Organizing Committee
Abstract

Mathematicians have studied elliptic curves for decades, owing to their beautiful abstract structure, powerful applications in number theory and algebraic geometry, and practical relevance in cryptography. It is surprising, therefore, that the so-called murmuration phenomenon was first observed in 2022.

Murmurations can be observed through studying databases of arithmetic and automorphic objects, rather than through studying individual objects. The availability of such databases facilitates the application of machine learning (ML) and other data scientific tools. Indeed, murmuration was first discovered by simply taking averages of certain elliptic curve datasets, and it has been shown that various invariants of arithmetic objects can be learned successfully through standard ML techniques such as logistic regression, random forest and neural networks with high (often greater than 95%) accuracy in classification. This approach opens up many possible directions for other ML experiments, their interpretation, and, subsequently, new understanding. In this workshop, we will explore murmuration structures for other arithmetic and automorphic objects, explore the utility of other tools from ML, and seek to establish conjectures, heuristics, and, where possible, rigorous mathematical explanations.

This workshop will provide the opportunity to gather together a wide array of perspectives on elliptic curves, and other number theoretic objects, in the hope of developing structural theorems and applications of this new discovery to outstanding questions in arithmetic. The topic of this workshop also offers a timely opportunity to find directions along which we may further explore this new paradigm of research.

This workshop is partially funded by a Simons Foundation Targeted Grant to Institutes.

Image for "Murmurations in Arithmetic"
Photo by Walter Baxter / A Murmuration of Starlings at Gretna / CC BY-SA 2.0

Confirmed Speakers & Participants

Talks will be presented virtually or in-person as indicated in the schedule below.

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee
  • Kimball Martin
    University of Oklahoma
  • Alexey Pozdnyakov
    University of Connecticut
  • Joseph Silverman
    Brown University
  • Andrew Sutherland
    MIT
  • Zina Zubrilina
    Princeton University

Application Information

ICERM welcomes applications from faculty, postdocs, graduate students, industry scientists, and other researchers who wish to participate. Some funding may be available for travel and lodging. Graduate students who apply must have their advisor submit a statement of support in order to be considered.

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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 8:00am - 4:00pm during this event. See our facilities page for more info about ICERM and Brown's available facilities.
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. In-depth directions and transportation information are available on our travel page.
Lodging
ICERM's special rate will soon be made available via this page for our preferred hotel, the Hampton Inn & Suites Providence Downtown. ICERM also regularly works with the Graduate Hotel and Hilton Garden Inn who both have discounted rates available. Contact housing@icerm.brown.edu before booking anything.
The only way ICERM participants should book a room is through the hotel reservation links located on this page or through links emailed to them from an ICERM email address (first_last@icerm.brown.edu). ICERM never works with any conference booking vendors and never collects credit card information.
Childcare/Schools
Those traveling with family who are interested in information about childcare and/or schools should contact housing@icerm.brown.edu.
Technology Resources
Wireless internet access ("Brown-Guest") and wireless printing is available for all ICERM visitors. Eduroam is available for members of participating institutions. Thin clients in all offices and common areas provide open access to a web browser, SSH terminal, and printing capability. See our Technology Resources page for setup instructions and to learn about all available technology.
Accessibility
To request special services, accommodations, or assistance for this event, please contact accessibility@icerm.brown.edu as far in advance of the event as possible. Thank you.
Discrimination and Harassment Policy
ICERM is committed to creating a safe, professional, and welcoming environment 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 ICERM participants and staff. Participants with concerns or requests for assistance on a discrimination or harassment issue should contact the ICERM Director or Assistant Director of Finance & Administration; they are the responsible employees at ICERM under this policy.
Fundamental Research
ICERM research programs aim to promote Fundamental Research and mathematical sciences education. If you are engaged in sensitive or proprietary work, please be aware that ICERM programs often have participants from countries and entities subject to United States export control restrictions. Any discoveries of economically significant intellectual property supported by ICERM funding should be disclosed.
Exploring Providence
Providence's world-renowned culinary scene provides ample options for lunch and dinner. Neighborhoods near campus, including College Hill Historic District, have many local attractions. Check out the map on 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 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 in economy class to either Providence airport (PVD) or Boston airport (BOS)
  • Ground Transportation to and from airports and ICERM.
Unacceptable Costs
  • 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
  • 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: $250
  • Other contiguous US: $750
  • Asia & Oceania: $2,000
  • All other locations: $1,500
  • Note these rates were updated in Spring 2022 and superseded any prior invitation rates. Any invitations without travel support will still not receive travel support.
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 pdf of Google Maps result
  • Keep all documentation until you receive your reimbursement!
Reimbursement Timing

6 - 8 weeks after all documentation is sent to ICERM. All reimbursement requests are reviewed by numerous central offices at Brown who may request additional documentation.

Reimbursement Deadline

Submissions must be received within 30 days of ICERM departure to avoid applicable taxes. Submissions after thirty days will incur applicable taxes. No submissions are accepted more than six months after the program end.