[Alta-Logic] Geoff Cruttwell's Talk on Thursday, next week!

[Jonathan Gallagher]

Dear Peripatetic Seminar,

Details for Geoff Cruttwell's talk next week are below.

*Speaker: *Geoff Cruttwell

*Location: MS 452*, Thursday, *September 12* @ *12:30--2:30 pm*

*Title*: Vector fields and flows, categorically



*Abstract*: In this talk we’ll investigate how to define vector fields and
their flows in a tangent category, and how to prove a result about
commutation of vector fields and flows in this setting.  In the first half
of the talk, we’ll introduce the notion of a “curve object” in a tangent
category: an object which “uniquely solves ordinary differential equations
in the tangent category”.    In the second half of the talk, we’ll see how
considering “vector fields and flows in the tangent categories of vector
fields and flows” leads to a new proof of the commutation theorem for
vector fields and flows (Proposition 18.5 in Lee’s “Introduction to Smooth
Manifolds”).



*Bio*: Geoff is an Associate Professor at Mount Allison University in
Sackville, NB.  His general interest is category theory.  He is currently
investigating how to generalize as much of differential geometry as
possible to the setting of tangent categories.  Geoff received his PhD at
Dalhousie University in 2009 under the supervision of Richard Wood, and
subsequently did postdoctoral research at the University of Calgary
(supervised by Robin Cockett) and the University of Ottawa (supervised by
Rick Blute) before taking up his current position at Mount Allison.


- Jonathan
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