## March 24, 2020

### ACT@UCR Seminar

#### Posted by John Baez

Coronavirus is forcing massive changes on the academic ecosystem, and here’s another:

We’re having a seminar on applied category theory at U. C. Riverside, organized by Joe Moeller and Christian Williams.

It will take place on Wednesdays at 5 pm UTC, which is 10 am in California or 1 pm on the east coast of the United States, or 6 pm in England. It will be held online via Zoom, here:

https://ucr.zoom.us/j/607160601

We will have discussions online here:

https://categorytheory.zulipchat.com/

The first two talks will be:

• Wednesday April 1st, John Baez: Structured cospans and double categories.

Abstract. One goal of applied category theory is to better understand networks appearing throughout science and engineering. Here we introduce “structured cospans” as a way to study networks with inputs and outputs. Given a functor $L \colon A \to X$, a structured cospan is a diagram in $X$ of the form $L(a) \to x \leftarrow L(b).$ If $A$ and $X$ have finite colimits and $L$ is a left adjoint, we obtain a symmetric monoidal category whose objects are those of $A$ and whose morphisms are certain equivalence classes of structured cospans. However, this arises from a more fundamental structure: a symmetric monoidal double category where the horizontal 1-cells are structured cospans, not equivalence classes thereof. We explain the mathematics and illustrate it with an example from chemistry.

• Wednesday April 8th, Prakash Panangaden: A categorical view of conditional expectation.

Abstract. This talk is a fragment 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 versions of the familiar cones in vector spaces — of measures and related categories cones of $L_p$ functions. We will state a number of dualities and isomorphisms between these categories. Then we will define conditional expectation by exploiting these dualities: it will turn out that we can define conditional expectation with respect to certain morphisms. These generalize 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 the matrix sense not the categorical sense) and the other looks like a right adjoint. I will review concepts like image measure, Radon-Nikodym derivatives and the traditional definition of conditional expectation. This is joint work with Philippe Chaput, Vincent Danos and Gordon Plotkin.

Here is some information provided by Zoom. There are lots of ways to attend, though the simplest for most of you will be going to

https://ucr.zoom.us/j/607160601

at the scheduled times.

Topic: ACT@UCR seminar

Time: Apr 1, 2020 10:00 AM Pacific Time (US and Canada)

Every 7 days, 10 occurrence(s)

• Apr 1, 2020 10:00 AM

• Apr 8, 2020 10:00 AM

• Apr 15, 2020 10:00 AM

• Apr 22, 2020 10:00 AM

• Apr 29, 2020 10:00 AM

• May 6, 2020 10:00 AM

• May 13, 2020 10:00 AM

• May 20, 2020 10:00 AM

• May 27, 2020 10:00 AM

• Jun 3, 2020 10:00 AM

Join Zoom Meeting: https://ucr.zoom.us/j/607160601

Meeting ID: 607 160 601

One tap mobile +16699006833,,607160601# US (San Jose)

+13462487799,,607160601# US (Houston)

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+1 346 248 7799 US (Houston)

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Meeting ID: 607 160 601

Join by SIP 607160601@zoomcrc.com

Join by H.323

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Meeting ID: 607 160 601

Posted at March 24, 2020 5:29 AM UTC

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### Re: ACT@UCR Seminar

Fantastic! I’m looking forward to it. And thank you for timing it so that it’s accessible to lots of us around the world.

The link to the seminar web page (https://sites.google.com/ucr.edu/actucr/) doesn’t work for me. When I click it, I get taken to a Google login page.

Posted by: Tom Leinster on March 24, 2020 12:49 PM | Permalink | Reply to this

### Michael

I get a 404.

Posted by: Mike Stay on March 24, 2020 4:43 PM | Permalink | Reply to this

### Re: ACT@UCR Seminar

I think this bug has been fixed now.

Posted by: John Baez on March 25, 2020 6:34 AM | Permalink | Reply to this

### Re: ACT@UCR Seminar

Yup, works for me now.

Posted by: Tom Leinster on March 25, 2020 11:54 AM | Permalink | Reply to this

### Re: ACT@UCR Seminar

The Zulip page requires an invitation; is there a way to make the page open to all visitors?

Posted by: David Jaz Myers on March 24, 2020 2:59 PM | Permalink | Reply to this

### Re: ACT@UCR Seminar

Posted by: Mike Stay on March 24, 2020 4:45 PM | Permalink | Reply to this

### Re: ACT@UCR Seminar

In case you haven’t already heard of it, Zoombombing is now a phenomenon that everyone should be aware of (and prepared to deal with) if hosting online events with public links.

Posted by: Mark Meckes on March 24, 2020 9:59 PM | Permalink | Reply to this

### Re: ACT@UCR Seminar

Thanks. I can make people register.

Posted by: John Baez on March 25, 2020 5:41 AM | Permalink | Reply to this

### Re: ACT@UCR Seminar

The first two talks will be:

• Wednesday April 1st, John Baez: Structured cospans and double categories.

Abstract. One goal of applied category theory is to better understand networks appearing throughout science and engineering. Here we introduce “structured cospans” as a way to study networks with inputs and outputs. Given a functor $L \colon A \to X$, a structured cospan is a diagram in $X$ of the form $L(a) \to x \leftarrow L(b).$ If $A$ and $X$ have finite colimits and $L$ is a left adjoint, we obtain a symmetric monoidal category whose objects are those of $A$ and whose morphisms are certain equivalence classes of structured cospans. However, this arises from a more fundamental structure: a symmetric monoidal double category where the horizontal 1-cells are structured cospans, not equivalence classes thereof. We explain the mathematics and illustrate it with an example from chemistry.

• Wednesday April 8th, Prakash Panangaden: A categorical view of conditional expectation.

Abstract. This talk is a fragment 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 versions of the familiar cones in vector spaces — of measures and related categories cones of $L_p$ functions. We will state a number of dualities and isomorphisms between these categories. Then we will define conditional expectation by exploiting these dualities: it will turn out that we can define conditional expectation with respect to certain morphisms. These generalize 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 the matrix sense not the categorical sense) and the other looks like a right adjoint. I will review concepts like image measure, Radon-Nikodym derivatives and the traditional definition of conditional expectation. This is joint work with Philippe Chaput, Vincent Danos and Gordon Plotkin.

Posted by: John Baez on March 26, 2020 1:23 AM | Permalink | Reply to this

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