UNAM, the National Autonomous University of Mexico is having an online category theory seminar on Wednesdays at 18:00 UTC (11 am Pacific Time). The talks will appear in streaming video, and they will be recorded. (See below for where.)
I don't have a full schedule of talks, but I'm giving the first talk, and my student @Joe Moeller is giving the second.
- Speaker: John Baez
- Time: Wednesday October 7th, 18:00 UTC
- Title: Fock space techniques for stochastic physics
- Abstract: Some ideas from quantum theory are beginning to percolate back to classical probability theory. For example, the master equation for a chemical reaction network---also known as a stochastic Petri net---describes particle interactions in a stochastic rather than quantum way. If we look at this equation from the perspective of quantum theory, this formalism turns out to involve creation and annihilation operators, coherent states and other well-known ideas — but with a few big differences.
- Talk slides available here: https://math.ucr.edu/home/baez/networks_oxford/Fock_space.pdf
- Speaker: Joe Moeller
- Time: Wednesday October 14th, 18:00 UTC
- Title: Network models
- Abstract: Networks can be combined in various ways, such as overlaying one on top of another or setting two side by side. We introduce 'network models' to encode these ways of combining networks. Different network models describe different kinds of networks. We show that each network model gives rise to an operad, whose operations are ways of assembling a network of the given kind from smaller parts. Such operads, and their algebras, can serve as tools for designing networks. Technically, a network model is a lax symmetric monoidal functor from the free symmetric monoidal category on some set to Cat, and the construction of the corresponding operad proceeds via a symmetric monoidal version of the Grothendieck construction.
- You can see the paper this talk is based on, and further discussion, here:
https://johncarlosbaez.wordpress.com/2017/10/31/complex-adaptive-systems-part-6/
Joe Moeller's talk "Network Models" will appear live on Wednesday October 14th, 18:00 UTC here:
https://www.youtube.com/Pa96YVgazQk
- Title: Network Models
- Abstract: Networks can be combined in various ways, such as overlaying one on top of another or setting two side by side. We introduce 'network models' to encode these ways of combining networks. Different network models describe different kinds of networks. We show that each network model gives rise to an operad, whose operations are ways of assembling a network of the given kind from smaller parts. Such operads, and their algebras, can serve as tools for designing networks. Technically, a network model is a lax symmetric monoidal functor from the free symmetric monoidal category on some set to Cat, and the construction of the corresponding operad proceeds via a symmetric monoidal version of the Grothendieck construction.
- You can see the paper this talk is based on, and further discussion, here:
https://johncarlosbaez.wordpress.com/2017/10/31/complex-adaptive-systems-part-6/
That link's broken - I think it should be https://johncarlosbaez.wordpress.com/2020/10/07/network-models/
Actually this one is better:
https://johncarlosbaez.wordpress.com/2017/10/31/complex-adaptive-systems-part-6/
Thanks, though! The link I originally gave was certainly broken.
Here's the next talk at the UNAM category seminar:
- Speaker: Jade Master
- Time: Wednesday October 21st at 18:00 UTC (11 am Pacific Time)
- Title: Open Petri nets and their categories of processes
- Abstract: In this talk we will discuss Petri nets from a categorical perspective. A Petri net freely generates a symmetric monoidal category whose morphisms represent its executions. We will discuss how to make Petri nets 'open'---i.e., equip them with input and output boundaries where resources can flow in and out. Open Petri nets freely generate open symmetric monoidal categories: symmetric monoidal categories which can be glued together along a shared boundary. The mapping from open Petri nets to their open symmetric monoidal categories is functorial and this gives a compositional framework for reasoning about the executions of Petri nets.
