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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:The stack &\;#34\;Broken&\;#34\; and associa
tive algebras - Hiro Tanaka (Harvard University)
DTSTART;TZID=Europe/London:20181030T140000
DTEND;TZID=Europe/London:20181030T150000
UID:TALK113851AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/113851
DESCRIPTION: \;After reviewing some aspects of Morse theor
y\, I'\;ll talk about "Broken\," the moduli sta
ck of constant Morse trajectories (possibly broken
) on a point. Surprisingly\, this stack has the fo
llowing property: Factorizable sheaves on it are t
he same thing as (possibly non-unital) associative
algebras. We all know that having geometric descr
iptions of algebraic structures should buy us mile
age\; so what mileage does this property buy us? I
f time allows\, I'\;ll try to explain why this
theorem leads to a roadmap for constructing Morse
chain complexes\, and in fact\, for constructing t
he stable homotopy type of a compact manifold with
a Morse function. (That is\, this gives a differe
nt way to realize ideas of Cohen-Jones-Segal.) The
motivation is to construct a stable homotopy type
for Lagrangian Floer Theory--the latter is an imp
ortant invariant in symplectic geometry and mirror
symmetry. This is all joint work with Jacob Lurie
.
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:info@newton.ac.uk
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