Combinatorial algebraic geometry comprises the parts of algebraic geometry where basic geometric phenomena can be described with combinatorial data, and where combinatorial methods are essential for further progress.
Research in combinatorial algebraic geometry utilizes combinatorial techniques to answer questions about geometry. Typical examples include predictions about singularities, construction of degenerations, and computation of geometric invariants such as Gromov-Witten invariants, Euler characteristics, the number of points in intersections, multiplicities, genera, and many more. The study of positivity properties of geometric invariants is one of the driving forces behind the interplay between geometry and combinatorics. Flag manifolds and Schubert calculus are particularly rich sources of invariants with positivity properties.
In the opposite direction, geometric methods provide powerful tools for studying combinatorial objects. For example, many deep properties of polytopes are consequences of geometric theorems applied to associated toric varieties. In other cases geometry is a source of inspiration. For instance, long-standing conjectures about matroids have recently been resolved by proving that associated algebraic structures behave as if they are cohomology rings of smooth algebraic varieties.
Much research in combinatorial algebraic geometry relies on mathematical software to explore and enumerate combinatorial structures and compute geometric invariants. Writing the required programs is a considerable part of many research projects. The development of new mathematics software is therefore prioritized in the program.
The program will bring together experts in both pure and applied parts of mathematics as well mathematical programmers, all working at the confluence of discrete mathematics and algebraic geometry, with the aim of creating an environment conducive to interdisciplinary collaboration. The semester will include four week-long workshops, briefly described as follows.
- A 'boot-camp' aimed at introducing graduate students and early-career researchers to the main directions of research in the program.
- A research workshop dedicated to geometry arising from flag manifolds, classical and quantum Schubert calculus, combinatorial Hodge theory, and geometric representation theory.
- A research workshop dedicated to polyhedral spaces and tropical geometry, toric varieties, Newton-Okounkov bodies, cluster algebras and varieties, and moduli spaces and their tropicalizations.
- A Sage/Oscar Days workshop dedicated to development of programs and software libraries useful for research in combinatorial algebraic geometry. This workshop will also feature a series of lectures by experts in polynomial computations.
Confirmed Speakers & Participants
- Poster Presenter
Brown UniversityFeb 1-May 7, 2021
Georgia Institute of TechnologyFeb 1-May 7, 2021
Université Grenoble AlpesFeb 1-May 7, 2021
Rutgers UniversityFeb 1-May 7, 2021
Brown UniversityFeb 1-May 7, 2021
University of MichiganFeb 1-May 7, 2021
University of AberdeenFeb 1-May 7, 2021
Stony Brook UniversityFeb 1-May 7, 2021
Institute for Advanced Study and Princeton UniversityFeb 1-May 7, 2021
TU BerlinFeb 1-May 7, 2021
University of MichiganFeb 1-May 7, 2021
Eberhard Karls University of TübingenFeb 25-Mar 31, 2021
Virginia Polytechnic Institute and State UniversityFeb 1-May 7, 2021
University of Texas at AustinFeb 1-May 7, 2021
Versailles Saint-Quentin-en-Yvelines UniversityFeb 1-May 7, 2021
King's College LondonFeb 1-May 7, 2021
Texas A&M UniversityFeb 1-May 7, 2021
MPI LeipzigFeb 1-May 7, 2021
Harvard UniversityFeb 1-May 7, 2021
University of Illinois at Urbana-ChampaignFeb 1-May 7, 2021
Universite de Paris VI (Pierre et Marie Curie)Feb 1-May 7, 2021
Visit dates listed on the participant list may be tentative and subject to change without notice.
ICERM welcomes applications from faculty, postdocs, graduate students, industry scientists, and other researchers who wish to participate in one of our semester-long programs. Some funding may be available for travel and lodging. Applications will be accepted up until the start of the semester program and will be considered as long as funds and space are available.
Any graduate student who applies should have research interests that relate to the program topic; a statement of support from the advisor is required. In addition, graduate students will only be considered if they can remain in-residence for a minimum of six weeks.
Interested in applying for a salaried postdoc position for this program? Applications are accepted via Mathjobs.org (search under “B” for Brown University/ICERM) between June and December in the year prior to the program’s start 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 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.
- Visiting ICERM for longer than a week-long workshop? ICERM staff works with participants to locate accommodations that fit their needs. Since short-term furnished housing is in very high demand, take advantage of the housing options ICERM may recommend. Contact firstname.lastname@example.org for more details.
- Those traveling with family who are interested in information about childcare and/or schools should contact email@example.com.
- Technology Resources
- Wireless internet access 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.
- 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. Both the Brown University "Code of Conduct" and the "Discrimination and Workplace Harassment 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; they are the responsible employees at ICERM under this policy.
- 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.
Contact firstname.lastname@example.org for assistance.
- Need a US Visa?
- J-1 visa requested via ICERM staff
- Eligible to be reimbursed
- B-1 or Visa Waiver Business (WB) –if you already have either visa – contact ICERM staff for a visa specific invitation letter.
- Ineligible to be reimbursed
- B-2 or Visa Waiver Tourist (WT)
- Already in the US?
F-1 and J-1 not sponsored by ICERM: 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.
- 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 airlines
- 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.)
- Reimbursement Request Form
Refer to the back of your ID badge for more information. Checklists are available at the front desk.
- 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.