group is infinite. In the K3 case, where the Mori dream classification was already known via lattice theory, our approach gives a combinatorial interpretation together with explicit Cox ring presentations in the Mori dream cases.
This is joint work with Antonio Laface and Luca Ugaglia.
3:30 - 4:00 PM EDT
Coffee Break
11th Floor Collaborative Space
4:00 - 4:45 PM EDT
Open Collaboration Time
Open Collaboration Time
5:00 - 6:30 PM EDT
Semester Program Welcome Reception
Reception - 11th Floor Collaborative Space
Tuesday, September 15, 2026
9:00 - 11:00 AM EDT
Minicourse: Local/global principles, Brauer groups, and obstructions
Tutorial - 11th Floor Lecture Hall
Brendan Hassett, ICERM/Brown University
11:30 AM - 12:30 PM EDT
Minicourse: TBA
Tutorial - 11th Floor Lecture Hall
Edgar Costa, MIT
12:30 - 2:30 PM EDT
Lunch/Free Time
2:30 - 3:15 PM EDT
Arithmetic Properties of K3 Surfaces with Large Automorphism Groups
11th Floor Lecture Hall
Joseph Silverman, Brown University
Abstract
I will discuss arithmetic properties of K3 surfaces of type (2,2,2) in P^1xP^1xP^1, with some remarks on the Markoff-Hurwitz surfaces x^2+y^2+z^2=axyz+k (which are affine log-K3 analogues) and higher dimensional Calabi-Yau varieties given by the vanishing of a (2,2,...,2) form in P^1xP^1x...xP^1.
3:30 - 4:00 PM EDT
Coffee Break
11th Floor Collaborative Space
4:00 - 4:45 PM EDT
Short Talks
Short Talks - 11th Floor Lecture Hall
Wednesday, September 16, 2026
9:00 - 10:00 AM EDT
Minicourse Problem Session: Isogenies of K3 surfaces
Problem Session - 11th Floor Lecture Hall
Brendan Hassett, ICERM/Brown University
10:30 AM - 12:30 PM EDT
Minicourse: TBA
Tutorial - 11th Floor Lecture Hall
Edgar Costa, MIT
12:30 - 12:35 PM EDT
Group Photo (Immediately After Talk)
11th Floor Lecture Hall
12:35 - 2:30 PM EDT
Lunch/Free Time
2:30 - 3:30 PM EDT
Minicourse: K3 surfaces quotients of K3 surfaces
Tutorial - 11th Floor Lecture Hall
Alice Garbagnati, Università Statale di Milano
Abstract
The K3 surfaces are regular surfaces which admit an holomorphic symplectic form. We will consider finite order symplectic automorphisms: the minimal resolution of the quotient of a K3 surface by such an automorphism is another K3 surface.
This creates a relation between families (a priori different) of K3 surfaces, which can be described in terms of lattice polarized K3 surfaces. We will review the classical results for the symplectic involutions and we describe the more recent generalizations for the order 3 automorphisms.
Then, we will concentrate on specific subsets of K3 surfaces admitting symplectic involutions, characterized by the following property: the K3 surface which admits the symplectic automorphism and the one which is the desingularization of its quotient (by the symplectic automorphisms) lie in the same family of K3 surface. This property can be characterized in a lattice theoretically way, but it is not equivalent to be polarized with a prescribed lattice.
3:30 - 4:00 PM EDT
Coffee Break
11th Floor Collaborative Space
4:00 - 4:45 PM EDT
Short Talks
Short Talks - 11th Floor Lecture Hall
Thursday, September 17, 2026
9:00 - 10:00 AM EDT
Minicourse Problem Session: K3 surfaces quotients of K3 surfaces
Problem Session - 11th Floor Lecture Hall
Alice Garbagnati, Università Statale di Milano
Abstract
The K3 surfaces are regular surfaces which admit an holomorphic symplectic form. We will consider finite order symplectic automorphisms: the minimal resolution of the quotient of a K3 surface by such an automorphism is another K3 surface.
This creates a relation between families (a priori different) of K3 surfaces, which can be described in terms of lattice polarized K3 surfaces. We will review the classical results for the symplectic involutions and we describe the more recent generalizations for the order 3 automorphisms.
