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Paolo Perrone (Jun 02 2020 at 15:18):Hello all! This is the thread related to Carmen Constantin's talk, "Topos theoretic perspective on entropy".
Zoom meeting:
https://mit.zoom.us/j/280120646
Meeting ID: 280 120 646
Youtube live stream:
https://youtu.be/_1nc6hZXgI4
eric brunner (Jun 04 2020 at 03:11):paolo, are there pre-talk reading recommendations? tia.
Paolo Perrone (Jun 04 2020 at 12:49):Hello. Not as far as I know. But in case the talk turns out to require significant previous knowledge, it will be recorded, so that we can do some reading and watch it again just in case :)
Paolo Perrone (Jun 04 2020 at 15:45):We start in 15 minutes!
Paolo Perrone (Jun 04 2020 at 15:59):1 minute!
Paolo Perrone (Jun 04 2020 at 16:04):The text that Carmen referred to is this one:
https://www.cambridge.org/core/books/an-invitation-to-applied-category-theory/D4C5E5C2B019B2F9B8CE9A4E9E84D6BC
http://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf
Paolo Perrone (Jun 04 2020 at 16:05):David Jaz Myers has added this reference as well:
https://marieetgonzalo.files.wordpress.com/2004/06/generic-figures.pdf
Paolo Perrone (Jun 04 2020 at 16:24):Here's the reference that Carmen is recommending:
https://arxiv.org/abs/0803.0417
Morgan Rogers (he/him) (Jun 04 2020 at 16:46):Darn I thought this was happening at 6pm where I am and now I've missed most of it. Looking forward to the youtube video..!
Paolo Perrone (Jun 04 2020 at 16:47):Morgan Rogers said:
Darn I thought this was happening at 6pm where I am and now I've missed most of it. Looking forward to the youtube video..!
try to connect to the live stream, and see if there's enough buffer so that you can watch the delayed video from the start.
Morgan Rogers (he/him) (Jun 04 2020 at 16:53):There is! Thank you so much.
Tomáš Gonda (Jun 04 2020 at 17:23):The presheaf approach to QM seems somewhat related to the approach that QBism takes - i.e., thinking of quantum data as a collection of predictions for (or, in the case of QBism, beliefs about) future experiments/measurements. Does anyone know about any more direct relation between the two formalisms?
Todd Trimble (Jun 04 2020 at 17:35):It was an interesting talk and I do find this approach to QM philosophically attractive, but unfortunately there were audio difficulties throughout the talk. Any ideas why and how to avoid them in the future?
Paolo Perrone (Jun 04 2020 at 17:41):Todd Trimble said:
It was an interesting talk and I do find this approach to QM philosophically attractive, but unfortunately there were audio difficulties throughout the talk. Any ideas why and how to avoid them in the future?
I think the connection was not optimal. The recorded video should hopefully be better.
Paolo Perrone (Jun 04 2020 at 17:41):Sorry about that, I hope the concepts were still understandable.
Morgan Rogers (he/him) (Jun 04 2020 at 17:47):@Carmen Constantin, are you aware of the work of @Emily Roff and @Tom Leinster on entropy of metric spaces? I'm curious how the enriched category notion of entropy that they employ compares with the entropy that one might get by taking the entropy you defined on an associated topos.
Morgan Rogers (he/him) (Jun 04 2020 at 17:49):I suppose one would need some grasp of the infinite dimensional/continuous state space case to say much with confidence, but I'll let you be the judge of whether it's just a case of common inspiration or not!
Juan Pablo Vigneaux (Jun 04 2020 at 18:02):Links posted during the talk:
A nice introductory textbook on presheaf toposes: https://marieetgonzalo.files.wordpress.com/2004/06/generic-figures.pdf
What is a Thing: https://arxiv.org/abs/0803.0417
Seven Sketches in Compositionality: https://arxiv.org/abs/1803.05316
Reconstruction of classical states from classical entropy (Sec. 2.3): https://arxiv.org/pdf/1907.04242.pdf
Lee Mondshein (Jun 04 2020 at 18:12):Thanks for the links!
Carmen Constantin (Jun 04 2020 at 18:21):@Morgan Rogers, thanks for the link to metric spaces entropy - I hadn’t seen it before, but it looks like there may well be connections
Emily Roff (Jun 04 2020 at 19:28):Thanks for the mention, @[Mod] Morgan Rogers ; it's reminded me that I was looking forward to this talk. Something got in the way today but I'll be watching the recording at the weekend.
Paolo Perrone (Jun 04 2020 at 20:29):Here's the recording!
https://youtu.be/fUr9Z7D1dTo
Paolo Perrone (Jun 08 2020 at 20:30):Hi all. The preprint related to this talk is out!
https://arxiv.org/abs/2006.03139