Paolo Perrone
@paolopmath.bsky.social
Mathematician & Math Teacher
Pinned
Paolo Perrone
@paolopmath.bsky.social
· Nov 7
My book is out!
www.worldscientific.com/worldscibook...
www.worldscientific.com/worldscibook...
Descent in Probability Theory: the first steps down
youtu.be/VG2RTE1R0BY?...
youtu.be/VG2RTE1R0BY?...
[Oxford Seminar] Paolo Perrone | Descent in Probability Theory: the first steps downward
YouTube video by Topos Institute
youtu.be
November 7, 2025 at 7:53 AM
Descent in Probability Theory: the first steps down
youtu.be/VG2RTE1R0BY?...
youtu.be/VG2RTE1R0BY?...
Anyone in Milan tomorrow?
November 5, 2025 at 12:40 PM
Anyone in Milan tomorrow?
"Independent States Are Orthogonal", a talk at GSI 2025 bridging probability and geometry.
youtu.be/mUPJEt3FeiU
youtu.be/mUPJEt3FeiU
Paolo Perrone - Independent States Are Orthogonal - GSI 2025
YouTube video by Paolo Perrone
youtu.be
November 5, 2025 at 10:40 AM
"Independent States Are Orthogonal", a talk at GSI 2025 bridging probability and geometry.
youtu.be/mUPJEt3FeiU
youtu.be/mUPJEt3FeiU
New introduction to Categorical Probability for Physicists, by Tomáš Gonda:
www.youtube.com/live/eVfFuIG...
www.youtube.com/live/eVfFuIG...
TOMAS GONDA: Introduction to Categorical Probability
YouTube video by IQOQI Vienna
www.youtube.com
September 23, 2025 at 3:01 PM
New introduction to Categorical Probability for Physicists, by Tomáš Gonda:
www.youtube.com/live/eVfFuIG...
www.youtube.com/live/eVfFuIG...
Great work by Areeb Shah-Mohammed on partial morphisms in Markov categories.
arxiv.org/abs/2509.05094
arxiv.org/abs/2509.05094
Partializations of Markov categories
The present work develops a construction of a CD category of partial kernels from a particular type of Markov category called a partializable Markov category. These are a generalization of earlier mod...
arxiv.org
September 9, 2025 at 10:26 AM
Great work by Areeb Shah-Mohammed on partial morphisms in Markov categories.
arxiv.org/abs/2509.05094
arxiv.org/abs/2509.05094
We should call it 'connecting the DOTS'.
August 15, 2025 at 7:57 PM
We should call it 'connecting the DOTS'.
A categorical definition of independence!
Here is a recording of the talk I gave at CT 2025, for anyone who might have missed it.
youtu.be/ls6zOX8L1eI
Here is a recording of the talk I gave at CT 2025, for anyone who might have missed it.
youtu.be/ls6zOX8L1eI
Categories of relations which compose independently - Paolo Perrone
YouTube video by Paolo Perrone
youtu.be
August 5, 2025 at 6:38 PM
A categorical definition of independence!
Here is a recording of the talk I gave at CT 2025, for anyone who might have missed it.
youtu.be/ls6zOX8L1eI
Here is a recording of the talk I gave at CT 2025, for anyone who might have missed it.
youtu.be/ls6zOX8L1eI
New paper out!
arxiv.org/abs/2508.01146
arxiv.org/abs/2508.01146
Dagger categories of relations: the equivalence of dilatory dagger categories and epi-regular independence categories
Several categories look like categories of relations, but do not fit the established theory of relations in regular categories. They include the category of surjective multivalued functions, the categ...
arxiv.org
August 5, 2025 at 7:23 AM
New paper out!
arxiv.org/abs/2508.01146
arxiv.org/abs/2508.01146
The document that started categorical probability, part of secret work from 1962, has reappeared, together with new commentaries of its author, Bill Lawvere.
lawverearchives.com/wp-content/u...
Thanks to Tobias Fritz and to the Lawvere Archives for the work.
lawverearchives.com/wp-content/u...
Thanks to Tobias Fritz and to the Lawvere Archives for the work.
lawverearchives.com
July 23, 2025 at 9:00 AM
The document that started categorical probability, part of secret work from 1962, has reappeared, together with new commentaries of its author, Bill Lawvere.
lawverearchives.com/wp-content/u...
Thanks to Tobias Fritz and to the Lawvere Archives for the work.
lawverearchives.com/wp-content/u...
Thanks to Tobias Fritz and to the Lawvere Archives for the work.
I'm excited to be in Bologna for the week!
(If anyone is here and wants to meet, write me an email.)
(If anyone is here and wants to meet, write me an email.)
June 16, 2025 at 7:44 AM
I'm excited to be in Bologna for the week!
(If anyone is here and wants to meet, write me an email.)
(If anyone is here and wants to meet, write me an email.)
Me, every time the EU "wants to attract researchers":
May 5, 2025 at 6:56 PM
Me, every time the EU "wants to attract researchers":
We start in 10 minutes!
May 2, 2025 at 8:50 AM
We start in 10 minutes!
What are point-free measurable spaces, and what is their quantum equivalent?
Great work by Tobias Fritz and Antonio Lorenzin.
arxiv.org/abs/2504.13708
Great work by Tobias Fritz and Antonio Lorenzin.
arxiv.org/abs/2504.13708
Categories of abstract and noncommutative measurable spaces
Gelfand duality is a fundamental result that justifies thinking of general unital $C^*$-algebras as noncommutative versions of compact Hausdorff spaces. Inspired by this perspective, we investigate wh...
arxiv.org
April 21, 2025 at 9:13 AM
What are point-free measurable spaces, and what is their quantum equivalent?
