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Workshop

Introductory Workshop: Derived Algebraic Geometry and Birational Geometry and Moduli Spaces January 31, 2019 - February 08, 2019
Registration Deadline: February 04, 2019 4 months ago
To apply for Funding you must register by: October 15, 2018 7 months ago
Parent Program:
Location: MSRI: Simons Auditorium, Atrium
Organizers Julie Bergner (University of Virginia), Bhargav Bhatt (University of Michigan), Christopher Hacon (University of Utah), LEAD Mircea Mustaţă (University of Michigan), Gabriele Vezzosi (Università di Firenze)
Speaker(s)

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Description
Tuelle picture
A picture of a singularity, courtesy of Herwig Hauser
The workshop will survey several areas of algebraic geometry, providing an introduction to the two main programs hosted by MSRI in Spring 2019. It will consist of 7 expository mini-courses and 7 separate lectures, each given by top experts in the field.  The focus of the workshop will be the recent progress in derived algebraic geometry, birational geometry and moduli spaces. The lectures will be aimed at a wide audience including advanced graduate students and postdocs with a background in algebraic geometry. Bibliography
Keywords and Mathematics Subject Classification (MSC)
Tags/Keywords
  • singularities

  • moduli spaces

  • birational geometry

  • stacks and higher stacks

  • derived stacks

  • \infty-categories

  • dg-categories

  • model categories

  • derived dg-categories

  • moduli problems

  • simplicial algebras

  • dg-algebras

  • de Rham cohomology

  • Hochschild and cyclic cohomology

  • minimal model program

  • rationality

  • derived categories

  • fibrations

  • degenerations

  • vanishing theorems

  • positive characteristic methods

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Funding & Logistics Show All Collapse

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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

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MSRI does not hire an outside company to make hotel reservations for our workshop participants, or share the names and email addresses of our participants with an outside party. If you are contacted by a business that claims to represent MSRI and offers to book a hotel room for you, it is likely a scam. Please do not accept their services.

MSRI has preferred rates at the Hotel Shattuck Plaza, depending on room availability. Guests can call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Institute discount. To book online visit this page (the MSRI rate will automatically be applied).

MSRI has preferred rates at the Graduate Berkeley, depending on room availability. Reservations may be made by calling 510-845-8981. When making reservations, guests must request the MSRI preferred rate. Enter in the Promo Code MSRI123 (this code is not case sensitive).

MSRI has preferred rates at the Berkeley Lab Guest House, depending on room availability. Reservations may be made by calling 510-495-8000 or directly on their website. Select "Affiliated with the Space Sciences Lab, Lawrence Hall of Science or MSRI." When prompted for your UC Contact/Host, please list Chris Marshall (coord@msri.org).

MSRI has a preferred rates at Easton Hall and Gibbs Hall, depending on room availability. Guests can call the Reservations line at 510-204-0732 and ask for the MSRI- Mathematical Science Research Inst. rate. To book online visit this page, select "Request a Reservation" choose the dates you would like to stay and enter the code MSRI (this code is not case sensitive).

Additional lodging options may be found on our short term housing page.

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Schedule, Notes/Handouts & Videos
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Jan 31, 2019
Thursday
09:15 AM - 09:30 AM
  Welcome
09:30 AM - 10:30 AM
  DAG I: the cotangent complex and derived de Rham cohomology
Benjamin Antieau (University of Illinois, Chicago)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Moduli of canonical models
János Kollár (Princeton University)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  The uniqueness of K-polystable Fano degeneration
Chenyang Xu (Massachusetts Institute of Technology)
03:00 PM - 03:30 PM
  Tea
Feb 01, 2019
Friday
09:30 AM - 10:30 AM
  Birational algebraic geometry in positive characteristic
Karl Schwede (University of Utah)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  DAG II: moduli of objects in derived categories
Benjamin Antieau (University of Illinois, Chicago)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Moduli of canonical models
János Kollár (Princeton University)
03:00 PM - 03:30 PM
  Tea
03:30 PM - 04:30 PM
  Infinity categories and why they are useful, I
Carlos Simpson (Universite de Nice Sophia Antipolis)
Feb 04, 2019
Monday
09:00 AM - 10:00 AM
  Infinity categories and why they are useful, II
Carlos Simpson (Universite de Nice Sophia Antipolis)
10:00 AM - 10:30 AM
  Break
10:30 AM - 11:30 AM
  Moduli of canonical models
János Kollár (Princeton University)
11:30 AM - 12:30 PM
  DAG III: examples
Benjamin Antieau (University of Illinois, Chicago)
12:30 PM - 02:30 PM
  Lunch
02:30 PM - 03:30 PM
  Birational algebraic geometry in positive characteristic
Karl Schwede (University of Utah)
03:30 PM - 04:00 PM
  Tea
04:00 PM - 05:00 PM
  The notion of singular support in DAG and its applications I
Sam Raskin (University of Texas, Austin)
Feb 05, 2019
Tuesday
09:30 AM - 10:30 AM
  Infinity categories and why they are useful, III
Carlos Simpson (Universite de Nice Sophia Antipolis)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Stable birational invariants
Claire Voisin (Collège de France; Institut de Mathématiques de Jussieu)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  The notion of singular support in DAG and its applications II
Sam Raskin (University of Texas, Austin)
03:00 PM - 03:30 PM
  Tea
03:30 PM - 04:30 PM
  Birational algebraic geometry in positive characteristic
Karl Schwede (University of Utah)
04:30 PM - 06:20 PM
  Reception
Feb 06, 2019
Wednesday
09:00 AM - 10:00 AM
  Topological Hochschild homology and topological cyclic homology: from classical to modern - I
Kathryn Hess (École Polytechnique Fédérale de Lausanne (EPFL))
10:00 AM - 10:30 AM
  Break
10:30 AM - 11:30 AM
  Stable birational invariants
Claire Voisin (Collège de France; Institut de Mathématiques de Jussieu)
11:30 AM - 11:45 AM
  Break
11:45 AM - 12:45 PM
  Rationality problems
Yuri Tschinkel (New York University, Courant Institute)
Feb 07, 2019
Thursday
09:00 AM - 10:00 AM
  Topological Hochschild homology and topological cyclic homology: from classical to modern - II
Kathryn Hess (École Polytechnique Fédérale de Lausanne (EPFL))
10:00 AM - 10:30 AM
  Break
10:30 AM - 11:30 AM
  Stable birational invariants
Claire Voisin (Collège de France; Institut de Mathématiques de Jussieu)
11:30 AM - 11:45 AM
  Break
11:45 AM - 12:45 PM
  Shifted symplectic structures and applications
Tony Pantev (University of Pennsylvania)
12:45 PM - 02:30 PM
  Lunch
02:30 PM - 03:30 PM
  The notion of singular support in DAG and its applications III
Sam Raskin (University of Texas, Austin)
03:30 PM - 04:00 PM
  Tea
04:00 PM - 05:00 PM
  Extending holomorphic forms from the regular locus of a complex space to a resolution
Christian Schnell (State University of New York, Stony Brook)
Feb 08, 2019
Friday
09:30 AM - 10:30 AM
  Topological Hochschild homology and topological cyclic homology: from classical to modern - III
Kathryn Hess (École Polytechnique Fédérale de Lausanne (EPFL))
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Derived categories of cubic fourfolds and non-commutative K3 surfaces
Emanuele Macri (Northeastern University)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  (Derived) moduli of local systems in number theory
Akshay Venkatesh (Institute for Advanced Study)
03:00 PM - 03:30 PM
  Tea