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Organizing Committee
University of Liverpool
University of Southampton
Harvard University
University of Liverpool
Smith College
Abstract
The workshop will foster collaborations between the adjacent areas of Rigidity Theory and Geometric Data Science for practically important applications to solid crystalline materials and molecular structures, including proteins.
Since many real objects are often given in a coordinate-dependent form, a practical answer to the fundamental question "Same or Different?" requires us to formalize the concept of the "same" object through an equivalence relation. The key example is a cloud of unordered points such as atomic centers considered equivalent under rigid motion in a Euclidean space.
Since real coordinates are always noisy, the second fundamental question "How much different?" asks for a distance on equivalence classes that satisfies all metric axioms and continuously Changes under perturbations of given data.
The same questions can be stated for many other data objects (periodic and discrete point sets, embedded graphs, and simplicial complexes) under other equivalence relations (isometry, dilations, affine and projective transformations). Practical answers to these questions should include polynomial-time algorithms for a complete invariant to identify any object under a
given equivalence and a distance metric quantifying the similarity between different objects.
The ultimate condition for a complete and continuous invariant is its realizability that would allow us to choose a new invariant value that can be converted into a real object. All these conditions form the geo-mapping problem in Geometric Data Science whose aim is to bi-continuously parametrize moduli spaces of all important objects and their equivalences.
For example, the space of all triangles (including degenerate ones) under isometry is parametrized by three inter-point distances a,b,c, whose realizability is described by the inequalities 0<a≤b≤c≤a+b. However, the space of even four unordered points in the plane had no similarly efficient parametrization.
Since many real objects are often given in a coordinate-dependent form, a practical answer to the fundamental question "Same or Different?" requires us to formalize the concept of the "same" object through an equivalence relation. The key example is a cloud of unordered points such as atomic centers considered equivalent under rigid motion in a Euclidean space.
Since real coordinates are always noisy, the second fundamental question "How much different?" asks for a distance on equivalence classes that satisfies all metric axioms and continuously Changes under perturbations of given data.
The same questions can be stated for many other data objects (periodic and discrete point sets, embedded graphs, and simplicial complexes) under other equivalence relations (isometry, dilations, affine and projective transformations). Practical answers to these questions should include polynomial-time algorithms for a complete invariant to identify any object under a
given equivalence and a distance metric quantifying the similarity between different objects.
The ultimate condition for a complete and continuous invariant is its realizability that would allow us to choose a new invariant value that can be converted into a real object. All these conditions form the geo-mapping problem in Geometric Data Science whose aim is to bi-continuously parametrize moduli spaces of all important objects and their equivalences.
For example, the space of all triangles (including degenerate ones) under isometry is parametrized by three inter-point distances a,b,c, whose realizability is described by the inequalities 0<a≤b≤c≤a+b. However, the space of even four unordered points in the plane had no similarly efficient parametrization.
This is a satellite event of the International Congress of Mathematicians.
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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.
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.