2 citations · 3 across the 15 of their papers we have counts for
15 papers
Three-Dimensional Geometry in Exceptional Algebra
John C. Baez, Susanne Pumpluen
We review some topics in "exceptional mathematics'' from the perspective of 3-dimensional geometry: the octonions , the split octonions , the bioctonions $…
Double Categories of Open Systems: the Cospan Approach
John C. Baez
This is an overview of double categories of "open systems": systems that can interact with their environment. We focus on the variable sharing paradigm, where we compose open syste…
Second Quantization for the Kepler Problem
John C. Baez
The Kepler problem concerns a point particle in an attractive inverse square force. After a brief review of the classical and quantum versions of this problem, focused on their hid…
Motifs and Emergent Feedback in Labeled Graphs
John C. Baez, Adittya Chaudhuri
In fields ranging from business to systems biology, directed graphs with edges labeled by signs are used to model systems in a simple way: the nodes represent entities of some sort…
Tannaka Reconstruction and the Monoid of Matrices
John C. Baez, Todd Trimble
Settling a conjecture from an earlier paper, we prove that the monoid of matrices in a field of characteristic zero is the "walking monoid with a…
Dirichlet Species and Arithmetic Zeta Functions
John C. Baez
Though Joyal's species are known to categorify generating functions in enumerative combinatorics, they also categorify zeta functions in algebraic geometry. The reason is that any…
Groupoid Cardinality and Random Permutations
John C. Baez
If we treat the symmetric group as a probability measure space where each element has measure , then the number of cycles in a permutation becomes a random variable. Th…
The Hexagonal Tiling Honeycomb
John C. Baez
The hexagonal tiling honeycomb is a beautiful structure in 3-dimensional hyperbolic space. It is called {6,3,3} because each hexagon has 6 edges, 3 hexagons meet at each vertex in…
2-Rig Extensions and the Splitting Principle
John C. Baez, Joe Moeller, Todd Trimble
Classically, the splitting principle says how to pull back a vector bundle in such a way that it splits into line bundles and the pullback map induces an injection on -theory. H…
What is Entropy?
John C. Baez
This short book is an elementary course on entropy, leading up to a calculation of the entropy of hydrogen gas at standard temperature and pressure. Topics covered include informat…
The Moduli Space of Acute Triangles
John Carlos Baez
As an introduction to the concept of "moduli space" we consider the moduli space of similarity classes of acute and right triangles in the plane. This has a map to the moduli space…
The Beauty of Roots
John C. Baez
A "Littlewood polynomial" is a polynomial whose coefficients are all 1 or -1. The set of all complex roots of all Littlewood polynomials exhibits many complicated, beautiful and fa…
The Icosidodecahedron
John C. Baez
The icosidodecahedron has 30 vertices, one at the center of each edge of a regular icosahedron -- or equivalently, one at the center of each edge of a regular dodecahedron. It is a…
Isbell Duality
John C. Baez
Mathematicians love dualities. After a brief explanation of dualities, with examples, we turn to one of the purest and most beautiful: Isbell duality. For any category …
Network Models
John C. Baez, John Foley, Joe Moeller +1
Networks can be combined in various ways, such as overlaying one on top of another or setting two side by side. We introduce "network models" to encode these ways of combining netw…