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CATEGORIES:Conferences/Seminars/Lectures
DESCRIPTION:Speaker: Melody Chan (Brown University)\n\nTitle: Configurat
ion spaces on graphs\, phylogenetic trees\, and moduli spaces of tropical c
urves\n\nAbstract: \n\nI will discuss joint work with Christin Bibby\, Nir
Gadish\, and Claudia Yun. The historical antecedents are in earlier work of
Billera-Holmes-Vogtmann around 2000 and others\, who study an interesting
space of metric trees on n labelled taxa. This is a space that is shellable
and whose top homology was calculated\, as an S_n-representation\, by Robi
nson-Whitehouse. These spaces have a reinterpretation as moduli of tropical
curves of genus 0. Other historical antecedents of our work are in the stu
dy of configuration spaces of n points on a graph\, whose topological invar
iants are quite interesting. For example\, Ko-Park proved that failure of p
lanarity of a graph can be detected by torsion in H_1 of its unordered conf
iguration space. \n\nThe work I will then describe concerns a genus g>0 ana
logue of the space of phylogenetic trees: the moduli space of tropical curv
es of genus g. Roughly speaking\, this space parametrizes n-marked graphs o
f first Betti number g. These spaces are no longer shellable for g>1\, and
their homology groups\, as S_n-representations\, are quite mysterious. I wi
ll explain how making precise connections to compactified configuration spa
ces on graphs made it possible for us to make calculations in Sage when g=2
in a range beyond what was previously accessible. These in turn produced n
ew calculations and conjectures concerning the rational cohomology of M_{2\
,n}. No tropical geometry prerequisites are assumed in this talk.
DTEND:20221116T221500Z
DTSTAMP:20240415T165301Z
DTSTART:20221116T211500Z
LOCATION:Harvard Science Center - 232\, One Oxford Street\, Cambridge\, MA
SEQUENCE:0
SUMMARY:MIT-Harvard-MSR Combinatorics Seminar
UID:tag:localist.com\,2008:EventInstance_41591214927063
URL:https://calendar.mit.edu/event/mit-harvard-msr_combinatorics_seminar_45
4
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