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Summer Graduate School

Cluster Algebras and Cluster Combinatorics August 01, 2011 - August 12, 2011
Parent Program: Cluster Algebras
Organizers Gregg Musiker (University of Minnesota), Lauren Williams* (University of California, Berkeley)
Lecturer(s) No Lecturers Assigned Yet.
Speaker(s)

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Description

Cluster algebras are a class of combinatorially defined rings that provide a unifying structure for phenomena in a variety of algebraic and geometric contexts. A partial list of related areas includes quiver representations, statistical physics, and Teichmuller theory. This summer workshop for graduate students will focus on the combinatorial aspects of cluster algebras, thereby providing a concrete introduction to this rapidly-growing field. Besides providing background on the fundamentals of cluster theory, the summer school will cover complementary topics such as total positivity, the polyhedral geometry of cluster complexes, cluster algebras from surfaces, and connections to statistical physics. No prior knowledge of cluster algebras will be assumed.

The workshop will consist of four mini-courses with accompanying tutorials. Students will also have opportunities for further exploration using computer packages in Java and Sage.

List of Minicourses:

  1. Nathan Reading (North Carolina State University)
    "Cluster algebras and Coxeter combinatorics"
  2. Lauren Williams (University of California, Berkeley)
    "Total positivity"
  3. Gregg Musiker (University of Minnesota)
    "Cluster algebras from surfaces"
  4. Ralf Schiffler (University of Connecticut)
    "Cluster algebras and tilting theory"

Bibliography (PDF)

For eligibility and how to apply, see the Summer Graduate Workshop homepage

SAGE DEMO LINKS:

(software) = http://sage.lacim.uqam.ca/)  
(notes) = http://arxiv.org/abs/1102.4844


 

