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Home » Chip Firing and Tropical Curves

Summer Graduate School

Chip Firing and Tropical Curves July 25, 2016 - August 05, 2016
Parent Program: --
Location: MSRI: Simons Auditorium, Baker Board Room, Atrium
Organizers LEAD Matthew Baker (Georgia Institute of Technology), David Jensen (University of Kentucky), Sam Payne (Yale University)
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Description

Tropical geometry uses a combination of techniques from algebraic geometry, combinatorics, and convex polyhedral geometry to study degenerations of algebraic varieties; the simplest tropical objects are tropical curves, which one can think of as "shadows" of algebraic curves.  Linear equivalence of divisors on an abstract tropical curve is determined by a simple but rich combinatorial process called "chip firing", which was discovered independently in the discrete setting by physicists and graph theorists.  From a pedagogical point of view, one can view tropical curves as a combinatorial model for the highly analogous but more abstract theory of algebraic curves, but there is in fact much more to the story than this: one can use tropical curves and chip firing to prove theorems in algebraic geometry and number theory.  This field is relatively new, so participants will have the opportunity to start from scratch and still get a glimpse of the cutting edge in this active research area.

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

 

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Keywords and Mathematics Subject Classification (MSC)
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Secondary Mathematics Subject Classification
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Schedule, Notes/Handouts & Videos
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Jul 25, 2016
Monday
09:15 AM - 09:30 AM
  Welcome to MSRI
09:30 AM - 10:30 AM
  Lecture
Matthew Baker (Georgia Institute of Technology)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Lecture
Matthew Baker (Georgia Institute of Technology)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session
03:00 PM - 03:30 PM
  Tea
03:30 PM - 04:30 PM
  Problem Sets
Jul 26, 2016
Tuesday
09:30 AM - 10:30 AM
  Lecture
David Jensen (University of Kentucky)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Lecture
David Jensen (University of Kentucky)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session
03:00 PM - 03:30 PM
  Tea
03:30 PM - 04:30 PM
  Problem Sets
Jul 27, 2016
Wednesday
09:30 AM - 10:30 AM
  Lecture
Sam Payne (Yale University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Lecture
Sam Payne (Yale University)
11:30 AM - 02:00 PM
  BBQ at Tilden Park
02:00 PM - 03:00 PM
  TA Session
03:00 PM - 03:30 PM
  Tea
03:30 PM - 04:30 PM
  Problem Sets
Jul 28, 2016
Thursday
09:30 AM - 10:30 AM
  Lecture
Matthew Baker (Georgia Institute of Technology)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Lecture
Matthew Baker (Georgia Institute of Technology)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session
03:00 PM - 03:30 PM
  Tea
03:30 PM - 04:30 PM
  Problem Sets
Jul 29, 2016
Friday
09:30 AM - 10:30 AM
  Lecture
David Jensen (University of Kentucky)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Lecture
David Jensen (University of Kentucky)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session
03:30 PM - 04:30 PM
  Problem Sets
Aug 01, 2016
Monday
09:30 AM - 10:30 AM
  Lecture
Sam Payne (Yale University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Lecture
Sam Payne (Yale University)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session
03:30 PM - 04:30 PM
  Tea
03:30 PM - 04:30 PM
  Problem Sets
Aug 02, 2016
Tuesday
09:30 AM - 10:30 AM
  Lecture
Matthew Baker (Georgia Institute of Technology)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Lecture
Matthew Baker (Georgia Institute of Technology)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session
03:00 PM - 03:30 PM
  Tea
03:30 PM - 04:30 PM
  Problem Sets
Aug 03, 2016
Wednesday
09:30 AM - 10:30 AM
  Lecture
David Jensen (University of Kentucky)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Lecture
David Jensen (University of Kentucky)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session
03:00 PM - 03:30 PM
  Tea
03:30 PM - 04:30 PM
  Problem Sets
Aug 04, 2016
Thursday
09:30 AM - 10:30 AM
  Lecture
Sam Payne (Yale University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Lecture
Sam Payne (Yale University)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Lecture
Matthew Baker (Georgia Institute of Technology)
03:00 PM - 03:30 PM
  Tea
03:30 PM - 04:30 PM
  Problem Sets
Aug 05, 2016
Friday
09:30 AM - 10:30 AM
  Lecture
Yoav Len (Fields Institute for Research in Mathematical Sciences)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Lecture
Dhruv Ranganathan (Massachusetts Institute of Technology)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Lecture
David Jensen (University of Kentucky)
03:00 PM - 03:30 PM
  Tea
03:30 PM - 04:30 PM
  Lecture
Sam Payne (Yale University)