Fall 2012 MATH 276 001 LEC

Topics in Topology
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4NONELimit:0 Enrolled:0 Waitlist:0 Avail Seats:0 [on 11/02/12]
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Prerequisites: Consent of instructor.

Syllabus: There is a surprising amount of structure contained in the seemingly simple topic of curves on surfaces.  In particular, by measuring the
hyperbolic lengths of the curves, we are naturally led to the theory of cluster algebras, an intriguing recent family of recurrence
relations with strong integrality and positivity properties.

In this course, we will study the many avatars of the cluster algebra from surfaces, including the tropical variant (related to intersection
numbers), the algebraic variant (related to hyperbolic lengths), and the quantum variant (related to the Jones polynomial).  Along the way,
we will see many topics in the study of surfaces, including the W. Thurston--Nielsen classification of surface automorphisms and the
theory of measured laminations.


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