Then, we will concentrate on specific subsets of K3 surfaces admitting symplectic involutions, characterized by the following property: the K3 surface which admits the symplectic automorphism and the one which is the desingularization of its quotient (by the symplectic automorphisms) lie in the same family of K3 surface. This property can be characterized in a lattice theoretically way, but it is not equivalent to be polarized with a prescribed lattice.
10:00 - 10:45 AM EDT
Zeta functions of K3 surfaces over finite fields
11th Floor Lecture Hall
Kiran Kedlaya, University of California San Diego
Abstract
The zeta function of an algebraic variety over a finite field is a fundamental invariant which reflects many geometric properties. In the special case of K3 surfaces, we survey some of these connections; discuss techniques for computing zeta functions, both individually at scale; and indicate some open questions which we may see some progress on during the semester.
11:30 AM - 12:15 PM EDT
TBA
11th Floor Lecture Hall
Dino Festi, Università degli Studi di Napoli 'Federico II'
12:30 - 2:30 PM EDT
Lunch/Free Time
2:30 - 3:15 PM EDT
Mincourse Problem Session:TBA
Problem Session - 11th Floor Lecture Hall
Edgar Costa, MIT
3:30 - 4:00 PM EDT
Coffee Break
11th Floor Collaborative Space
4:00 - 4:45 PM EDT
Open Collaboration Time
Open Collaboration TIme
Friday, September 18, 2026
9:00 - 9:45 AM EDT
Automorphisms of quartic surfaces and Cremona transformations
11th Floor Lecture Hall
Carolina Araujo, IMPA
Abstract
In this talk, I will address the following question, attributed to Gizatullin: Which automorphisms of a smooth quartic surface in projective 3-space are restrictions of Cremona transformations of the ambient space? Techniques from birational geometry, and in particular the Minimal Model Program, provide powerful tools for studying this problem. I will report on recent progress on Gizatullin's problem, obtained in joint works with Alessio Corti and Alex Massarenti, and with Daniela Paiva and Sokratis Zikas.
10:00 - 10:45 AM EDT
Logarithmic Enriques varieties
11th Floor Lecture Hall
Samuel Boissière, Université de Poitiers
Abstract
In a recent work in collaboration with Chiara Camere and Alessandra Sarti, we introduce logarithmic Enriques varieties as a singular analogue of Enriques manifolds, generalizing the notion of log-Enriques surfaces introduced by Zhang in 1991. In this talk, I will mainly focus on the possible torsion indices of the subfamily of logarithmic Enriques varieties that admit a quasi-étale cover by a singular symplectic variety, and I will give some examples.
11:30 AM - 12:30 PM EDT
Short Talks
Short Talks - 11th Floor Lecture Hall
12:30 - 2:30 PM EDT
Lunch/Free Time
2:30 - 3:15 PM EDT
Density of degree d points on surfaces
11th Floor Lecture Hall
Isabel Vogt, Brown University
Abstract
Given a variety defined over a nonclosed field, the structure of the points defined over degree d extensions of the ground field reflects both the geometry and arithmetic of the variety. In this talk I will discuss some results and avenues for study about the Zariski density of such degree d points on surfaces, both building on our more complete picture for curves, and illustrating the difficulty in moving up in dimension. This talk is based on joint works with Viray, Chen--Church--Pasten, and Berg--Fu--Gazaki--Porzio--Rawson.
3:30 - 4:00 PM EDT
Coffee Break
11th Floor Collaborative Space
4:00 - 4:45 PM EDT
Open Collaboration Time
Open Collaboration Time
Application Information
This opening workshop serves as an introduction for participants in the Fall Semester Program on "Computations on K3 Surfaces and Related Varieties." It is not open to outside applications.
Applications are not currently open. Please check back at a later date.
Your Visit to ICERM
- ICERM Facilities
- ICERM is located on the 10th & 11th floors of 121 South Main Street in Providence, Rhode Island. ICERM's business hours are 8:30am - 5:00pm during this event. See our facilities page for more info.
- Traveling to ICERM
- ICERM is located at Brown University in Providence, Rhode Island. Providence's T.F. Green Airport (15 minutes south) and Boston's Logan Airport (1 hour north) are the closest airports. Providence is also on Amtrak's Northeast Corridor. See our travel page for full directions.
