Uploaded June 2024 | Updated September 2026, 2 weeks ago
Topos Institute Colloquium, 27th of June 2024.
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I will discuss topological data analysis (TDA), which uses ideas from topology to quantify the "shape" of data. I will focus in particular on persistent homology (PH), which one can use to find "holes" of different dimensions in data sets. I will briefly introduce these ideas and then discuss a series of examples of TDA of spatial systems. The examples that I'll discuss include voting data, the locations of polling sites, and the webs of spiders under the influence of various drugs.
Topos Institute Colloquium, 27th of June 2024.
———
I will discuss topological data analysis (TDA), which uses ideas from topology to quantify the "shape" of data. I will focus in particular on persistent homology (PH), which one can use to find "holes" of different dimensions in data sets. I will briefly introduce these ideas and then discuss a series of examples of TDA of spatial systems. The examples that I'll discuss include voting data, the locations of polling sites, and the webs of spiders under the influence of various drugs.
![[Oxford Seminar] David Jaz Myers | A modal proof of the nerve theorem](https://i.ytimg.com/vi/pKHjMXSfAX4/mqdefault.jpg "[Oxford Seminar] David Jaz Myers | A modal proof of the nerve theorem
Oxford Seminar, 24th of July 2025
Joint work with Mitchell Riley.
The nerve theorem is a classical result in homotopy theory,
usually attributed to Borsuk, which computes the homotopy type of a
(paracompact) topological space from a good open cover of it. An
open cover is good when finite intersections of opens in the cover
are contractible whenever they contain a point; the nerve of a good
open cover is the simplicial complex with a point for each open in the
cover, and an -simplex for each inhabited intersection of opens in the
cover. The nerve theorem states that the homotopy type of is the same
as the nerve of any good open cover of it.
In this talk, well prove the nerve theorem in the setting of modal
homotopy type theory. The key concepts in the nerve theorem — the
homotopy type of a space, the homotopy type presented by a simplicial
set, and even the Čech nerve itself — may all be understood as
modalities which act on simplicial, spatial homotopy types (that is,
simplicial stacks on a suitably topological site). Once we understand
the idea of modalities, well see that the nerve theorem is a
completely modal statement concerning the commutation of two sorts of
cohesion possible for types (in Lawveres sense): the combinatorial
cohesion of simplices, and the continuous cohesion of topology. As a
result, well actually be proving a nerve theorem for all spatial
stacks in a direct, conceptual way.")
![[DOTS Lectures] 10. LTL and specifications of behaviours](https://i.ytimg.com/vi/qpWD16mOwr0/mqdefault.jpg "[DOTS Lectures] 10. LTL and specifications of behaviours
*The paper referred to at the end was Temporal Landscapes: A Graphical Logic of Behavior by Brendan Fong, Alberto Speranzon and David I. Spivak.
This talk is part of a lecture series on the Double Operadic Theory of Systems (DOTS) presented by David Jaz Myers.
Some material from these lectures can be found in Davids book on categorical systems theory:
https://www.davidjaz.com/Papers/DynamicalBook.pdf")
![[Oxford Seminar] David Jaz Myers | Composing flavoured Petri nets](https://i.ytimg.com/vi/s793leHjc_4/mqdefault.jpg "[Oxford Seminar] David Jaz Myers | Composing flavoured Petri nets
Oxford seminar, 28th of August 2025
Abstract: Well describe a doctrine of various flavors of Petri nets in the double operadic theory of systems framework.")
![[Oxford Seminar] David Jaz Myers | Compositionality of Flavoured Petri Nets](https://i.ytimg.com/vi/sQW9KI9hdTI/mqdefault.jpg "[Oxford Seminar] David Jaz Myers | Compositionality of Flavoured Petri Nets
Oxford Seminar, 11th of September 2025
In this talk, we will see a natural notion of nesting composition for flavoured Petri nets: Petri nets whose places and transitions come with extra data determined by a symmetric monoidal double category and which determine the intended semantics of the Petri net.")
