Posts by Simon Willerton

Research Fellowships in Representation Theory and/or Low Dimensional Topology at Leeds (Jun 19, 2023)
Apply for a job in Leeds.
Metric Spaces as Enriched Categories II (May 3, 2023)
See the definition of enriched category and marvel at how metric spaces can be treated as enriched categories.
Metric Spaces as Enriched Categories I (Apr 17, 2023)
Read about how we don’t always want our hom-sets in category theory to be sets!
Concepts and Profunctor Nuclei (Feb 8, 2022)
Read about one of the presentations at the 2021 Applied Category Theory Adjoint School.
Optimal Transport and Enriched Categories IV: Examples of Kan-type Centres (Jan 7, 2022)
See the centres of some enriched adjunctions.
Why Aren't You Making Math(s) Videos? (Aug 7, 2021)
Over at 3Blue1Brown Grant Sanderson is asking the provocative question “Why aren’t you making math videos?” Certainly for many of us there are reasons which include things such as lack of time or energy. However, if you have time,…
Optimal Transport and Enriched Categories III: Duality Within Pricing (Aug 7, 2021)
Learn how conjugation between optimal prices comes from an enriched adjunction.
Optimal Transport and Enriched Categories II (Jun 19, 2021)
Read about how the dual transport problem arises from general linear programming duality (and how that arises from general Lagrangian duality).
Optimal Transport and Enriched Categories I (Jun 6, 2021)
Read about the optimal transport problem and its dual.
Stellenbosch is Hiring (Nov 18, 2020)
Guest post by Bruce Bartlett The sunny campus of Stellenbosch University in South Africa is hiring! We’re looking to make a permanent appointment of a mathematician at Lecturer or Senior Lecturer level. Job description and application webpage. Deadline 30…
Online Magnitude Talk by Mark Meckes (May 30, 2020)
See Mark Meckes give a online talk on June 6th
Chair in Pure Mathematics at Sheffield (Nov 19, 2019)
Apply for a professorship in Sheffield!
Motion Group Workshop in Leeds (Apr 1, 2019)
Read about a meeting in Leeds on loop braid groups.
The Kantorovich Monad (Mar 24, 2019)
Read Paolo Perrone’s introduction to a probability monad on a category of metric spaces
On the Magnitude Function of Domains in Euclidean Space, IV: Questions and Examples from a Geometric Analyst's Perspective (b) (Jan 27, 2019)
See questions in geometry and analysis arising from a geometric analyst’s perspective
On the Magnitude Function of Domains in Euclidean Space, III: Questions and Examples from a Geometric Analyst's Perspective (a) (Jan 23, 2019)
See questions in topology arising from a geometric analyst’s perspective
The Passing of Michael Atiyah and Andrew Ranicki (Jan 21, 2019)
Read about two Edinburgh topologists.
More Papers on Magnitude (Nov 2, 2018)
Look at a list of recent papers on magnitude homology and cohomology.
Research Fellowship at the University of Leeds (May 14, 2018)
Apply for a research fellowship in Leeds
Torsion: Graph Magnitude Homology Meets Combinatorial Topology (Apr 11, 2018)
Work through an example of torsion in magnitude homology based on the work of Kaneta and Yoshinaga.
Magnitude Homology Reading Seminar, II (Apr 5, 2018)
Read the second installment of the reading seminar notes.
On the Magnitude Function of Domains in Euclidean Space, II (Mar 25, 2018)
Continue reading about the work of Gimperlein and Goffeng
Magnitude Homology Reading Seminar, I (Mar 19, 2018)
See the first in a Sheffield seminar series on the Leinster-Shulman paper on magnitude homology.
On the Magnitude Function of Domains in Euclidean Space, I (Jan 10, 2018)
Read about a recent paper of Gimperlein and Goffeng.
SageMath and 3D Models in Webpages (Dec 19, 2017)
Emded 3d models of surfaces into your websites using SageMath.
Lattice Paths and Continued Fractions II (Sep 22, 2017)
Contemplate further continued fractions.
Lattice Paths and Continued Fractions I (Sep 18, 2017)
Feel flabbergasted by Flajolet’s Fundamental Lemma
Schröder Paths and Reverse Bessel Polynomials (Aug 28, 2017)
See how the reverse Bessel polynomials (which make an appearance in the magnitude of balls) have a combinatorial interpretation.
Instantaneous Dimension of Finite Metric Spaces via Magnitude and Spread (Aug 5, 2017)
Download a talk on instantaneous dimension.
Barceló and Carbery on the Magnitude of Odd Balls (Sep 9, 2016)
Read about Barcel'o and Carbery’s calculation of the magnitude of odd dimensional balls, utilizing the potential theory developed by Meckes.
Feynman's Fabulous Formula (Jun 29, 2015)
Bruce describes a graph-theoretic result
Categorifying the Magnitude of a Graph (May 13, 2015)
See how there’s a homology theory for graphs with magnitude as its Euler characteristic.
