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CATEGORIES:Geometry and Mathematical Physics seminar
SUMMARY:Witten conjecture for Mumford's kappa classes - Re
nzo Cavalieri (Colorado State)
DTSTART:20190529T123000Z
DTEND:20190529T133000Z
UID:TALK3703AT
URL:/talk/index/3703
DESCRIPTION:Kappa classes were introduced by Mumford\, as a to
ol to explore the intersection theory of the modul
i space of curves. Iterated use of the projection
formula shows there is a close connection between
the intersection theory of kappa classes on the mo
duli space of unpointed curves\, and the intersect
ion theory of psi classes on all moduli spaces. In
terms of generating functions\, we show that the
potential for kappa classes is related to the Grom
ov-Witten potential of a point via a change of var
iables essentially given by complete symmetric pol
ynomials\, rediscovering a theorem of Manin and Zo
kgraf from '99. Surprisingly\, the starting point
of our story is a combinatorial formula that relat
es intersections of kappa classes and psi classes
via a graph theoretic algorithm (the relevant grap
hs being dual graphs to stable curves). Further\,
this story is part of a large wall-crossing pictur
e for the intersection theory of Hassett spaces\,
a family of birational models of the moduli space
of curves.\nThis is joint work with Vance Blankers
(arXiv:1810.11443) .
LOCATION:Watson Building (Mathematics\, R15 on map) Lecture
Room C
CONTACT:Tyler Kelly
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