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pro vyhledávání: '"BAEZ, JOHN C."'
Autor:
Baez, John C.
If we treat the symmetric group $S_n$ as a probability measure space where each element has measure $1/n!$, then the number of cycles in a permutation becomes a random variable. The Cycle Length Lemma describes the expected values of products of thes
Externí odkaz:
http://arxiv.org/abs/2412.16386
Autor:
Baez, John C.
Publikováno v:
Notices Amer. Math. Soc. 71 (2024), 1390-1391
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 a Euclidean plane tiled by regular hexagons, and 3 such planes meet al
Externí odkaz:
http://arxiv.org/abs/2412.00048
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 $K$-theory. Here we categorify the splitting principle and generalize it to the con
Externí odkaz:
http://arxiv.org/abs/2410.05598
Autor:
Baez, John C.
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 information, Shannon entropy and Gibbs entropy, the principle of maximum entro
Externí odkaz:
http://arxiv.org/abs/2409.09232
Autor:
Baez, John C.
Publikováno v:
Notices Amer. Math. Soc. 70 (2023), 1495-1497
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 fascinating patterns. Some fractal regions of this set closely resemble
Externí odkaz:
http://arxiv.org/abs/2310.00326
Autor:
Baez, John C.
Publikováno v:
Notices Amer. Math. Soc. 70 (2023), 821-823
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 beautiful, highly symmetrical shape. But it is just a projection down
Externí odkaz:
http://arxiv.org/abs/2309.15774
Autor:
Baez, John C.
During what Vietnamese call the American War, Alexander Grothendieck spent three weeks teaching mathematics in and near Hanoi. Ho\`ang Xu\^an S\'inh took notes on his lectures and later did her thesis work with him by correspondence. In her thesis sh
Externí odkaz:
http://arxiv.org/abs/2308.05119
Autor:
Baez, John C.
Underlying the Riemann Hypothesis there is a question whose full answer still eludes us: what do the zeros of the Riemann zeta function really mean? As a step toward answering this, Andr\'e Weil proposed a series of conjectures that include a simplif
Externí odkaz:
http://arxiv.org/abs/2304.08737
Autor:
Baez, John C.
These are the third 50 issues of This Week's Finds of Mathematical Physics, from April 9, 1997 to June 18, 2000. These issues discuss quantum gravity, topological quantum field theory, n-categories and other topics in mathematics and physics. They al
Externí odkaz:
http://arxiv.org/abs/2303.02785
Autor:
Baez, John C.
Young diagrams are ubiquitous in combinatorics and representation theory. Here we explain these diagrams, focusing on how they are used to classify representations of the symmetric groups $S_n$ and various "classical groups": famous groups of matrice
Externí odkaz:
http://arxiv.org/abs/2302.07971