A group blog on math, physics and philosophy

- 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.

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