A Scale-Dependent Notion of Dimension for Metric Spaces (Part 1) (Mar 11, 2015)
Try to understand how dimension can depend on scale
Mathematics and Magic: the de Bruijn Card Trick (Jan 5, 2015)
Perform a magic trick using the power of maths.
Quasistrict Symmetric Monoidal 2-Categories via Wire Diagrams (Sep 10, 2014)
Guest post by Bruce Bartlett I recently put an article on the arXiv: Bruce Bartlett, Quasistrict symmetric monoidal 2-categories via wire diagrams. It’s about Chris Schommer-Pries’s recent strictification result from his updated thesis, that every symmetric monoidal bicategory is…
Enrichment and the Legendre-Fenchel Transform II (May 22, 2014)
Get the second installment of how Legendre-Fenchel duality is an example of the profunctor nucleus construction.
Enrichment and the Legendre--Fenchel Transform I (Apr 16, 2014)
Remind yourself about basics of the Legendre–Fenchel transform.
universo.math (Apr 14, 2014)
Check out a new Spanish language maths magazine
The Modular Flow on the Space of Lattices (Apr 7, 2014)
See Bruce tell of Ghys’ modular knots.
Fuzzy Logic and Enriching Over the Category [0,1] (Mar 15, 2014)
Watch me try to understand fuzzy logic from an enriched category theory perspective
Galois Correspondences and Enriched Adjunctions (Feb 5, 2014)
Translate from category theory to order theory
Ends (Jan 5, 2014)
End your ignorance of ends!
New Teaching Method Improves Math Skills (Sep 19, 2013)
A novel teaching method involves figuring out what students do and don’t understand
Classical Dualities and Formal Concept Analysis (Sep 12, 2013)
Find out what algebraic varieties, convex sets, linear subspaces, real numbers, logical theories and extension fields have in common with formal concepts.
Formal Concept Analysis (Sep 2, 2013)
Have a peek at the notion of formal concept analysis
The Nucleus of a Profunctor: Some Categorified Linear Algebra (Aug 19, 2013)
Watch some linear algebra being categorified.
Oxford Workshop in Quantum Mathematics and Computation (Aug 15, 2013)
Read about the October workshop.
Torsors and Enriched Categories (Jun 3, 2013)
Read about a different take on torsors
Philosophy Talks in Oxford (May 22, 2013)
Read about recent talks by Kremnitzer and Corfield
The Michael and Lily Atiyah Portrait Gallery (Apr 24, 2013)
View the gallery online.
Koudenburg on Algebraic Weighted Colimits (Apr 17, 2013)
Read about my student’s thesis.
Project Scheduling and Copresheaves (Mar 24, 2013)
Find out what PERT graphs have to do with enriched categories
Lectureship in Sheffield (Mar 6, 2013)
Apply for a lectureship in Sheffield.
Spivak on Category Theory (Mar 3, 2013)
See a new book for scientists about category theory that’s been put on the arXiv.
Tight Spans, Isbell Completions and Semi-Tropical Modules (Jan 20, 2013)
See how these three things are related.
The Spread of a Metric Space (Sep 5, 2012)
Read how this notion of size for metric spaces has some interesting properties.
Entailment and Implication (Jan 4, 2011)
Tell me the difference between these related ideas.
Integral Transforms and the Pull-Push Perspective, I (Nov 7, 2010)
Start to see how enriched profunctors can be viewed as categorifications of integral kernels.
Enriching Over a Category of Subsets (Aug 30, 2010)
Discover how enriched category theory leads to the definition of some generalized metrics on the space of continuous functions on the unit interval.
Workshop on Music, Patterns and Mathematics (Jun 18, 2010)
A three-day meeting during August in England on Music, Patterns and Mathematics.
On the Magnitude of Spheres, Surfaces and Other Homogeneous Spaces (Apr 21, 2010)
See the details of a new paper on the magnitude of metric spaces.
Modeling Surface Diagrams (Mar 24, 2010)
Watch some videos to see how I’m trying to make 3d models of categorical surface diagrams.
Intrinsic Volumes and Weyl's Tube Formula (Mar 12, 2010)
Read about how the volume of a tube around a surface in 3-space depends only on intrinsic invariants of the surface.
A Look at the Mathematical Origins of Western Musical Scales (Feb 26, 2010)
See how the rational numbers 2 and 3/2 gave birth to the Western musical scale.
Newton Fellowships at Sheffield (Nov 26, 2009)
Apply for a post-doc in Sheffield.
Halmos on Writing Mathematics (Oct 19, 2009)
Over in a discussion at Math Overflow I was reminded about Halmos’ great article on writing mathematics, which I highly recommend to all graduate students (or anyone else, for that matter). P. R. Halmos, How to write mathematics, L’Enseignement…
More Magnitude of Metric Spaces and Problems with Penguins (Oct 10, 2009)
Learn about the tenuous link between emperor penguins and the magnitude of metric spaces.