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CATEGORIES:Lecture / Talk / Workshop
DESCRIPTION:Hiro Lee Tanaka\, Texas State University\n\nAbstract: One of th
e great applications of infinity-categories is the ability to compute local
izations without model categories. We apply this to prove a surprising resu
lt in symplectic geometry: A certain 1-category of symplectic manifolds (re
ally\, Liouville sectors) localizes to an infinity-category that computes t
he homotopy type of the correct geometric mapping spaces! Even better\, one
can construct a further localization that (conjecturally) allows for purel
y symplectic constructions of localizations of the stable homotopy category
. This is based on joint work with Oleg Lazarev and Zack Sylvan. If I have
time (which I will not)\, I hope to talk about applications and some intere
sting consequences of some of our techniques -- for example\, a proof that
stabilized manifolds are the same thing as spaces over BO\; that wrapped Fu
kaya categories are functorially sensitive to the homotopy type of embeddin
g spaces\; and that (geometric) flexibilization is a (categorical) localiza
tion.
DTEND:20230307T020000Z
DTSTAMP:20240910T184231Z
DTSTART:20230307T010000Z
GEO:34.022409;-118.291027
LOCATION:Kaprielian Hall (KAP)\, 145
SEQUENCE:0
SUMMARY:LA Joint Topology Seminar at USC: Universal properties in symplecti
c geometry
UID:tag:localist.com\,2008:EventInstance_42544977413326
URL:https://calendar.usc.edu/event/la_joint_topology_seminar_at_usc_univers
al_properties_in_symplectic_geometry
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