Posts by Tom Leinster

Welcome, Emily (Jun 1, 2013)
Emily Riehl joins us as a host on this blog.
Bounded Gaps Between Primes (May 14, 2013)
Report on recent work of Yi Tang Zhang, taking us a step closer to a proof of the Twin Primes Conjecture.
Tutte Polynomials and Magnitude Functions (Apr 16, 2013)
The magnitude function is a mysterious invariant of graphs. It’s closely related to invariants that have proven meaningful and useful in other branches of mathematics. But uncovering its meaning for graphs poses a challenge.
Colouring a Graph (Apr 12, 2013)
A categorical perspective on graph colourings, and a fundamental gap in our knowledge.
The Convex Magnitude Conjecture (Mar 30, 2013)
An unsolved problem about measure of convex sets, arising from category theory.
Five Positions at Edinburgh (Mar 22, 2013)
Jobs at Edinburgh.
Mark on Magnitude (Mar 21, 2013)
Mark Meckes mouths magnificently on metric magnitude.
7th Scottish Category Theory Seminar (Jan 29, 2013)
Conference announcement.
This Week's Finds at 20 (Jan 26, 2013)
The 20th birthday of John’s column.
Carleson's Theorem (Jan 17, 2013)
The twisty turny history of beliefs about pointwise convergence of Fourier series.
Category Theory 2013 (Dec 24, 2012)
Announcement of Category Theory 2013, Sydney.
Rethinking Set Theory (Dec 18, 2012)
Expository paper on set theory done categorically.
Bob on TAC (Dec 8, 2012)
Bob Rosebrugh’s article about Theory and Applications of Categories in the Notices of the AMS.
Research Fellowships in Edinburgh (Dec 7, 2012)
Five postdoc positions available.
Almost All of the First 50 Billion Groups Have Order 1024 (Nov 28, 2012)
More than 99 per cent of the groups of order at most 2000 have order 1024.
Parametrized Mates and Multivariable Adjunctions (Nov 1, 2012)
Guest post by Emily Riehl.
The Zorn Identity (Oct 26, 2012)
Zorn’s lemma is trivially equivalent to a theorem provable without the axiom of choice.
The Curious Dependence of Set Theory on Order Theory (Oct 13, 2012)
Is set theory as dependent on order theory as it seems to be, and if so, why?
Analysis Fellowship in Edinburgh (Oct 11, 2012)
Job ad.
Symmetric Monoidal Bicategories (Oct 4, 2012)
Guest post by Nick Gurski.
Where Do Ultraproducts Come From? (Sep 30, 2012)
Are ultraproducts categorically inevitable?
Where Do Linearly Compact Vector Spaces Come From? (Sep 25, 2012)
What should it mean for a topological vector space to be compact?
Where Do Ultrafilters Come From? (Sep 23, 2012)
The notion of ultrafilter is inherent in the notion of finiteness of a set.
Where Do Monads Come From? (Sep 20, 2012)
Monads don’t just come from adjunctions.
Jech (1973), page 118 (Aug 29, 2012)
An amusing page of Thomas Jech’s book “The Axiom of Choice”.
Integrating Against the Euler Characteristic (May 17, 2012)
Euler characteristic is something like a measure. So what does integrating against it do?
The Mathematics of Biodiversity (Apr 26, 2012)
Conference in Barcelona.
10,000 (Apr 23, 2012)
News on Elsevier boycott.
Wellcome Joins In (Apr 9, 2012)
I just looked at the front page of The Guardian, a quality British newspaper that’s especially widely read online… and I was amazed to see that their second-leading story was on The Cost of Knowledge: The news is that…
Reader Survey: log|x| + C (Mar 19, 2012)
On a worrying tradition in the teaching of calculus.
6th Scottish Category Theory Seminar (Mar 19, 2012)
Conference announcement.
Types, Homotopy and Univalent Foundations: Special Issue (Feb 26, 2012)
Announcement of a special journal issue on homotopy type theory
Vorsicht! Funktor! (Jan 15, 2012)
Sign in Germany.
A Semigroup Approach to Finite Markov Chains (Jan 3, 2012)
Guest post by Benjamin Steinberg, proving the basic results on finite Markov chains using semigroup theory.
The Eventual Image, Part 2 (Dec 25, 2011)
In which categories do endomorphisms have eventual images? A solution to the problem posed in Part 1.
On the Law of Large Numbers (Such As 60) (Dec 20, 2011)
Alex Simpson’s work on randomness and locales.
What Do You Think of EPSRC Policy? (Dec 19, 2011)
Problems with EPSRC funding policy, and a call for comments by Burt Totaro and Michael Singer.
The Eventual Image (Dec 8, 2011)
Three different categories exhibit very similar dynamical behaviour. Why?
Measuring Diversity (Oct 23, 2011)
A way of quantifying diversity, especially biological diversity, that takes similarity between species into account.
Do You Know This Idempotent? (Oct 19, 2011)
Every endomorphism of a finite set has a unique idempotent power. Can you describe it?
