Focused Research Group Workshop — Algebraic and Symplectic Geometry of Uniruled and Rationally Connected Manifolds

Saturday and Sunday, March 1st and 2nd, Stony Brook University Mathematics Department

All are welcome at the workshop, especially Stony Brook participants! But registration for funding has now passed.

This workshop is funded by the National Science Foundation.

The organizers thank all the participants for making this a successful workshop.

This workshop will focus on recent results in the algebraic geometry and symplectic geometry of uniruled and rationally connected manifolds. The Saturday lectures will be especially focused on the emerging field of symplectically uniruled and symplectically rationally connected manifolds, with a discussion section promoting dialogue between algebraic and symplectic geometers.

Confirmed participants

  • Bhargav Bhatt (Princeton University)
  • Benjamin Bakker (Princeton University)
  • Roya Beheshti (Washington University)
  • Larry Chang (George Washington University)
  • Michael Chance (Stony Brook University)
  • Johan de Jong (Columbia University)
  • Matt DeLand (Columbia University)
  • Barbara Fantechi (SISSA and IAS)
  • Tom Graber (California Institute of Technology)
  • Ning Hao (Stony Brook University)
  • Brendan Hassett (Rice University)
  • János Kollár (Princeton University)
  • Li Li (UIUC)
  • Shuijing Li (Rice University)
  • Tian-Jun Li (University of Minnesota)
  • Max Lieblich (Princeton University)
  • Chiu-chu Melissa Liu (Northwestern and Columbia University)
  • Davesh Maulik (Clay Mathematics Institute and Columbia University)
  • Dusa McDuff (Stony Brook University and Barnard College)
  • James McKernan (Massachusetts Institute of Technology)
  • Rahul Pandharipande (Princeton University)
  • Tim Perutz (Columbia University)
  • Thibaut Pugin (Columbia University)
  • Alice Rizzardo (Columbia University)
  • Joe Ross (Columbia University)
  • Yongbin Ruan (University of Michigan, Ann Arbor)
  • Iman Setayesh (Princeton University)
  • Mingmin Shen (Columbia University)
  • Vivek Shende (Princeton University)
  • Jason Starr (Stony Brook University)
  • Yuri Tschinkel (Courant Institute of Mathematical Sciences)
  • Chenyang Xu (Princeton University)
  • Fei Xu (Rice University)
  • Aleksey Zinger (Stony Brook University)
  • Organizers: Johan de Jong, Brendan Hassett, Yuri Tschinkel, Jason Starr, Aleksey Zinger.

    Hotel and travel information

  • We are now near our budget limit, so official registration is closed. Additional participants will be considered on a case-by-case basis. Of course, anybody who would like to attend and is willing to pay their own way is very welcome. To get the Stony Brook discounted rate at Holiday Inn Express, please mention the reservation code FRG MATH when reserving.
  • We have reserved a block of rooms at the Holiday Inn Express in Stony Brook. We need an accurate estimate no later than January 29th. So if you have not already done so, please contact Jason Starr very soon to confirm your participation and accommodation. The hotel does have a shuttle service.
  • For all participants who requested a hotel, we anticipate check-in on Friday, February 29th and check-out on Sunday, March 2nd. However, if you would like to arrive or depart at another time, please just let us know.
  • Here are some directions on getting to the mathematics department. For visitors who are flying in, most visitors find it convenient to fly in to JFK or LGA (LaGuardia) and then transfer to the Long Island Rail Road at Jamaica station. There is an AirTrain connecting JFK to the Jamaica LIRR station, but it costs $5 to "escape" from the AirTrain. From LGA it is simplest to take a taxi to the Jamaica LIRR station (although there are many other options for the adventurous). For travellers who intend to use the LIRR for at least part of their journey, please see the next item.
  • For visitors travelling through New York City, here is the schedule for the Long Island Rail Road. The Stony Brook station is on campus, a few minutes walk from the mathematics department. Some visitors may prefer to arrive at the Ronkonkoma LIRR station and take a taxi to campus or your hotel.
  • Here is an online map of Stony Brook's campus. The LIRR station is in B2 and B3 on the map. To get to the math department, walk along Circle Road south to Gym Road in the NW corner of B4, then walk along Gym Road east to the gym parking lot on the E edge of B4. Then cross John S. Toll road, proceed up the concrete stairs, and continue to the Math Tower at the S edge of C4 (about a 7 minute walk total). A webpage with more maps is here.
  • For participants who are driving, please contact Jason Starr and Nancy Rohring about getting a visitor's parking permit for campus parking lots.
  • Aleksey Zinger compiled a nice list of on-campus and off-campus dining options here.

    Wireless internet access

    Non-Stony Brook participants who would like wireless access should contact Pat Tonra in advance and let him know all of the following information.
  • First Name
  • Last Name
  • E-mail
  • Phone Number
  • Institution

    Workshop dinner

    There will be a workshop dinner on the evening of Saturday, March 1st at Eastern Pavilion, a Chinese restaurant within walking distance from the department. For speakers and for non-Stony Brook participants, the dinner is free. For Stony Brook participants who are not speakers, the cost of the dinner is $20 (this is after the subsidy). Please confirm whether or not you will attend the workshop dinner and let us know about any dietary restrictions.

