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free book: "The Discrete Algebra of the Fourier Transform"
mathematical-tours.github.io/daft/
LaTeX source is available, pull requests (especially to improve English, the author translated it from French) are encouraged
LaTeX source is available, pull requests (especially to improve English, the author translated it from French) are encouraged
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Rereading "An introduction to quantaloid-enriched categories"
I used to understand this material in 2012-2014 (I even mentioned it in our own paper published in those years), and it turned out recently that I no longer could reproduce the detailed definitions from memory.
So I am rereading this paper by Isar Stubbe, it's really nice, not excessively difficult (I usually have difficult time reading categorical papers, but this one is a pleasant exception).
Links are in the comments.
So I am rereading this paper by Isar Stubbe, it's really nice, not excessively difficult (I usually have difficult time reading categorical papers, but this one is a pleasant exception).
Links are in the comments.
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"Towards Categorical Foundations of Learning"
When one tries to use category theory for the applied work, a number of questions arise: Is it just too difficult to be used at all by me given my level of technical skills? Is it fruitful enough, and is the fruitfulness/efforts ratio high enough for all this to make sense?
I recently discovered Bruno Gavranović, a graduate student in Glasgow, whose work is promising in this sense. They are really trying hard to keep things simple and also trying to make sure that there are non-trivial applications. Here is one of his essays and papers (March 2021, so it's not the most recent one, but probably the most central):
www.brunogavranovic.com/posts/2021-03-03-Towards-Categorical-Foundations-Of-Neural-Networks.html
(I am posting this here because there are people who read this blog who are interested in applied category theory and like it, not because I am trying to convince those who formed a negative opinion of this subject. I am non-committal myself, I have not decided whether applied categories have strong enough fruitfulness/efforts ratio, but this particular entry seems to be one of the best shots in this sense, so I am going to try to go deeper with their work.)
Update: their collection of papers in the intersection between Category Theory and Machine Learning: github.com/bgavran/Category_Theory_Machine_Learning
I recently discovered Bruno Gavranović, a graduate student in Glasgow, whose work is promising in this sense. They are really trying hard to keep things simple and also trying to make sure that there are non-trivial applications. Here is one of his essays and papers (March 2021, so it's not the most recent one, but probably the most central):
www.brunogavranovic.com/posts/2021-03-03-Towards-Categorical-Foundations-Of-Neural-Networks.html
(I am posting this here because there are people who read this blog who are interested in applied category theory and like it, not because I am trying to convince those who formed a negative opinion of this subject. I am non-committal myself, I have not decided whether applied categories have strong enough fruitfulness/efforts ratio, but this particular entry seems to be one of the best shots in this sense, so I am going to try to go deeper with their work.)
Update: their collection of papers in the intersection between Category Theory and Machine Learning: github.com/bgavran/Category_Theory_Machine_Learning
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9th International Symposium of Domain Theory and its Applications
Yesterday, today, tomorrow (12 hours diff between that and US East Coast):
math.nie.edu.sg/isdt09/
math.nie.edu.sg/isdt09/programme/9th_ISDT_Program1.pdf
Free zoom; I am listening to some of this right now... Very nostalgic...
But... it's just too difficult (and they don't even seem to record).
In any case, that's the kind of "intelligent assistant" I want - a piece of software with which I could discuss a talk and a slide deck like one of those, and which would help me to understand the details of what's going on.
math.nie.edu.sg/isdt09/
math.nie.edu.sg/isdt09/programme/9th_ISDT_Program1.pdf
Free zoom; I am listening to some of this right now... Very nostalgic...
But... it's just too difficult (and they don't even seem to record).
In any case, that's the kind of "intelligent assistant" I want - a piece of software with which I could discuss a talk and a slide deck like one of those, and which would help me to understand the details of what's going on.
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Internation Congress of Mathematicians will be online, free of charge
The event in Russia is cancelled. Международный конгресс математиков в "Ленинграде" отменён.
The dates remain July 6 - July 14: www.mathunion.org/fileadmin/IMU/ICM2022/ICM_2022_statement.pdf
en.wikipedia.org/wiki/International_Congress_of_Mathematicians
The dates remain July 6 - July 14: www.mathunion.org/fileadmin/IMU/ICM2022/ICM_2022_statement.pdf
en.wikipedia.org/wiki/International_Congress_of_Mathematicians
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Manin: "Forgotten Motives: the Varieties of Scientific Experience"
Про многие научные темы, мне хотелось понять, что в них происходит на самом деле, без того, чтобы достигать уровня, когда умеешь решать задачи. И есть темы, которые никакая популярная литература даже и не пытается покрывать (насколько я знаю).
Вот, оказывается, что эта замечательная неформальная статья Манина в сборнике памяти Гротендика проливает свет на целый ряд понятий, которые я считал совершенно недоступными:
arxiv.org/abs/1402.2155
Вот, оказывается, что эта замечательная неформальная статья Манина в сборнике памяти Гротендика проливает свет на целый ряд понятий, которые я считал совершенно недоступными:
arxiv.org/abs/1402.2155
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MSML21: Mathematical and Scientific Machine Learning
Starts in 5 minutes:
msml21.github.io/
No registration is needed - they are just handling it in a relaxed fashion
msml21.github.io/
No registration is needed - they are just handling it in a relaxed fashion