Spectra of Operators and Rings (Oct 16, 2011)
Connecting notions of spectra, and a question on characteristic polynomials.
The 5th Scottish Category Theory Seminar (Oct 10, 2011)
Announcement of Scotcats 5.
Universal Measures (Sep 14, 2011)
Groemer’s integral theorem, recast as a universal property.
Hadwiger's Theorem, Part 2 (Aug 29, 2011)
Generalizing Hadwiger’s theorem to arbitrary metric spaces, especially R^n with the 1-norm.
Mixed Volume (Aug 26, 2011)
Several explanations of the mixed volume of convex bodies.
All Job Ads Should Be Like This (Aug 21, 2011)
Poetic ad for a job at the University of Strathclyde.
Definitions of Ultrafilter (Jul 2, 2011)
Several equivalent definitions of ultrafilter, including a particularly simple one that I’d like to find a reference for.
Hadwiger's Theorem, Part 1 (Jun 29, 2011)
Expository account of Hadwiger’s theorem characterizing invariant valuations on convex sets.
The Magnitude of an Enriched Category (Jun 13, 2011)
An analogue of cardinality for enriched categories.
Möbius Inversion for Categories (May 31, 2011)
The relationships between Euler characteristic and different kinds of Möbius inversion.
An Operadic Introduction to Entropy (May 18, 2011)
Summary of recent results on entropy, and introduction to entropy for the categorically minded.
Entropies vs. Means (May 10, 2011)
Connections between the two concepts.
The Colours of Infinity — A Review (Apr 26, 2011)
Review of a popular mathematics book.
The 4th Scottish Category Theory Seminar (Apr 7, 2011)
Seminar announcement.
Which Graphs Can be Given a Category Structure? (Mar 27, 2011)
A report on Samer Allouch’s thesis.
Characterizing the Generalized Means (Mar 2, 2011)
A new characterization of generalized means?
Characterizing the p-Norms (Mar 1, 2011)
Exactly what makes the p-norms special?
Category Theory 2011 (Jan 17, 2011)
The invited speakers for CT2011 have been announced.
Another Editorial Board Resigns (Jan 11, 2011)
Not-so-new news about the Journal of Group Theory.
Magnitude of Metric Spaces: A Roundup (Jan 8, 2011)
Resources on magnitude of metric spaces.
An Informal Introduction to Topos Theory (Dec 25, 2010)
A short paper on basic topos theory.
The Boyd Orr Centre, or: What is a Severed Horse Leg? (Dec 17, 2010)
Interdisciplinarity for mathematicians.
Poetic Refereeing (Dec 17, 2010)
Snappy excerpts from referees’ reports.
Pri la Funkcia Ekvacio f(x + y) = f(x) + f(y) (Dec 10, 2010)
Fréchet, a functional equation, and a curious piece of history.
What is Integral Geometry? (Nov 29, 2010)
A quick and dirty explanation.
A Short Warning (Oct 26, 2010)
On plagiarism.
Benoît Mandelbrot (Oct 18, 2010)
Remarks on the Mandelbrot set and its wider context.
The Scottish Category Theory Seminar (Oct 13, 2010)
Announcement of the third meeting.
An Invitation (Oct 8, 2010)
Come in, come in!
Fetishizing p-Values (Sep 23, 2010)
The “cult of statistical significance”.
Bacard on Segal Enriched Categories (Sep 22, 2010)
Short description of a new paper on homotopy-enrichment
Integral Geometry in Barcelona (Sep 6, 2010)
Short report from a meeting.
The Difference between Measure Zero and Empty Interior (Aug 28, 2010)
…is the difference between Lebesgue and Riemann integrability.
Free High School Science Texts Needs You! (Aug 25, 2010)
Proof-reading needed for open source textbooks.
What is the Langlands Programme? (Aug 21, 2010)
Please?
Means (Aug 7, 2010)
Means of numbers and means of structures.
Pullback-homomorphisms (Aug 1, 2010)
What does it signify for a map of algebras for a monad to be a pullback square?
The Dold–Kan Theorem: Two Questions (Jul 12, 2010)
In Ab, many things become true.
Algebraic Model Structures (Jun 16, 2010)
Algebraic model categories and weak factorization systems.
The Scottish Category Theory Seminar (May 8, 2010)
The second meeting of the Scottish Category Theory Seminar.
Normal Service is Resumed! (Mar 22, 2010)
Temporary software glitch is over.
A Perspective on Higher Category Theory (Mar 8, 2010)
Extended ramblings.
Sheaves Do Not Belong to Algebraic Geometry (Feb 5, 2010)
They come out of thin categorical air.
F and the Shibboleth (Jan 14, 2010)
Thompson’s group F and free structured categories.
What You're Doing is Good for You (Jan 6, 2010)
Open access articles get cited more.
An Adventure in Analysis (Nov 4, 2009)
How a problem about magnitude of metric spaces was solved.