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Konrad Voelkel
1,712 followers -
Mathematician
Mathematician

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Not sure about the Journal/Software system Distill, but this article does resonate with me on many points:

http://distill.pub/2017/research-debt/
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So HTT (Lurie's Higher Topos Theory http://www.math.harvard.edu/~lurie/papers/HTT.pdf ) now has hyperlinks. This is good news. I doubt I will use my printed copy ever again except for its aesthetic shelf value.
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Looking for a PostDoc position in Germany (somewhat algebraically oriented)?

https://www.uni-osnabrueck.de/universitaet/arbeiten_an_der_universitaet/stellenausschreibung/76_fb_6_postdoctoral_position.html

If you know someone, better tell quickly; the deadline is early April.
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For small kids: can you spot all the differences?

Side Note: we may have enough Lego Duplo now...
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Ich hatte ja keine Ahnung! Hörenswert und kurz und kompakt. Sorry, german
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There is a very long article, with interesting end.
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Now this is actually pleasant to read (at least up to page 25, I don't know yet what's coming in later pages).

Who didn't wonder how and why the squaring trick works to solve the Gaussian integral? I certainly did when I learned about it!

Mochizuki might be read after all...
THE MATHEMATICS OF MUTUALLY ALIEN COPIES

Shinichi Mochizuki, of abc-conjecture fame, has a new paper out:

The Mathematics of Mutually Alien Copies: from Gaussian Integrals to Inter-universal Teichmuller Theory (115 pages, pdf: http://www.kurims.kyoto-u.ac.jp/~motizuki/Alien%20Copies,%20Gaussians,%20and%20Inter-universal%20Teichmuller%20Theory.pdf)

He has used a lot of metaphors to try to convey the essence of his work, since most of it was done in isolation, and so the community hasn't absorbed the big conceptual ideas he has introduced. In one sense this is exactly what one should be doing, but sometimes it doesn't come across quite so easily, or one gets the sense that there is a lot of analogy and not much substance. There is a lot of substance, just wholly unfamiliar to the rest of us. I do find his typographical idiosyncrasies slightly off-putting, but that shouldn't detract from the actual mathematics.

Abstract (emphasis in the original): Inter-universal Teichmüller theory may be described as a construction of

certain canonical deformations of the ring structure of a number field

equipped with certain auxiliary data, which includes an elliptic curve over the number field and a prime number ≥ 5. In the present paper, we survey this theory by focusing on the rich analogies between this theory and the classical computation of the Gaussian integral. The main common features that underlie these analogies may be summarized as follows:

- the introduction of two mutually alien copies of the object of interest;
- the computation of the effect — i.e., on the two mutually alien copies of the object of interest — of two-dimensional changes of coordinates by considering the effect on infinitesimals;
- the passage from planar cartesian to polar coordinates and the resulting splitting, or decoupling, into radial — i.e., in more abstract valuation theoretic terminology, "value group" — and angular — i.e., in more abstract valuation-theoretic terminology, "unit group" — portions;
- the straightforward evaluation of the radial portion by applying the quadraticity of the exponent of the Gaussian distribution;
- the straightforward evaluation of the angular portion by considering the metric geometry of the group of units determined by a suitable version of the natural logarithm function.

[Here, the intended sense of the descriptive "alien" is that of its original Latin root, i.e., a sense of abstract, tautological "otherness".] After reviewing the classical computation of the Gaussian integral, we give a detailed survey of inter-universal Teichmüller theory by concentrating on the common features listed above. The paper concludes with a discussion of various historical aspects of the mathematics that appears in inter-universal Teichmüller theory.


#mochizuki   #IUTT  
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Addictive. Somewhere between 2048 and proving theorems.
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About 20 short minutes on peer review, well narrated and very balanced. It's worth spending some time on these issues.
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