    Tentative schedule

    For travellers, we currently intend to end the workshop at 12:30PM on Sunday, March 2nd. If there is significant interest by local people or travellers who have late connections, we may schedule more activity after lunch on Sunday.

    Saturday

    Event

    Sunday

    Event

    9:00AM-10:00AM Registration and coffee 9:00AM-10:00AM Coffee
    10:00AM-11:00AM Yongbin Ruan, Uniruled symplectic manifolds and their birational invariance 10:00AM-11:00AM Chenyang Xu, Fundamental Groups of Smooth Loci of Log Del Pezzo Surfaces
    11:00AM-11:30AM Break 11:00AM-11:30AM Break
    11:30AM-12:30PM Tian-Jun Li, Dichotomy of uniruled submanifolds 11:30AM-12:30PM R. Pandharipande, Rational curves, relative invariants, and the vertex group
    12:30PM-2:00PM Lunch 12:30PM-2:00PM Workshop officially ends
    2:00PM-3:00PM Dusa McDuff, Hamiltonian S1 manifolds are uniruled 2:00PM-3:00PM
    3:00PM-4:00PM Tea 3:00PM-4:00PM
    4:00PM-5:00PM J. Starr, Report on a theorem of C. Voisin 4:00PM-5:00PM
    5:00PM-5:15PM Break 5:00PM-5:15PM
    5:15PM-6:15PM Discussion Session 5:15PM-6:15PM
    6:15PM-7:00PM Open schedule 6:15PM-7:00PM
    7:00PM Banquet 7:00PM

    Joint Columbia-Courant-Princeton Algebraic Geometry Seminar

    On "Leapday" - Friday, February 29th - there will be a Joint Columbia-Courant-Princeton Algebraic Geometry Seminar at Columbia University. The scheduled speakers are Mikhail Kapranov (Yale), Kiran Kedlaya (MIT) and James McKernan (MIT). More information is available here. Workshop participants who are travelling through the New York City area are encouraged to attend the lectures at Columbia. In particular, Jason Starr will be at the Columbia seminars and will bring participants from Columbia back to Stony Brook on the Long Island Rail Road.

    Abstracts


    Yongbin Ruan (University of Michigan, Ann Arbor) Uniruled symplectic manifolds and their birational invariance

    One of the early applications of GW-theory was an extension of some elements of the Mori program to symplectic geometry. We will start the talk by presenting these early evidences of "symplectic birational geometry". Then, we will use Guillemin-Sternberg's notion of Hamiltonian S^1-cobordism to set up the symplectic birational equivalence and sketch the proof of birational invariance of uniruledness. In the end of the talk, we will speculate a conjectural generalization of uniruledness to the open string category and its invariance under transition.


    Tian-Jun Li (University of Minnesota) Dichotomy of uniruled submanifolds

    In this talk we discuss uniruled submanifolds, especially those with real codimension 2, in symplectic manifolds. If they are non-negative in an appropriate sense, we show that the ambient manifold must be uniruled as well. We also show that many negative ones can be contracted in a 6 dimension symplectic manifold. If times permits we will speculate on the notion of minimality. This is a joint work with Yongbin Ruan.


    Dusa McDuff (Stony Brook University and Barnard College) Hamiltonian S1 manifolds are uniruled

    I will try to explain the result and its proof, without assuming the audience knows much symplectic geometry. So I will start by describing the structure of symplectic manifolds that support a Hamiltonian circle action, and the structure of the quantum homology of non uniruled symplectic manifolds and their pointwise blowups. Then I will talk about the image of a circle action under the Seidel representation in quantum homology, and show how one can use it to prove the theorem.


    Jason Starr (Stony Brook University) Report on a theorem of Claire Voisin

    Unfortunately Claire Voisin could not participate in this workshop. So Jason Starr will deliver a report on Voisin's recent article Rationally connected 3-folds and symplectic geometry.


    Chenyang Xu (Princeton University) Fundamental Groups of Smooth Loci of Log Del Pezzo Surfaces

    Log del Pezzo surfaces have interesting arithmetic and geometry properties. In particular, it is known that the fundamental groups of their smooth loci are finite groups. In this talk, based on the classification results of Dolgachev and Iskovskikh on finite subgroups of Cremona groups, we study these finite groups. We will describe a short table containing these groups and how we get it.


    Rahul Pandharipande (Princeton University) Rational curves, relative invariants, and the vertex group

    I will discuss rational curve enumeration on surfaces in the log Calabi-Yau setting. I will explain a peculiar new multiple cover formula for all such relative geometries. My motivation comes from the Gross-Siebert program and in particular recent conjectures relating the multiplication in their vertex group to rational curve counts. The lecture will make contact with both classical and modern questions.


    Back to my home page.


    Jason Starr
    3-119 Math Tower
    Department of Mathematics
    Stony Brook University
    Stony Brook, NY 11794-3651
    Phone: 631-632-8622
    Fax: 631-632-7631
    Jason Starr