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SUMMARY:Dani Kaufman (University of Maryland)
DTSTART:20210420T150000Z
DTEND:20210420T160000Z
DTSTAMP:20260423T021132Z
UID:OCAS/27
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OCAS/27/">Mu
 tation Invariant Functions On Cluster Algebras</a>\nby Dani Kaufman (Unive
 rsity of Maryland) as part of Online Cluster Algebra Seminar (OCAS)\n\n\nA
 bstract\nExamples of functions of cluster variables which remain unchanged
  after mutation arise naturally when studying cluster algebras. They appea
 r as nontrivial elements of upper cluster algebras\, elements of a theta b
 asis\, trace functions\, cluster characters\, and Diophantine equations wh
 ose solutions are parameterized by a cluster algebra. Interestingly\, one 
 often finds that the same mutation invariant function can be interpreted i
 n several distinct ways\, but it is not immediately clear why this would b
 e.\n \nI will give a concise definition of a mutation invariant function i
 n terms of an action of the cluster modular group\, and give many more int
 eresting examples. I will also discuss a classification of invariants for 
 Dehn twists on surface cluster algebras\, and more generally for "cluster 
 Dehn twists" on mutation finite cluster algebras. This is the primary resu
 lt of my recent PhD thesis.  \n \nIt is my hope that this classification a
 llows us to begin to see why the same types functions appear in many disti
 nct guises\; each of these constructions (theta basis\, trace functions\, 
 cluster characters\, etc.) produce functions which are manifestly mutation
  invariant.\n
LOCATION:https://researchseminars.org/talk/OCAS/27/
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