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Home » Hot Topics: Cluster algebras and wall-crossing

Workshop

Hot Topics: Cluster algebras and wall-crossing March 28, 2016 - April 01, 2016
To apply for Funding you must register by: January 01, 2016 over 3 years ago
Parent Program: --
Series: Hot Topic, Hot Topic
Location: MSRI: Simons Auditorium, Atrium
Organizers LEAD Mark Gross (University of Cambridge), Paul Hacking (University of Massachusetts, Amherst), Sean Keel (University of Texas, Austin), Lauren Williams (University of California, Berkeley)
Speaker(s)

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Description
Cluster algebras were introduced in 2001 by Fomin and Zelevinsky to capture the combinatorics of canonical bases and total positivity in semisimple Lie groups. Since then they have revealed a rich combinatorial and group-theoretic structure, and have had significant impact beyond these initial subjects, including string theory, algebraic geometry, and mirror symmetry. Recently Gross, Hacking, Keel and Kontsevich released a preprint introducing mirror symmetry techniques into the subject which resolved several long-standing conjectures, including the construction of canonical bases for cluster algebras and positivity of the Laurent phenomenon. This preprint reformulates the basic construction of cluster algebras in terms of scattering diagrams (or wall-crossing structures). This leads to the proofs of the conjectures and to new constructions of elements of cluster algebras. But fundamentally they provide a new tool for thinking about cluster algebras. The workshop will bring together many of the different users of cluster algebras to achieve a synthesis of these new techniques with many of the different aspects of the subject. There will be lecture series on the new techniques, and other lecture series on connections with Lie theory, quiver representation theory, mirror symmetry, string theory, and stability conditions. Bibliography (PDF) Group Photo  
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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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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Schedule, Notes/Handouts & Videos
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Mar 28, 2016
Monday
09:45 AM - 10:00 AM
  Welcome
10:00 AM - 11:00 AM
  SYZ mirror symmetry in the complement of a divisor and regular functions on the mirror
Denis Auroux (University of California, Berkeley)
11:00 AM - 11:30 AM
  Break
11:30 AM - 12:30 PM
  Cluster algebras and cluster varieties
Lauren Williams (University of California, Berkeley)
12:30 PM - 02:30 PM
  Lunch
02:30 PM - 03:30 PM
  Theta Functions for Log Calabi-Yau manifolds I -II
Sean Keel (University of Texas, Austin)
03:30 PM - 04:00 PM
  Tea
04:00 PM - 05:00 PM
  Scattering diagrams, broken lines and theta functions
Mark Gross (University of Cambridge)
Mar 29, 2016
Tuesday
10:00 AM - 11:00 AM
  Examples of cluster varieties and their scattering diagrams.
Paul Hacking (University of Massachusetts, Amherst)
11:00 AM - 11:30 AM
  Break
11:30 AM - 12:30 PM
  Scattering diagrams, broken lines and theta functions
Mark Gross (University of Cambridge)
12:00 PM - 02:30 PM
  Lunch
02:30 PM - 03:30 PM
  Theta Functions for Log Calabi-Yau manifolds I -II
Sean Keel (University of Texas, Austin)
03:30 PM - 04:00 PM
  Tea
04:00 PM - 05:00 PM
  Hitchin systems, spectral networks and noncommutative clusters
Andrew Neitzke (University of Texas, Austin)
05:00 PM - 06:20 PM
  Reception
Mar 30, 2016
Wednesday
10:00 AM - 11:00 AM
  Scattering diagrams from stability conditions
Tom Sutherland (Johannes Gutenberg-Universität Mainz)
11:00 AM - 11:30 AM
  Break
11:30 AM - 12:30 PM
  Donaldson-Thomas transformations for moduli spaces of G-local systems on surfaces
Linhui Shen (Northwestern University)
Mar 31, 2016
Thursday
10:00 AM - 11:00 AM
  Donaldson-Thomas transformations for moduli spaces of G-local systems on surfaces
Linhui Shen (Northwestern University)
11:00 AM - 11:30 AM
  Break
11:30 AM - 12:30 PM
  Mirror symmetry for homogeneous spaces
Clelia Pech (University of Kent at Canterbury)
12:30 PM - 02:30 PM
  Lunch
02:30 PM - 03:30 PM
  Cluster duality and mirror symmetry for the Grassmannian
Lauren Williams (University of California, Berkeley)
03:30 PM - 04:00 PM
  Tea
04:00 PM - 05:00 PM
  Cluster Algebras and Exact Lagrangian Surfaces
Harold Williams (University of Texas, Austin)
Apr 01, 2016
Friday
10:00 AM - 11:00 AM
  Wall structures in mirror symmetry
Bernd Siebert (Universität Hamburg)
11:00 AM - 11:30 AM
  Break
11:30 AM - 12:30 PM
  Mirror symmetry for homogeneous spaces
Clelia Pech (University of Kent at Canterbury)
12:30 PM - 02:30 PM
  Lunch
02:30 PM - 03:30 PM
  Generic bases are dual semicanonical bases for unipotent cells
Christof Geiss (UNAM - Universidad Nacional Autonoma de Mexico)
03:30 PM - 04:00 PM
  Tea
04:00 PM - 05:00 PM
  Stability conditions and cluster varieties
Tom Sutherland (Johannes Gutenberg-Universität Mainz)