Algebraic Geometry: Presentations by Young Researchers

Sunday July 4 -- Thursday July 8, 2004 in Snowbird, Utah


Organizing committee: Herb Clemens (Ohio State), Rob Lazarsfeld (Michigan), Ravi Vakil (Stanford).

This is one of the 2004 Joint Summer Research Conferences.

Even at its modern inception, algebraic geometry was technically quite demanding. Today the field is broad and deep enough that most new Ph.D.'s narrowly focus on a small part of it in order to produce original research. Thus the postdoctoral years are the best time to broaden their knowledge and to build the connections, both personal and intellectual, that will nourish a lifelong research career.

This conference is intended for recent Ph.D.'s, who have already developed an area of expertise. The conference is intended to widen the participants' horizons, by exposing them to the ideas and problems of other parts of the field, and to introduce them to future colleagues and collaborators. Hence there will be ample time for and emphasis on small group discussions and networking.

In the mornings, there will be ten Bourbaki-style talks, in which participants will present important results in the field. In the afternoons, the participants will break up into groups and work with a senior mentor and each other. (The mentors are listed below.)


  • Check in on Saturday, July 3; check out on Friday, July 9
  • Morning: Ten expository lectures. Abstracts are here. The revised notes have appeared in the book Snowbird Lectures in Algebraic Geometry. Snowbird
    Sunday Nick Proudfoot Geometric Invariant Theory and projective toric varieties
    Brian Osserman Two degeneration techniques for maps of curves
    Monday Julianna Tymoczko Equivariant cohomology, following Goresky, Kottwitz, and MacPherson
    Sam Grushevsky Multiplier ideals in algebraic geometry
    Tuesday Carolina Araujo Rationally connected varieties and a theorem by Graber, Harris and Starr
    Mihran Papikian Rigid analytic geometry and abelian varieties (notes; Owen Jones warns that the inequalities are going in the wrong direction when R and M are defined on p. 2 par. 2)
    Wednesday Max Lieblich Quotients by groupoids (following Keel-Mori)
    Andrei Caldararu Why Hochschild? An algebraic geometer's point of view
    Thursday David Lehavi Real algebraic curves and amoebas (following Mikhalkin)
    Izzet Coskun The arithmetic and the geometry of Kobayashi hyperbolicity (notes)

  • Afternoon: Working groups (which will likely be fairly introductory, depending on the mentor and participants)
    Mentor Topic
    A Linda Chen Schubert calculus
    B Gabi Farkas Moduli spaces of abelian varieties
    C Angela Gibney Moduli of curves and the Fulton-Macpherson configuration space
    D Allen Knutson Group actions and degeneration
    E Sándor Kovács Introduction to the minimal model program
    F Diane Maclagan Introduction to toric varieties
    G Mike Nakamaye Applications of positivity in diophantine geometry
    H Tony Pantev Geometric dualities

  • There will be a welcome party on Sunday night after the first full day. Mealtimes will be 7-8:30 am, 12:15-1:45 pm, 6-7:30 pm; there will also be morning and afternoon coffee breaks. There will be an afternoon off (suitable for a hike).
  • In The Lodge (where the conference office will be), there will be an email room with four machines and a printer, open 24 hours a day. It is a wireless hub, so anyone whose laptop has the necessary software will be able to connect. There will be a copy machine in the office for participants' use. There will also be a hospitality room next door to the email room, open Monday-Wednesday evenings. It will have a refrigerator stocked with beer, wine, and soft drinks (money will be collected on the honor system to cover costs) and some chips.

    Invited participants

    Name Aft. working group Field of interest (please e-mail me updates)
    Kursat Aker, Penn D
    Carolina Araujo, Princeton / IMPA D rational curves, Fano varieties
    Daniele Arcara, Utah C vector bundles on curves and surfaces
    Roya Beheshti, Max Planck / Queens C
    Aaron Bertram, Utah (visiting mentor) moduli problems and Gromov-Witten invariants
    Nero Budur, Johns Hopkins H higher dimensional geometry
    Charles Cadman, Columbia / Michigan E stacks and enumerative geometry
    Andrei Caldararu, Penn G
    Sebastian Casalaina-Martin, Columbia B
    Paolo Cascini, NYU H
    Linda Chen, Columbia / Ohio State (mentor) A moduli problems, orbifold cohomology
    Zhao Chen, NYC College of Technology F
    Herb Clemens, Ohio State (organizing committee) algebraic cycles, deformation theory
    Izzet Coskun, Harvard / MIT E
    Gabi Farkas, Princeton / UT Austin (mentor) B moduli of curves, abelian varieties
    Alexandru Ghitza, McGill G moduli of abelian varieties in positive characteristic and applications to modular forms
    Angela Gibney, Yale / Penn (mentor) C moduli of curves and the Fulton-Macpherson configuration space
    Sam Grushevsky, Princeton A moduli of curves, abelian varieties
    Tawanda Gwena, Georgia F moduli of curves and abelian varieties
    Milena Hering, Michigan A toric varieties
    Jason Howald, Johns Hopkins D
    Amanda Johnson, NSF F
    Michael Joyce, Brown E arithmetic of almost Fano varieties
    Allen Knutson, Berkeley (mentor) D
    Sándor Kovács, Washington (mentor) E higher-dimensional geometry
    Gabriele La Nave, NYU H
    Rob Lazarsfeld, Michigan (organizing committee) higher-dimensional algebraic geometry
    David Lehavi, Ohio State B classical algebraic geometry
    Maxim Leyenson, Chicago H moduli of vector bundles
    Max Lieblich, MIT / Brown/ Princeton E algebraic stacks, moduli of sheaves, and arithmetic applications
    Diane Maclagan, Stanford / Rutgers (mentor) F toric varieties and grobner bases
    Leonardo Mihalcea, Michigan D Schubert calculus, equivariant and quantum cohomology
    Maciej Mizerski, UBC C Schubert calculus and Gromov-Witten invariants
    Anca-Magdalena Mustata, UBC H
    Andrei Mustata, UBC B
    Mike Nakamaye, New Mexico (mentor) G base loci of linear series
    Brian Osserman, RIMS / Berkeley F
    Tony Pantev, Penn (mentor) H Hodge theory and mathematical physics
    Mihran Papikian, Stanford G
    Sam Payne, Michigan G
    Nick Proudfoot, Berkeley / UT Austin G hyperkahler quotients
    Kevin Purbhoo, Berkeley C
    Julius Ross, Columbia H stability of polarised varieties; relation to metrics of constant scalar curvature
    Fumitoshi Sato, Utah E Gromov-Witten invariants
    James Spencer, Rice H
    Matt Szczesny, Penn E
    Evgeni Tevelev, UT Austin C
    Csilla Tamás, Georgia H higher-dimensional geometry, abelian varieties
    Howard Thompson, Michigan B toric varieties
    Will Traves, US Naval Academy A intersection theory, invariant theory, and D-modules
    Julianna Tymoczko, Michigan A
    Ravi Vakil, Stanford (organizing committee) intersection theory on moduli spaces
    Michael Van Opstall, Washington / Utah A moduli of stable surfaces
    Stephanie Yang, Harvard / Michigan F
    Alexander Yong, Berkeley B Schubert calculus, quantum cohomology, group actions and degenerations
    Jing Zhang, Washington University E
    Aleksey Zinger, Stanford D

    This page is maintained by Ravi Vakil (, and will be updated only sporadically. Please send me any updates (but be patient). Many thanks to Donna Salter and the AMS!