- Lodging
- Confirmed participants will receive an email to book a room at our preferred hotel, the Hampton Inn & Suites Providence Downtown. Contact programstaff@icerm.brown.edu with questions.Only use hotel links from ICERM’s official emails or this page. ICERM never uses third-party booking vendors.
- Childcare/Schools
- Those traveling with family can contact housing@icerm.brown.edu for childcare and school information.
- Technology Resources
- Wireless internet access and wireless printing are available for all ICERM visitors. Eduroam is supported. Thin clients provide access to web browsers, SSH terminals, and printing. See our Technology Resources page for setup info.
- Accessibility
- For special services, accommodations, or assistance, please contact accessibility@icerm.brown.edu in advance. Thank you.
- Discrimination and Harassment Policy
- ICERM is committed to a safe, professional, and welcoming environment. Brown University's Code of Conduct and related policies apply to all ICERM participants. Contact the ICERM Director or Associate Director Jenna Sousa for concerns.
- Fundamental Research
- ICERM programs promote Fundamental Research and mathematical education. Participants involved in sensitive or proprietary work should be aware of U.S. export control restrictions.
- Exploring Providence
- Providence offers world-class dining and attractions. Visit our Explore Providence page to see what’s near ICERM.
Visa Information
Contact visa@icerm.brown.edu for assistance.
- Eligible to be reimbursed
- B-1 or Visa Waiver Business (WB)
- Ineligible to be reimbursed
- B-2 or Visa Waiver Tourist (WT)
- Already in the US?
F-1 and J-1 not sponsored by ICERM: need to obtain a letter approving reimbursement from the International Office of your home institution prior to travel.
H-1B holders do not need a letter of approval.
All other visas: alert ICERM staff immediately about your situation.
ICERM does not reimburse visa fees. This chart is to inform visitors whether the visa they enter the US on allows them to receive reimbursement for the items outlined in their invitation letter.
Financial Support
This section is for general purposes only and does not indicate that all attendees receive funding. Please refer to your personalized invitation to review your offer.
- ORCID iD
- As this program is funded by the National Science Foundation (NSF), ICERM is required to collect your ORCID iD if you are receiving funding to attend this program. Be sure to add your ORCID iD to your Cube profile as soon as possible to avoid delaying your reimbursement.
- Acceptable Costs
- 1 roundtrip between your home institute and ICERM
- Flights on U.S. or E.U. airlines – economy class to either Providence airport (PVD) or Boston airport (BOS)
- Ground Transportation to and from airports and ICERM.
- Unacceptable Costs
- Flights on non-U.S. or non-E.U. airlines
- Flights on U.K. airlines
- Seats in economy plus, business class, or first class
- Change ticket fees of any kind
- Multi-use bus passes
- Meals or incidentals
- Advance Approval Required
- Personal car travel to ICERM from outside New England
- Multiple-destination plane ticket; does not include layovers to reach ICERM
- Arriving or departing from ICERM more than a day before or day after the program
- Multiple trips to ICERM
- Rental car to/from ICERM
- Flights on a Swiss, Japanese, or Australian airline
- Arriving or departing from airport other than PVD/BOS or home institution’s local airport
- 2 one-way plane tickets to create a roundtrip (often purchased from Expedia, Orbitz, etc.)
- Travel Maximum Contributions
- New England: $350
- Other contiguous US: $850
- Asia & Oceania: $2,000
- All other locations: $1,500
- Note these rates were updated in Spring 2023 and supersede any prior invitation rates.
- Reimbursement Requests
Request Reimbursement with Cube
Refer to the back of your ID badge for more information. Checklists are available at the front desk and in the Reimbursement section of Cube.
- Reimbursement Tips
- Scanned original receipts are required for all expenses
- Airfare receipt must show full itinerary and payment
- ICERM does not offer per diem or meal reimbursement
- Allowable mileage is reimbursed at prevailing IRS Business Rate and trip documented via Google Maps PDF
- Keep all documentation until you receive your reimbursement!
- Reimbursement Timing
6–8 weeks after all documentation is sent to ICERM. All reimbursements are reviewed by multiple Brown University offices.
- Reimbursement Deadline
Submissions must be received within 30 days of ICERM departure to avoid applicable taxes. No submissions are accepted after six months.
