Home /  Hot Topics: Perfectoid Spaces and their Applications

Workshop

Hot Topics: Perfectoid Spaces and their Applications February 17, 2014 - February 21, 2014
Registration Deadline: February 21, 2014 almost 11 years ago
To apply for Funding you must register by: November 17, 2013 about 11 years ago
Parent Program: --
Series: Hot Topic
Location: SLMath: Eisenbud Auditorium, Atrium
Organizers Sophie Morel (Princeton University), Peter Scholze (Universität Bonn), LEAD Richard Taylor (Stanford University), 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) Organized in partnership with:  
Keywords and Mathematics Subject Classification (MSC)
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 PhDs, 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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For information about recommended hotels for visits of under 30 days, visit Short-Term Housing. Questions? Contact coord@slmath.org.

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Schedule, Notes/Handouts & Videos
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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 de Paris XI)
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 (Imperial College, London)
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)
10:00 AM - 10:30 AM
  Tea
10:30 AM - 11:30 AM
  The Pro-etale site
Johan 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 (Institut de Mathématiques de Jussieu)
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 (Rheinische Friedrich-Wilhelms-Universität Bonn)
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 (Institut de Mathématiques de Jussieu)
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