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Workshop

The Commutative Algebra of Singularities in Birational Geometry: Multiplier Ideals, Jets, Valuations, and Positive Characteristic Methods May 06, 2013 - May 10, 2013
Registration Deadline: May 24, 2013 about 10 years ago
To apply for Funding you must register by: February 06, 2013 over 10 years ago
Parent Program:
Organizers Craig Huneke (University of Virginia), Yujiro Kawamata (University of Tokyo), Mircea Mustaţă (University of Michigan), Karen Smith (University of Michigan), Kei-ichi Watanabe (Nihon University)
Speaker(s)

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Description
The workshop will examine the interplay between measures of singularities coming both from characteristic p methods of commutative algebra, and invariants of singularities coming from birational algebraic geometry. There is a long history of this interaction which arises via the "reduction to characteristic p" procedure. It is only in the last few years, however, that very concrete objects from both areas, namely generalized test ideals from commutative algebra and multiplier ideals from birational geometry, have been shown to be intimately connected. This workshop will explore this connection, as well as other topics used to study singularities such as jets schemes and valuations. Bibliography (pdf) Accommodation: A block of rooms has been reserved at the Rose Garden Inn. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show MSRI rate on all room types available. A block of rooms has been reserved at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate.  If you are making your reservations on line, please go to this link and enter the promo/corporate code MSRI123.  Our preferred rate is $129 per night for a Deluxe Queen/King, based on availability. Survey Link: https://docs.google.com/spreadsheet/viewform?formkey=dDIzQ18zQXdfQ1gwb0loUC1nOWxXZ3c6MA#gid=0
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
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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May 06, 2013
Monday
09:00 AM - 09:30 AM
  Welcome
09:30 AM - 10:20 AM
  Resolutions of dlt pairs
János Kollár (Princeton University)
10:30 AM - 11:00 AM
  Tea
11:00 AM - 11:50 AM
  Recent results on the grading of local cohomology modules
Gennady Lyubeznik (University of Minnesota Twin Cities)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 02:50 PM
  the core of an ideal
Claudia Polini (University of Notre Dame)
03:00 PM - 03:30 PM
  Tea
03:30 PM - 04:20 PM
  ACC for the log canonical threshold and termination of flips
James McKernan (University of California, San Diego)
May 07, 2013
Tuesday
09:00 AM - 09:50 AM
  Multiplicities of graded families of linear series
Steven Cutkosky (University of Missouri)
10:00 AM - 10:30 AM
  Tea
10:30 AM - 11:20 AM
  Ordinary varieties and the comparison between multiplier ideals and test ideals
Vasudevan Srinivas (Tata Institute of Fundamental Research)
11:30 AM - 12:20 PM
  F-singularities in families
Karl Schwede (University of Utah)
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 02:50 PM
  On the local uniformization of Abhyankar valuations using toric maps
Bernard Teissier (Institut de Mathématiques de Jussieu)
03:00 PM - 03:30 PM
  Tea
03:30 PM - 04:20 PM
  A local Lefschetz theorem
Bhargav Bhatt (Institute for Advanced Study)
04:30 PM - 06:20 PM
  Reception
May 08, 2013
Wednesday
09:00 AM - 09:50 AM
  The Nash problem on families of arcs
Tommaso de Fernex (University of Utah)
10:00 AM - 10:30 AM
  Tea
10:30 AM - 11:20 AM
  F-Signature and Relative Hilbert-Kunz Multiplicity
Kevin Tucker (University of Illinois at Chicago)
11:30 AM - 12:20 PM
  Some computations of Hilbert-Kunz functions
Vijaylaxmi Trivedi (Tata Institute of Fundamental Research)
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 02:25 PM
  F-pure thresholds of quasi-homogeneous polynomials
Emily Witt (University of Kansas)
02:00 PM - 02:25 PM
  Pluri-canonical maps in positive characteristic
Yuchen Zhang (University of Utah)
02:30 PM - 02:55 PM
  Degrees of relations, the Weak Lefschetz Property, and top socle degrees in positive characteristic
Adela Vraciu (University of South Carolina)
02:30 PM - 02:55 PM
  Generic linkage and regularity of algebraic varieties
Wenbo Niu (Purdue University)
03:00 PM - 03:30 PM
  Tea
03:30 PM - 03:55 PM
  Multiplier ideals and test ideals of complete intersection binomial ideals.
Takafumi Shibuta (Kyushu University)
03:30 PM - 03:55 PM
  Asymptotic test ideals and their possible applications to resolution problems
Angelica Benito (University of Michigan)
04:00 PM - 04:25 PM
  Frobenius splitting of orbit closures associated to type A quivers
Jenna Rajchgot (MSRI / Simons Laufer Mathematical Sciences Institute (SLMath))
04:00 PM - 04:25 PM
  Dual F-signature
Akiyoshi Sannai (Nagoya University)
May 09, 2013
Thursday
09:00 AM - 09:50 AM
  Globally F-regular and Frobenius split surfaces.
Shunsuke Takagi (University of Tokyo)
10:00 AM - 10:30 AM
  Tea
10:30 AM - 11:20 AM
  The index of a threefold canonical singularity
Masayuki Kawakita (Kyoto University)
11:30 AM - 12:20 PM
  Uniform Izumi's theorem
Charles Favre (École Polytechnique)
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 02:50 PM
  Singularities with respect to Mather-Jacobian discrepancies
Shihoko Ishii (Tsinghua University)
03:00 PM - 03:30 PM
  Tea
03:30 PM - 04:20 PM
  The monodromy conjecture for motivic and related zeta functions
Willem Veys (Katholieke Universiteit Leuven)
May 10, 2013
Friday
09:30 AM - 10:20 AM
  Mather multiplier ideals
Lawrence Ein (University of Illinois at Chicago)
10:30 AM - 11:00 AM
  Tea
11:00 AM - 11:50 AM
  Something is irrational in Hilbert-Kunz theory
Holger Brenner (Universität Osnabrück)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 02:50 PM
  The Singularities of the Moduli Spaces of Vector Bundles over Curves in characteristic p
Vikram Mehta (University of Bombay)
03:00 PM - 03:30 PM
  Tea
03:30 PM - 04:20 PM
  Stabilization of the Frobenius push-forward and the F-blowup sequence
Nobuo Hara (Tohoku University)