Graduate Student Warm-Up Workshop for AMS Summer Institute in Algebraic Geometry, Seattle 2005
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Academic program

The workshop will feature lectures and small working groups. On Sunday evening, there will be an orientation meeting (Cascade Room, at the dorm, 6-8 pm). During the week (Monday to Friday), the schedule will be as follows.

8:30-9:30 lecture (Savery Hall 239 )
9:45-10:45 lecture (Savery Hall 239 )
10:45-11:30 coffee break
11:30-12:30 lecture (Savery Hall 239 )
12:30-2:00 lunch
2:00-3:40 working groups
3:45-4:15 tea (Savery Hall 239 )
4:20-6:00 working groups
dinner

During the coffee break on Monday, everyone not yet signed up with a particular working group will meet with Herb Clemens, to be divided up.

There are two cafeteria options: one at McMahon (one of the dorms) and another in the Student Union Building ("HUB").

On Friday evening, there will be a concluding plenary meeting (Cascade room, at the dorm, 6:30-8:30 pm).

There will be access to a computer lab 7-8 pm Monday to Friday, in Communications B022. There should be other e-mail access available through the libraries.

(For a map of campus, click here.)

Lectures

The titles are below. Click here to read the abstracts. Click here to read the lecture notes. Chuck Doran has kindly offered to eventually post videos of all the lectures.

Monday

  • Introduction to Chevalley groups (Daniel Allcock)
  • What sorts of algebro-geometric objects arise in physics and why should we care? (Jim Bryan)
  • Spaces of arcs and birational geometry (Mircea Mustata)

    Tuesday

  • Introduction to stacks (Tom Graber)
  • From strings to standard models via algebraic geometry (Ron Donagi)
  • What is a moduli space and why do algebraic geometers love them? (Angela Gibney)

    Wednesday

  • The Hilbert scheme (Mike Roth)
  • Langlands' conjectures and Shimura varieties (Elena Mantovan)
  • Birational Classification of Varieties (James McKernan)

    Thursday

  • Why rational curves? (Stefan Kebekus)
  • Syzygies of algebraic varieties and Green's conjecture (Gavril Farkas)
  • Equivariant cohomology (Linda Chen)

    Friday

  • What's the deal with Geometric Langlands? (David Ben-Zvi)
  • Density of rational points (Brendan Hassett)
  • Positivity in combinatorial algebraic geometry (Ezra Miller)

    Working groups

    Each group will have 5-10 people in it. The titles and group members are given below. (The remaining participants will be placed into groups on the morning of the first day of the workshop.) Click on the titles to read the abstracts.

    A Introduction to algebraic groups (Daniel Allcock, Texas) MEB 251
    Jarod Alper, Roi Docampo Alvarez, Christian Grundh, Travis Kopp, Cameron McLeman, Kathryn Rouse, Kirsten Wickelgren

    B Geometry of derived categories (David Ben-Zvi, Texas) MEB 235
    Anthony Bak, Dimitri Boyarchenko, Sabin Cautis, Peter Dalakov, John Levitt, Mahdi Majidi-Zolbanin, Karl Schwede, David Stern, Hsian-Hua Tseng, Jonathan Wise

    C Stable maps and Gromov-Witten theory (Jim Bryan, British Columbia) SAV 311
    Mohammed Abouzaid, Elizabeth Baldwin, Matthew Ballard, Huai-Lian Chang, Maksym Fedorchuk, G. Michael Guy, Anne-Sophie Kaloghiros, Mike Rose, Makoto Sakurai, Ziyu Zhang

    D Introductory Schubert calculus (Linda Chen, Ohio State) SAV 315
    Jameel Al-Aidroos, Hannah Markwig, Johan Martens, Joe Rusinko, Elizabeth Scott

    E Algebraic geometry in string theory (Ron Donagi, Penn) MEB 250
    Stuart Ambler, Elena Andreini, Meng Chen, Hans Georg Freiermuth, Lotte Hollands, Afsaneh Mehran, Alexei Oblomkov, Gueorgui Todorov, Yu-jong Tzeng, Alexandr Usnich

    F Degeneration methods in algebraic geometry (Gavril Farkas, Texas) SAV 343
    Dawei Chen, Jimmy Dillies, Milena Hering, Zheng Hua, Yunfeng Jiang, Michael Korotiaev, Yusuf Mustopa, Ben Lee, Nikola Penev, Yinan Song