You can see the talk live, and also recorded later on, by going here and poking around:
https://www.youtube.com/channel/UCAt6kc74uY03ZGcNDb6VGAg
You can read more about this work here:
You can see Jade's slides for a related talk here:
- Title: Open Petri nets
- Slides: http://math.ucr/edu/home/baez/master_QPL2019.pdf
- Abstract: The reachability semantics for Petri nets can be studied using open Petri nets. For us an 'open' Petri net is one with certain places designated as inputs and outputs via a cospan of sets. We can compose open Petri nets by gluing the outputs of one to the inputs of another. Open Petri nets can be treated as morphisms of a category Open(Petri), which becomes symmetric monoidal under disjoint union. However, since the composite of open Petri nets is defined only up to isomorphism, it is better to treat them as morphisms of a symmetric monoidal double category Open(Petri). Various choices of semantics for open Petri nets can be described using symmetric monoidal double functors out of Open(Petri). Here we describe the reachability semantics, which assigns to each open Petri net the relation saying which markings of the outputs can be obtained from a given marking of the inputs via a sequence of transitions. We show this semantics gives a symmetric monoidal lax double functor from Open(Petri) to the double category of relations. A key step in the proof is to treat Petri nets as presentations of symmetric monoidal categories; for this we use the work of Meseguer, Montanari, Sassone and others.
When do the videos generally get posted? I missed @Jade Master 's talk
You didn't miss Jade Master's talk yet - it's on Wednesday October 21st. But if you do, the UNAM videos get posted on YouTube, and Jade's will eventually appear here:
https://www.youtube.com/watch?v=evz0QgPjbGQ&feature=youtu.be
Here's the talk information:
- Speaker: Jade Master
- Time: Wednesday October 21st at 18:00 UTC (11 am Pacific Time)
- Title: Open Petri nets and their categories of processes
- Abstract: In this talk we will discuss Petri nets from a categorical perspective. A Petri net freely generates a symmetric monoidal category whose morphisms represent its executions. We will discuss how to make Petri nets 'open'---i.e., equip them with input and output boundaries where resources can flow in and out. Open Petri nets freely generate open symmetric monoidal categories: symmetric monoidal categories which can be glued together along a shared boundary. The mapping from open Petri nets to their open symmetric monoidal categories is functorial and this gives a compositional framework for reasoning about the executions of Petri nets.
You can read more about this work here:
You can see Jade's slides for a related talk here:
- Title: Open Petri nets
- Slides: http://math.ucr/edu/home/baez/master_QPL2019.pdf
- Abstract: The reachability semantics for Petri nets can be studied using open Petri nets. For us an 'open' Petri net is one with certain places designated as inputs and outputs via a cospan of sets. We can compose open Petri nets by gluing the outputs of one to the inputs of another. Open Petri nets can be treated as morphisms of a category Open(Petri), which becomes symmetric monoidal under disjoint union. However, since the composite of open Petri nets is defined only up to isomorphism, it is better to treat them as morphisms of a symmetric monoidal double category Open(Petri). Various choices of semantics for open Petri nets can be described using symmetric monoidal double functors out of Open(Petri). Here we describe the reachability semantics, which assigns to each open Petri net the relation saying which markings of the outputs can be obtained from a given marking of the inputs via a sequence of transitions. We show this semantics gives a symmetric monoidal lax double functor from Open(Petri) to the double category of relations. A key step in the proof is to treat Petri nets as presentations of symmetric monoidal categories; for this we use the work of Meseguer, Montanari, Sassone and others.
I came to this topic to ask if these are posted somewhere, and the message right above says yes. It would be nice if someone could post the link @Paolo Perrone 's talk here once it has been uploaded to youtube.
It looks like the UNAM category seminar talks eventually appear here on YouTube.
The most recent talk posted there is currently David Spivak's talk on February 17th.
Jacques Carette said:
I came to this topic to ask if these are posted somewhere, and the message right above says yes. It would be nice if someone could post the link Paolo Perrone 's talk here once it has been uploaded to youtube.
@Jacques Carette Hi! The talk is here: https://www.youtube.com/watch?v=ynxfrlqr4I0
John Baez (Oct 02 2020 at 20:49):
