ACT@UCR Seminar

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 6 talks will be:

• 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: A → X, a structured cospan is a diagram in X of the form

L(a) → x ← 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 epidemiology.

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

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 Lp 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.

• April 15, Jules Hedges.

• April 22, Michael Shulman.

• May 6, Sarah Rovner-Frydman: Separation logic through a new lens.

• May 13, Tai-Danae Bradley.

• May 20, 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
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May 13, 2020 10:00 AM
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ACT

10 Responses to ACT@UCR Seminar

  1. Toby Bartels says:

    Starting next week, the UK is on Summer Time, so not UTC.

  2. Grant says:

    Hi John, It says I need an invitation to join the Zulip chat.

  3. John Baez says:

    Here is the April 8th talk:

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

    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 Lp 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.

  4. John Baez says:

    I’ve changed my talk a bit so it uses an example from epidemiology.

  5. John Baez says:

    More speakers:

    15 April: Jules Hedges

    22 April: Michael Shulman

    6 May: Sarah Rovner-Frydman: Separation Logic Through a New Lens

    13 May: Tai-Danae Bradley

    All this information can be found on our ACT@UCR webpage.

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