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Universal properties in symplectic geometry
Geometry/Topology| Speaker: | Hiro Tanaka, Texas State University |
| Location: | 3106 MSB |
| Start time: | Thu, Mar 2 2023, 1:10PM |
Description
One
of the great applications of infinity-categories is the ability to
compute localizations without model categories. We apply this to prove a
surprising result in symplectic geometry: A certain 1-category of
symplectic manifolds (really, Liouville sectors) localizes to an
infinity-category that computes the homotopy type of the correct
geometric mapping spaces! Even better, one can construct a further
localization that (conjecturally) allows for purely 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
interesting consequences of some of our techniques -- for example, a
proof that stabilized manifolds are the same thing as spaces over BO;
that wrapped Fukaya categories are functorially sensitive to the
homotopy type of embedding spaces; and that (geometric) flexibilization
is a (categorical) localization.