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SUMMARY:Claudia Yun (Brown)
DTSTART:20211023T153000Z
DTEND:20211023T155000Z
DTSTAMP:20260423T004754Z
UID:AGNES/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AGNES/4/">Ho
 mology representations of compactified configurations on graphs</a>\nby Cl
 audia Yun (Brown) as part of Algebraic Geometry NorthEastern Series (AGNES
 )\n\n\nAbstract\nThe $n$-th ordered configuration space of a graph paramet
 rizes ways of placing $n$ distinct and labelled particles on that graph. T
 he homology of the one-point compactification of such configuration space 
 is equipped with commuting actions of a symmetric group and the outer auto
 morphism group of a free group. We give a cellular decomposition of these 
 configuration spaces on which the actions are realized cellularly and thus
  construct an efficient free resolution for their homology representations
 . Using the Peter-Weyl Theorem for symmetric groups\, we consider each irr
 educible $S_n$-representation individually\, vastly simplifying the calcul
 ation of these homology representations from the free resolution. As our m
 ain application\, we obtain computer calculations of the top weight ration
 al cohomology of the moduli spaces $\\mathcal{M}_{2\,n}$\, equivalently th
 e rational homology of the tropical moduli spaces $\\Delta_{2\,n}$\, as a 
 representation of $S_n$ acting by permuting point labels for all $n\\leq 1
 0$. This is joint work with Christin Bibby\, Melody Chan\, and Nir Gadish.
 \n
LOCATION:https://researchseminars.org/talk/AGNES/4/
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