Great work by Tobias Fritz and Antonio Lorenzin.
arxiv.org/abs/2504.13708
Great work by Tobias Fritz and Antonio Lorenzin.
arxiv.org/abs/2504.13708
We finally have the strong law of large numbers in Markov categories.
arxiv.org/abs/2503.21576
arxiv.org/abs/2503.21576
Empirical Measures and Strong Laws of Large Numbers in Categorical Probability
The Glivenko-Cantelli theorem is a uniform version of the strong law of large numbers. It states that for every IID sequence of random variables, the empirical measure converges to the underlying dist...
arxiv.org
March 28, 2025 at 7:36 AM
We finally have the strong law of large numbers in Markov categories.
arxiv.org/abs/2503.21576
arxiv.org/abs/2503.21576
To all my UK-based mutual are into 'cybernetics', I very strongly recommend this exhibition in London.
www.tate.org.uk/whats-on/tat...
www.tate.org.uk/whats-on/tat...
Electric Dreams | Tate Modern
www.tate.org.uk
March 23, 2025 at 3:58 PM
To all my UK-based mutual are into 'cybernetics', I very strongly recommend this exhibition in London.
www.tate.org.uk/whats-on/tat...
www.tate.org.uk/whats-on/tat...
New great work by Dario Stein.
arxiv.org/abs/2503.02477
arxiv.org/abs/2503.02477
Random Variables, Conditional Independence and Categories of Abstract Sample Spaces
Two high-level "pictures" of probability theory have emerged: one that takes as central the notion of random variable, and one that focuses on distributions and probability channels (Markov kernels). ...
arxiv.org
March 5, 2025 at 8:57 AM
New great work by Dario Stein.
arxiv.org/abs/2503.02477
arxiv.org/abs/2503.02477
What do Beck-Chevalley monads have to do with conditional probability?
arxiv.org/abs/2502.14941
arxiv.org/abs/2502.14941
Categorical algebra of conditional probability
In the field of categorical probability, one uses concepts and techniques from category theory, such as monads and monoidal categories, to study the structures of probability and statistics. In this p...
arxiv.org
February 24, 2025 at 6:53 AM
What do Beck-Chevalley monads have to do with conditional probability?
arxiv.org/abs/2502.14941
arxiv.org/abs/2502.14941
Reposted by Paolo Perrone
If there was anybody competent in charge in Europe we would be passing emergency legislation this week so that starting next week we poach every scientist from the US who was previously funded by NSF, NIH etc. Oh well, we can dream.
January 28, 2025 at 12:24 PM
If there was anybody competent in charge in Europe we would be passing emergency legislation this week so that starting next week we poach every scientist from the US who was previously funded by NSF, NIH etc. Oh well, we can dream.
Never forget that you do can do natural gradient descent in Haskell!
github.com/alex404/goal
github.com/alex404/goal
GitHub - alex404/goal: The Geometric OptimizAtion Libraries
The Geometric OptimizAtion Libraries. Contribute to alex404/goal development by creating an account on GitHub.
github.com
January 23, 2025 at 8:14 PM
Never forget that you do can do natural gradient descent in Haskell!
github.com/alex404/goal
github.com/alex404/goal
Excited to be in Seattle for the JMM!
Besides ACT today and categorical probability on Saturday, which sessions are my fellow category theorists attending?
Besides ACT today and categorical probability on Saturday, which sessions are my fellow category theorists attending?
January 8, 2025 at 3:08 PM
Excited to be in Seattle for the JMM!
Besides ACT today and categorical probability on Saturday, which sessions are my fellow category theorists attending?
Besides ACT today and categorical probability on Saturday, which sessions are my fellow category theorists attending?
Here's a lecture at MIT on Markov categories, symmetries, and generative AI by Rob Cornish and myself.
youtu.be/ozN4zLEUCgs?...
#touchdesigner #streamdiffusion #bananas
youtu.be/ozN4zLEUCgs?...
#touchdesigner #streamdiffusion #bananas
ACT4ED Special Lecture - Paolo Perrone, Rob Cornish (Oxford): Markov Categories, Symmetries, & GenAI
YouTube video by Zardini Lab
youtu.be
November 27, 2024 at 8:55 PM
Here's a lecture at MIT on Markov categories, symmetries, and generative AI by Rob Cornish and myself.
youtu.be/ozN4zLEUCgs?...
#touchdesigner #streamdiffusion #bananas
youtu.be/ozN4zLEUCgs?...
#touchdesigner #streamdiffusion #bananas
New paper on Markov categories, proving Aldous-Hoover categorically, by Leihao Chen, Tobias Fritz, Tomáš Gonda, Andreas Klingler, Antonio Lorenzin.
arxiv.org/abs/2411.12840
arxiv.org/abs/2411.12840
The Aldous--Hoover Theorem in Categorical Probability
The Aldous-Hoover Theorem concerns an infinite matrix of random variables whose distribution is invariant under finite permutations of rows and columns. It states that, up to equality in distribution,...
arxiv.org
November 21, 2024 at 8:19 AM
New paper on Markov categories, proving Aldous-Hoover categorically, by Leihao Chen, Tobias Fritz, Tomáš Gonda, Andreas Klingler, Antonio Lorenzin.
arxiv.org/abs/2411.12840
arxiv.org/abs/2411.12840
The smartest thing the EU can do now is release a ton of funding for scientists, and relative visas. And I mean immediately.
November 12, 2024 at 1:47 PM
The smartest thing the EU can do now is release a ton of funding for scientists, and relative visas. And I mean immediately.
My book is out!
www.worldscientific.com/worldscibook...
www.worldscientific.com/worldscibook...
November 7, 2024 at 1:59 PM
My book is out!
www.worldscientific.com/worldscibook...
www.worldscientific.com/worldscibook...