BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Logic and Semantics Seminar (Computer Laboratory)
SUMMARY:A categorical view of conditional expectation - Pr
akash Panangaden\, McGill University and Universit
y of Edinburgh
DTSTART;TZID=Europe/London:20220225T140000
DTEND;TZID=Europe/London:20220225T150000
UID:TALK165307AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/165307
DESCRIPTION:*THIS TALK WILL BE IN SS03\, NOT FW26*\n\nThis tal
k is a fragment from a larger work on approximatin
g Markov processes. I will focus on a functorial
definition of conditional expectation without talk
ing about how it was used. We define categories o
f cones--which are abstract versions of the famili
ar cones in vector spaces--of measures and related
categories cones of L_p functions. We will state
a number of dualities and isomorphisms between t
hese categories. Then we will define conditional
expectation by exploiting these dualities: it will
turn out that we can define conditional expectati
on with respect to certain morphisms. These gener
alize the standard notion of conditioning with res
pect to a sub-sigma algebra. Why did I use the pl
ural? Because it turns out that there are two kin
ds of conditional expectation\, one of which looks
like a left adjoint (in the matrix sense not the
categorical sense) and the other looks like a righ
t adjoint. I will review concepts like image meas
ure\, Radon-Nikodym derivatives and the traditiona
l definition of conditional expectation. This is
joint work with Philippe Chaput\, Vincent Danos an
d Gordon Plotkin.
LOCATION:FW26
CONTACT:Jamie Vicary
END:VEVENT
END:VCALENDAR