    G Stable maps from rational curves to projective space (Angela Gibney, Penn) LOW 222
    Chris Brav, Patrick Clarke, Diane Davis, So Okada, Qiang Song

    H Introduction to stacks (Tom Graber, Berkeley) SAV 313
    Alex Boer, Shou-Xin Dai, Fabrizio Donzelli, Robert Easton, Kelly Jabbusch, Parker Lowrey, Francesco Noseda, Christian Schnell, Jan Tuitman, Robert Vollmert

    I Density of rational points (Brendan Hassett, Rice) SIG 230
    Anar Akhmedov, Jesse Kass, Jeremy Muskat, Sam Payne, Maria Sabitova, Andy Schultz, Damiano Testa

    J Foliations and rationally connected submanifolds (Stefan Kebekus, Cologne) SAV 316
    Arend Bayer, Ethan Cotterill, Su-Jeong Kung, Kyungyong Lee, Geoff Lynch

    K Deformation theory and moduli spaces of abelian varieties in positive characteristic (Elena Mantovan, Berkeley) SAV 335
    William Butske, Ishai Dan-Cohen, Manish Kumar, Carl Miller, Deepam Patel, Mehmet Sahin

    L Higher dimensional geometry and the minimal model program (James McKernan, Santa Barbara) MEB 103
    Marcello Bernardara, Emanuele Macri, Fabio Perroni, Victor Przyjalkowsky, Paolo Stellari, Alberta Della Vedova

    M Positivity in combinatorial algebraic geometry (Ezra Miller, Minnesota) MUE 154
    David Anderson, Jian He, Maciej Mizerski, Ivan Petrakiev, Hongyuan Wang

    N Singularities in birational geometry (Mircea Mustata, Michigan) SAV 245
    Kyle Hoffmann, Wenchuan Hu, Behzad Khazaie, Deepee Khosla, Radu Laza, Peter Petrov, Elizabeth Sell, Zachary Treisman, Masrour Zoghi

    O Brill-Noether theory (Mike Roth, Queens) MOR 226
    Oren Ben-Bassat, Chris Davis, Amin Gholampour, Dagan Karp, Michael Kunte, Songyun Xu, Cornelia Yuen

    P Points of order 11 on elliptic curves (Tom Weston, Massachusetts) SAV 341
    Lisa Berger, Wei Ho, Amanda Knecht, Yu-Han Liu, Joe Rabinoff

    Other events

    During the three-week conference, we will have a related talk: Miles Reid will give an expository lecture titled "K3s and Fano 3-folds, Tom and Jerry" (Tuesday, August 2, 7:30 pm, EE 105). Miles Reid is a spectacular lecturer and you are strongly encouraged to check this out.

    We will have a drop-in center on Tuesday and Thursday evenings during the three-week conference (Communications B006, 7-9 pm) where you are invited to come and ask questions related to the plenary lectures (no matter how seemingly simple or foundational the questions are). You can also just come to hear the answers to questions other people ask. We will have a volunteer expert on hand for most plenaries. The experts corresponding to each plenary speaker are listed below. (If you know of someone willing to volunteer for one of our empty slots, please let us know!)

    Week 1
    Hori: Charles Doran (Washington)
    Okounkov, Pandharipande: Davesh Maulik (Princeton, Tuesday), Dragos Oprea (MIT/Stanford, Thursday)
    Seidel: Mohammed Abouzaid (Chicago, Tuesday)
    Madsen: ---

    Week 2
    Haiman: Alex Woo (Berkeley/Davis)
    Harris: Sabin Cautis (Harvard)
    Voisin: Herb Clemens (Ohio State)
    Kollar, Shokurov: Michael van Opstall (Utah, Tuesday), Carolina Araujo (IMPA, Thursday), Karl Schwede (Washington), James McKernan (Santa Barbara)

    Week 3
    Conrad: Kiran Kedlaya (MIT, Tuesday), Max Lieblich (Brown/Princeton, Thursday), Brian Osserman (Berkeley, Thursday), Jordan Ellenberg (Princeton/Wisconsin)
    Gaitsgory: Dima Arinkin (Chicago)
    Loeser: ---

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