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Workshop

Hot Topics: Perfectoid Spaces and their Applications February 17, 2014 - February 21, 2014
Registration Deadline: February 21, 2014 2 months ago
To apply for Funding you must register by: November 17, 2013 5 months ago
Series: Hot Topic
Location: MSRI: Simons Auditorium, Atrium
Organizers Sophie Morel (Princeton University), Peter Scholze (Universität Bonn), LEAD Richard Taylor (Institute for Advanced Study), Jared Weinstein (Boston University)
Speaker(s)

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Description

Since their introduction just two years ago, perfectoid spaces have played a crucial role in a number of striking advances in arithmetic algebraic geometry: the proof of Deligne's weight-monodromy conjecture for complete intersections in toric varieties; the development of p-adic Hodge theory for rigid analytic spaces;  a p-adic analogue of Riemann's classification of abelian varieties over the complex numbers; and the construction of Galois representations for torsion classes in the cohomology of many locally symmetric spaces (for instance arithmetic hyperbolic 3-manifolds). We will start the week with an exposition of the foundations of the theory of perfectoid spaces, with the aim of teaching novices to work with them. Then we will discuss their current and potential applications.

Please email 731@msri.org if you are interested in presenting a poster at this workshop.

Bibliography (PDF)

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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 preferred rates at the Rose Garden Inn, depending on room availability. 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 the MSRI rate on all room types available.

MSRI has preferred rates 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.

MSRI has preferred rates of $149 - $189 plus tax at the Hotel Shattuck Plaza, depending on room availability. Guests can either call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Inst. discount; or go to www.hotelshattuckplaza.com and click Book Now. Once on the reservation page, click “Promo/Corporate Code“ and input the code: msri.

MSRI has preferred rates of $110 - $140 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 “I am an individual traveler affiliated with MSRI”.

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

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Schedule
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Feb 17, 2014
Monday
09:00 AM - 09:15 AM
  Welcome
09:15 AM - 10:15 AM
  Overview
Peter Scholze (Universität Bonn)
10:15 AM - 10:45 AM
  Tea
10:45 AM - 11:45 AM
  Almost ring theory 1
Bhargav Bhatt (Institute for Advanced Study)
11:45 AM - 01:15 PM
  Lunch
01:15 PM - 02:15 PM
  Adic Spaces 1
Eugen Hellman (Universität Bonn)
02:15 PM - 02:30 PM
  Break
02:30 PM - 03:30 PM
  Almost ring theory 2: Perfectoid rings
Bhargav Bhatt (Institute for Advanced Study)
03:30 PM - 04:00 PM
  Tea
04:00 PM - 04:45 PM
  Question and Discussion Session
Feb 18, 2014
Tuesday
09:00 AM - 10:00 AM
  Adic Spaces 2: Perfectoid rings
Peter Scholze (Universität Bonn)
10:00 AM - 10:30 AM
  Tea
10:30 AM - 11:30 AM
  Introduction to p-adic comparison theorems
Jean Marc Fontaine (Université Paris-Sud (Orsay))
11:30 AM - 11:45 AM
  Break
11:45 AM - 12:45 PM
  Adic spaces 3
Peter Scholze (Universität Bonn)
12:45 PM - 02:30 PM
  Lunch
02:30 PM - 03:30 PM
  The weight-monodromy conjecture
Ana Caraiani (Princeton University)
03:30 PM - 04:00 PM
  Tea
04:00 PM - 05:00 PM
  Lubin-Tate spaces 1
Jared Weinstein (Boston University)
05:00 PM - 06:20 PM
  Reception
Feb 19, 2014
Wednesday
09:00 AM - 10:00 AM
  The Fargues-Fontaine curve
Laurent Fargues (Institut de Mathématiques de Jussieu (CNRS))
10:00 AM - 10:30 AM
  Tea
10:30 AM - 11:30 AM
  The Pro-etale site
Aise de Jong (Columbia University)
11:30 AM - 11:45 AM
  Break
11:45 AM - 12:45 PM
  Relative p-adic Hodge theory
Kiran Kedlaya (University of California, San Diego)
Feb 20, 2014
Thursday
09:00 AM - 10:00 AM
  p-adic Hodge theroy for rigid spaces 1
Wieslawa Niziol (cnrs, ens-lyon)
10:00 AM - 10:45 AM
  Tea
10:45 AM - 11:45 AM
  Lubin-Tate spaces 2
Jared Weinstein (Boston University)
11:45 AM - 01:15 PM
  Lunch
12:00 PM - 01:00 PM
  Poster Session
Arthur-César Le Bras (École Normale Supérieure)
01:15 PM - 02:15 PM
  Shimura varieties and perectoid spaces 1: completed cohomology
Matthew Emerton (University of Chicago)
02:15 PM - 02:30 PM
  Break
02:30 PM - 03:30 PM
  Future directions 1: formal Q_p vector spaces of slope >1
Peter Scholze (Universität Bonn)
03:30 PM - 04:00 PM
  Tea
04:00 PM - 04:45 PM
  Question and Discussion Session
Feb 21, 2014
Friday
09:00 AM - 10:00 AM
  p-adic Hodge theory for rigid spaces 2
Wieslawa Niziol (cnrs, ens-lyon)
10:00 AM - 10:45 AM
  Tea
10:45 AM - 11:45 AM
  Shimura varieties and perfectoid spaces 2
Mark Kisin (Harvard University)
11:45 AM - 01:15 PM
  Lunch
01:15 PM - 02:15 PM
  Shimura varieties and perfectoid spaces 3
Mark Kisin (Harvard University)
02:15 PM - 02:30 PM
  Break
02:30 PM - 03:30 PM
  Future directions 2: the local Langlands and equivariant sheaves on projective space
Peter Scholze (Universität Bonn)
03:30 PM - 04:00 PM
  Tea
04:00 PM - 04:45 PM
  Question and Discussion Session