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Schedule
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Aug 01, 2011
Monday
09:25 AM - 09:40 AM
  Welcome to MSRI
09:40 AM - 11:10 AM
  Lecture
Lauren Williams (University of California, Berkeley)
11:10 AM - 11:30 AM
  Break
11:10 AM - 11:30 AM
  Coffee Break
11:30 AM - 12:30 PM
  Problem Session
11:30 AM - 12:30 PM
  Break
12:30 PM - 02:00 PM
  Lunch
12:30 PM - 02:00 PM
  Break
02:00 PM - 03:30 PM
  Lecture
Nathan Reading
02:00 PM - 03:30 PM
  Break
03:30 PM - 04:00 PM
  Tea
03:30 PM - 04:00 PM
  Break
04:00 PM - 05:00 PM
  SAGE (Computer) Demo
Aug 02, 2011
Tuesday
09:30 AM - 11:00 AM
  Lecture
Lauren Williams (University of California, Berkeley)
11:00 AM - 11:30 AM
  Coffee Break
11:00 AM - 11:30 AM
  Break
11:30 AM - 12:30 PM
  Break
11:30 AM - 12:30 PM
  Problem Session
12:30 PM - 02:00 PM
  Lunch
12:30 PM - 02:00 PM
  Break
02:00 PM - 03:30 PM
  Lecture
Nathan Reading
02:00 PM - 03:30 PM
  Break
03:30 PM - 04:00 PM
  Tea
03:30 PM - 04:00 PM
  Break
04:00 PM - 05:00 PM
  Problem Session
Aug 03, 2011
Wednesday
09:30 AM - 11:00 AM
  Lecture
Lauren Williams (University of California, Berkeley)
11:00 AM - 11:30 AM
  Coffee Break
11:00 AM - 02:00 PM
  Break
11:30 AM - 02:00 PM
  BBQ Lunch
11:30 AM - 03:30 PM
  Break
02:00 PM - 03:30 PM
  Lecture
Nathan Reading
02:00 PM - 05:00 PM
  Break
03:30 PM - 04:00 PM
  Tea
03:30 PM - 04:00 PM
  Break
04:00 PM - 05:00 PM
  Problem Session
05:00 PM - 06:00 PM
  Computer Office Hours
Aug 04, 2011
Thursday
09:30 AM - 11:00 AM
  Lecture
Lauren Williams (University of California, Berkeley)
11:00 AM - 11:30 AM
  Coffee Break
11:00 AM - 11:30 AM
  Break
11:30 AM - 12:30 PM
  Problem Session
11:30 AM - 12:30 PM
  Break
12:30 PM - 02:00 PM
  Lunch
12:30 PM - 02:00 PM
  Break
02:00 PM - 03:30 PM
  Lecture
Nathan Reading
02:00 PM - 03:30 PM
  Break
03:30 PM - 04:00 PM
  Tea
03:30 PM - 04:00 PM
  Break
04:00 PM - 05:00 PM
  Problem Session
Aug 05, 2011
Friday
09:30 AM - 11:00 AM
  Lecture
Lauren Williams (University of California, Berkeley)
11:00 AM - 11:30 AM
  Coffee Break
11:00 AM - 11:30 AM
  Break
11:30 AM - 12:30 PM
  Problem Session
11:30 AM - 12:30 PM
  Break
12:30 PM - 02:00 PM
  Lunch
12:30 PM - 02:00 PM
  Break
02:00 PM - 03:30 PM
  Lecture
Nathan Reading
02:00 PM - 03:30 PM
  Break
03:30 PM - 04:00 PM
  Tea
03:30 PM - 04:00 PM
  Break
04:00 PM - 05:00 PM
  Problem Session
Aug 08, 2011
Monday
09:30 AM - 11:00 AM
  Lecture
Ralf Schiffler
11:00 AM - 11:30 AM
  Coffee Break
11:00 AM - 11:30 AM
  Break
11:30 AM - 12:30 PM
  Problem Session
11:30 AM - 12:30 PM
  Break
12:30 PM - 02:00 PM
  Lunch
12:30 PM - 02:00 PM
  Break
02:00 PM - 03:30 PM
  Lecture
Gregg Musiker (University of Minnesota Twin Cities)
02:00 PM - 03:30 PM
  Break
03:30 PM - 04:00 PM
  Tea
03:30 PM - 04:00 PM
  Break
04:00 PM - 05:00 PM
  Problem Session
Aug 09, 2011
Tuesday
09:30 AM - 11:00 AM
  Lecture
Ralf Schiffler
11:00 AM - 11:30 AM
  Coffee Break
11:00 AM - 11:30 AM
  Break
11:30 AM - 12:30 PM
  Problem Session
11:30 AM - 12:30 PM
  Break
12:30 PM - 02:00 PM
  Lunch
12:30 PM - 02:00 PM
  Break
02:00 PM - 03:30 PM
  Lecture
Gregg Musiker (University of Minnesota Twin Cities)
02:00 PM - 03:30 PM
  Break
03:30 PM - 04:00 PM
  Tea
03:30 PM - 04:00 PM
  Break
04:00 PM - 05:00 PM
  Problem Session
Aug 10, 2011
Wednesday
09:30 AM - 11:00 AM
  Lecture
Ralf Schiffler
11:00 AM - 11:30 AM
  Coffee Break
11:00 AM - 11:30 AM
  Break
11:30 AM - 12:30 PM
  SAGE (Computer) Demo
11:30 AM - 12:30 PM
  Break
12:30 PM - 02:00 PM
  Lunch
12:30 PM - 02:00 PM
  Break
02:00 PM - 03:30 PM
  Lecture
Gregg Musiker (University of Minnesota Twin Cities)
02:00 PM - 03:30 PM
  Break
03:30 PM - 04:00 PM
  Tea
03:30 PM - 04:00 PM
  Break
04:00 PM - 05:00 PM
  Problem Session
Aug 11, 2011
Thursday
09:30 AM - 11:00 AM
  Lecture
Ralf Schiffler
11:00 AM - 11:30 AM
  Coffee Break
11:00 AM - 11:30 AM
  Break
11:30 AM - 12:30 PM
  Problem Session
11:30 AM - 12:30 PM
  Break
12:30 PM - 02:00 PM
  Lunch
12:30 PM - 02:00 PM
  Break
02:00 PM - 03:30 PM
  Lecture
Gregg Musiker (University of Minnesota Twin Cities)
02:00 PM - 03:30 PM
  Break
03:30 PM - 04:00 PM
  Tea
03:30 PM - 04:00 PM
  Break
04:00 PM - 05:00 PM
  Problem Session
Aug 12, 2011
Friday
09:30 AM - 11:00 AM
  Lecture
Ralf Schiffler
11:00 AM - 11:30 AM
  Coffee Break
11:00 AM - 11:30 AM
  Break
11:30 AM - 12:30 PM
  Problem Session
11:30 AM - 12:30 PM
  Break
12:30 PM - 02:00 PM
  Lunch
12:30 PM - 02:00 PM
  Break
02:00 PM - 03:30 PM
  Lecture
Gregg Musiker (University of Minnesota Twin Cities)
02:00 PM - 03:30 PM
  Break
03:30 PM - 04:00 PM
  Tea
03:30 PM - 04:00 PM
  Break
04:00 PM - 05:00 PM
  Future Topics