BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:A categorical view of conditional expectation - Prakash Panangaden
 \, McGill University and University of Edinburgh
DTSTART:20220225T140000Z
DTEND:20220225T150000Z
UID:TALK165307@talks.cam.ac.uk
CONTACT:Jamie Vicary
DESCRIPTION:*THIS TALK WILL BE IN SS03\, NOT FW26*\n\nThis talk is a fragm
 ent from a larger work on approximating Markov processes.  I will focus on
  a functorial definition of conditional expectation without talking about 
 how it was used.  We define categories of cones--which are abstract versio
 ns of the familiar cones in vector spaces--of measures and related categor
 ies cones of L_p functions.  We will state a number of dualities and isomo
 rphisms  between these categories.  Then we will define conditional expect
 ation by exploiting these dualities: it will turn out that we can define c
 onditional expectation with respect to certain morphisms.  These generaliz
 e the standard notion of conditioning with respect to a sub-sigma algebra.
   Why did I use the plural?  Because it turns out that there are two kinds
  of conditional expectation\, one of which looks like a left adjoint (in t
 he matrix sense not the categorical sense) and the other looks like a righ
 t adjoint.  I will review concepts like image measure\, Radon-Nikodym deri
 vatives and the traditional definition of conditional expectation.  This i
 s joint work with Philippe Chaput\, Vincent Danos and Gordon Plotkin.
LOCATION:FW26
END:VEVENT
END:VCALENDAR