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Workshop

Hot Topics: The Homological Conjectures March 12, 2018 - March 16, 2018
To apply for Funding you must register by: December 15, 2017 5 months ago
Parent Program: --
Series: Hot Topic, Hot Topic
Location: MSRI: Simons Auditorium
Organizers Bhargav Bhatt (University of Michigan), Srikanth Iyengar (University of Utah), Wieslawa Niziol (CNRS, Ecole Normale Superieure de Lyon), LEAD Anurag Singh (University of Utah)
Speaker(s)

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Description
The homological conjectures in commutative algebra are a network of conjectures that have generated a tremendous amount of activity in the last 50 years. They had largely been resolved for commutative rings that contain a field, but, with the exception of some low dimensional cases, several remained open in mixed characteristic --- until recently, when Yves André announced a proof of Hochster's Direct Summand Conjecture. The progress comes from systematically applying Scholze's theory of perfectoid spaces, which had already shown its value by solving formidable problems in number theory and representation theory. One of the goals of the workshop is to cover the ingredients going into the proofs of the Direct Summand Conjecture. Bibliography Group Photo
Keywords and Mathematics Subject Classification (MSC)
Tags/Keywords
  • Homological conjectures

  • perfectoid spaces

  • Cohen-Macaulay algebras

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification
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 has a 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. Click on "Promo/Corporate Code" at the top of the page and enter the code MSRI (this code is not case sensitive).

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 MSRI (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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Mar 12, 2018
Monday
09:45 AM - 10:00 AM
  Welcome
10:00 AM - 11:00 AM
  The homological conjectures: past, present, and future
Melvin Hochster (University of Michigan)
11:00 AM - 11:30 AM
  Break
11:30 AM - 12:30 PM
  Perfectoid fields
Hélène Esnault (Freie Universität Berlin)
12:30 PM - 02:30 PM
  Lunch
02:30 PM - 03:30 PM
  Almost mathematics and the homological conjectures
Paul Roberts (University of Utah)
03:30 PM - 04:00 PM
  Tea
04:00 PM - 05:00 PM
  Perfectoid rings
Wieslawa Niziol (CNRS, Ecole Normale Superieure de Lyon)
Mar 13, 2018
Tuesday
10:00 AM - 11:00 AM
  Adic spaces I
Brian Conrad (Stanford University)
11:00 AM - 11:30 AM
  Break
11:30 AM - 12:30 PM
  Adic spaces II
Brian Conrad (Stanford University)
12:30 PM - 02:30 PM
  Lunch
02:30 PM - 03:30 PM
  Perfectoid spaces I
Johan de Jong (Columbia University)
03:30 PM - 04:00 PM
  Tea
04:00 PM - 05:00 PM
  Perfectoid spaces II
Kestutis Cesnavicius (Centre National de la Recherche Scientifique (CNRS))
05:00 PM - 06:30 PM
  Reception
Mar 14, 2018
Wednesday
10:00 AM - 11:00 AM
  Almost purity
Yves Andre (Centre National de la Recherche Scientifique (CNRS))
11:00 AM - 11:30 AM
  Break
11:30 AM - 12:30 PM
  Complements on almost purity
Gerd Faltings (Max-Planck-Institut für Mathematik)
Mar 15, 2018
Thursday
10:00 AM - 11:00 AM
  Adjoining p-power roots of the discriminant
Judith Ludwig (Max-Planck-Institut für Mathematik)
11:00 AM - 11:30 AM
  Break
11:30 AM - 12:30 PM
  The Riemann extension theorem
Kiran Kedlaya (University of California, San Diego)
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  The direct summand conjecture and its derived variant
Bhargav Bhatt (University of Michigan)
03:00 PM - 03:30 PM
  Tea
03:30 PM - 05:00 PM
  The perfectoid Abhyankar lemma and big Cohen-Macaulay algebras
Yves Andre (Centre National de la Recherche Scientifique (CNRS))
Mar 16, 2018
Friday
10:00 AM - 11:00 AM
  Remarks on big Cohen-Macaulay algebras and on ramification over log-regular rings
Ofer Gabber (Institut des Hautes Études Scientifiques (IHES))
11:00 AM - 11:30 AM
  Break
11:30 AM - 12:30 PM
  Big Cohen-Macaulay modules, morphisms of perfect complexes, and intersection theorems
Luchezar Avramov (University of Nebraska)
12:30 PM - 02:30 PM
  Lunch
02:30 PM - 03:30 PM
  Perfectoid multiplier/test ideals and symbolic powers
Linquan Ma (University of Utah)
03:30 PM - 04:00 PM
  Tea
04:00 PM - 05:00 PM
  Singularities mod p, and singularities in mixed characteristic
Karl Schwede (University of Utah)