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1:40:27

John Baez and James Dolan, 2023-06-22+9

1:40:27

John Baez and James Dolan, 2023-06-22

2:08:10

John Baez and James Dolan, 2023-06-15

2:17:26

John Baez and James Dolan, 2023-06-08

2:03:57

John Baez and James Dolan, 2023-06-01

1:39:26

Life's Struggle to Survive

When pondering our future amid global warming, it is worth remembering how we got here. Even after it got started, the success of life on Earth was not a foregone conclusion! In this talk I recount some thrilling, chilling episodes from the history of our planet. For example: our collision with the planet Theia, the "snowball Earth events" when most of the oceans froze over, and the asteroid impact that ended the age of dinosaurs. Some are well-documented, others only theorized, but pondering them may give us some optimism about the ability of life to survive crises.
To see slides of this talk, go here:
math.ucr.edu/home/baez/struggle/struggle.pdf
You can click on anything in blue on these slides, or any picture, and get more information.

zhlédnutí: 311

Video

1:40:27

John Baez and James Dolan, 2023-06-29

zhlédnutí 109Před 3 měsíci

Artin reciprocity: classifying abelian extensions of the Gaussian field. Azumaya-Brauer-Picard theory: Niles Johnson, Azumaya objects in triangulated bicategories, arxiv.org/abs/1005.4878. John Baez, Grothendieck-Galois-Brauer Theory (Part 1), golem.ph.utexas.edu/category/2023/06/grothendieckgaloisbrauer_theor.html nLab, Picard 3-group, ncatlab.org/nlab/show/Picard 3-group For more on this whol...

1:40:27

John Baez and James Dolan, 2023-06-22+9

zhlédnutí 53Před 3 měsíci

2:08:10

John Baez and James Dolan, 2023-06-22

zhlédnutí 85Před 3 měsíci

Artin reciprocity: classifying abelian extensions of the Gaussian field. For more on this whole series of conversations, go here: math.ucr.edu/home/baez/conversations/

2:17:26

John Baez and James Dolan, 2023-06-15

zhlédnutí 109Před 4 měsíci

I'm afraid I'm too busy to write a description of this conversation now, but I hope to do it later. For more on this whole series of conversations, go here: math.ucr.edu/home/baez/conversations/

2:03:57

John Baez and James Dolan, 2023-06-08

zhlédnutí 76Před 4 měsíci

I'm afraid I'm too busy to write a description of this conversation now, but I hope to do it later. For more on this whole series of conversations, go here: math.ucr.edu/home/baez/conversations/

1:39:26

John Baez and James Dolan, 2023-06-01

zhlédnutí 119Před 4 měsíci

I'm afraid I'm too busy to write a description of this conversation now, but I hope to do it later. For more on this whole series of conversations, go here: math.ucr.edu/home/baez/conversations/

2:22:44

John Baez and James Dolan, 2023-05-25

zhlédnutí 83Před 4 měsíci

I'm afraid I'm too busy to write a description of this conversation now, but I hope to do it later. For more on this whole series of conversations, go here: math.ucr.edu/home/baez/conversations/

1:02:36

Category Theory in Epidemiology

zhlédnutí 597Před 6 měsíci

"Stock and flow diagrams" are widely used for modeling in epidemiology. Modelers often regard these diagrams as an informal step toward a mathematically rigorous formulation of a model in terms of ordinary differential equations. However, these diagrams have a precise syntax, which can be explicated using category theory. Although commercial tools already exist for drawing these diagrams and so...

This Week's Finds 18: categorifying the quantum harmonic oscillator

58:08

This Week's Finds 18: categorifying the quantum harmonic oscillator

zhlédnutí 1,1KPřed 6 měsíci

Classically, light in a mirrored box can be described as a collection of harmonic oscillators, one for each vibrational mode of the light. Planck ‘quantized’ the electromagnetic field by assuming that energy of each oscillator could only take on discrete, evenly spaced values. Later Einstein took this seriously, and realized that light comes in discrete energy packets called 'quanta'. Surprisin...

This Week's Finds 17: counting derangements

56:46

This Week's Finds 17: counting derangements

zhlédnutí 413Před 6 měsíci

A 'derangement' is a permutation where no element is mapped to itself: the cover picture lists the 24 permutations of the 4-element set {A,B,C,D}, and the 9 derangements are shown in blue. Here I show how to count derangements and find the generating function for derangements. A 'species' is a type of structure that can be put on finite sets: technically, it is a functor from the groupoid of fi...

The Answer to the Ultimate Question of Life, the Universe and Everything

53:46

The Answer to the Ultimate Question of Life, the Universe and Everything

zhlédnutí 2,5KPřed 6 měsíci

In The Hitchhiker's Guide to the Galaxy, by Douglas Adams, the number 42 was revealed to be the "Answer to the Ultimate Question of Life, the Universe, and Everything". But he didn't say what the question was! I will reveal that here. In fact it is a simple geometry question, which then turns out to be related to the mathematics underlying string theory. For more see: math.ucr.edu/home/baez/42/...

This Week's Finds 16: species and their generating functions

56:34

This Week's Finds 16: species and their generating functions

zhlédnutí 783Před 6 měsíci

The theory of species and their generating functions is a powerful tool in enumerative combinatorics, and here we use it to count trees. A 'species' is a type of structure that can be put on finite sets: technically, it is a functor from the groupoid of finite sets and bijections to the category of sets. Any species has a 'generating function', which is a formal power series whose coefficients ...

This Week's Finds 15: combinatorics, groupoid cardinality and species

56:49

This Week's Finds 15: combinatorics, groupoid cardinality and species

zhlédnutí 755Před 7 měsíci

The theory of generating functions is a simple and fun but powerful tool in enumerative combinatorics, which I will explain in the next few lectures. Digging into it, we shall see that it rests on some ideas from 'categorification': the more or less systematic replacement of sets by categories. One is 'groupoid cardinality': just as finite sets have cardinalities that are natural numbers, finit...

This Week's Finds 14: the 3-strand braid group

57:15

This Week's Finds 14: the 3-strand braid group

zhlédnutí 884Před 7 měsíci

The 3-strand braid group has striking connections to the group SL(2,ℤ) of invertible 2x2 matrices with integer entries, the Lorentz group from special relativity, modular forms (famous in number theory), and the trefoil knot. They all fit together in a neat package, which I explain here. This is one of a series of lectures at the University of Edinburgh on topics drawn from my column This Week'...