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Organizing Committee
Eastern Michigan University
Utrecht University
University of Wisconsin-Madison
University of Bath
Massachusetts Institute of Technology
Abstract
A conjecture of Malle predicts an asymptotic formula for the quantity of number fields with a given Galois group and whose discriminant is bounded by a growing parameter. This conjecture is foundational to the area of Arithmetic Statistics and has received considerable interest over the past 20 years, notably including Bhargava receiving the Fields Medal in part for his work on quartic and quintic field extensions.
Progress has been so rapid and varied, that there are now a host of cases known depending on a variety of group and number theoretic parameters. There are also numerous improvements to the original conjecture due to Bhargava, Wang, and Loughran--Santens that sharpen its predictions. The framework now consists of a range of mathematical tools, including permutation groups, embedding problems, group cohomology, algebraic stacks, and Brauer groups. Determining what follows from existing results for a particular Galois group, or even determining what the exact prediction should be, is a non-trivial endeavor.
The aims of the workshop are to overview the current state of the art in Malle's conjecture, to compile a living database regarding progress on the conjecture, and to develop algorithms to calculate the constants arising in Malle's conjecture. The first day will consist of talks. During the remaining time, participants will join focused working groups developing algorithms and inputting data into the L-functions and Modular Forms Database.
The deadline to apply for this workshop has been extended to February 16, 2026.
Progress has been so rapid and varied, that there are now a host of cases known depending on a variety of group and number theoretic parameters. There are also numerous improvements to the original conjecture due to Bhargava, Wang, and Loughran--Santens that sharpen its predictions. The framework now consists of a range of mathematical tools, including permutation groups, embedding problems, group cohomology, algebraic stacks, and Brauer groups. Determining what follows from existing results for a particular Galois group, or even determining what the exact prediction should be, is a non-trivial endeavor.
The aims of the workshop are to overview the current state of the art in Malle's conjecture, to compile a living database regarding progress on the conjecture, and to develop algorithms to calculate the constants arising in Malle's conjecture. The first day will consist of talks. During the remaining time, participants will join focused working groups developing algorithms and inputting data into the L-functions and Modular Forms Database.
The deadline to apply for this workshop has been extended to February 16, 2026.
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Application Information
The deadline to submit an application to this program has passed.
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.