Simon Pepin Lehalleur

@plain_simon

Mathematician on the good days... Trying to figure out the whole ghastly trick on the bad. Radboud University Nijmegen, Netherlands.

Nijmegen, Netherlands
Vrijeme pridruživanja: prosinac 2019.

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  1. Prikvačeni tweet
    19. sij
    Odgovor korisniku/ci

    "Presheafness precedes representability." Jean-Paul Cat, Being and co-Being

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  2. proslijedio/la je Tweet
    2. velj

    Improbawall by 3D Designer Matt Taylor

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  3. proslijedio/la je Tweet
    2. velj

    The Honduran white bat cuts the side veins extending out from the midrib of the large leaves of the Heliconia plant causing them to fold down to form a 'tent'. They cling to the roof of this tent in small colonies of up to half a dozen individuals

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  4. 2. velj

    Shimura varieties, with their triple analytic/algebraic/arithmetic nature, feature in the proofs of Mordell's conjecture by Faltings and of Fermat's last theorem by Wiles, among many other results in modern number theory. [19/n]

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  5. 2. velj

    The fact that Shimura varieties are algebraic and defined over a number field connects automorphic forms with the arithmetic of reduction of Shimura varieties over finite fields. Shimura varieties are often moduli spaces of abelian varieties and this is useful as well! [18/n]

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  6. 2. velj

    Basically, complex analysis on Shimura varieties is (a part of) the theory of modular and automorphic forms. Automorphic forms are a blend of representation and number theory which gives rise to well-understood L-functions (generalising the Riemann zeta function). [17/n]

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  7. 2. velj

    Ex: U=unit disk in C, G in SL_2(R) defined by integral matrices with congruence conditions. Then U/G is called a modular curve. Shimura varieties are central objects in modern number theory, in a way that's a bit difficult to summarize. [16/n]

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  8. 2. velj

    The theorem can be made a lot more precise: U/G is a quasi-projective variety, there is a natural projective compactification built from U, the complex algebraic variety U/G is actually defined over a number field. U/G is called a Shimura variety (small lie here!) [15/n]

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  9. 2. velj

    Arithmetic subgroups are particular discrete subgroups which (roughly) can be written with matrices with integral coeffs. Let G be such a (torsion-free) arithmetic subgroup acting on U. Then U/G is a complex manifold. Thm(Baily-Borel): U/G is an algebraic variety. [14/n]

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  10. 2. velj

    A more complicated example: the set S_n of symmetric complex n by n matrices Z such that Id- Z* Z is positive definite (Z* conjuguate-transpose). There is a real algebraic group acting on U by holomorphic automorphisms. In this group, there are many discrete subgroups. [13/n]

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  11. 2. velj

    c) Shimura varieties A bounded symmetric domain is an open subset U in C^n such that, for every x in U, there is an holomorphic involution of U with x as isolated fixed point. In other words, lots of holomorphic symmetries. Ex: open unit ball B_n in C^n. [12/n]

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  12. proslijedio/la je Tweet
    2. velj

    They could not wait one single working day after departure to blame EU for the future Not one single working day Not one

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  13. proslijedio/la je Tweet
    29. sij

    Dwarf Fortress bug reports are the highest form of art

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  14. proslijedio/la je Tweet
    1. velj

    I'm watching a lot of videos about ancient Rome and one thing that kills me every time is one historical figure getting mad at another and having to sustain that anger for several months as they travel across Italy to confront them

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    I tell people to stop worrying about futuristic runaway smart AI, because it's stupid current AI that will kill us, this is what I mean. Someone bought a product that *literally* text-matched the word "charity" as 'good' and "vodka" as 'bad' and is making hiring choices with it.

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  16. proslijedio/la je Tweet
    1. velj

    The fact that hundreds of millions of people have been spared the agony of losing a child - or of dying themselves as children - is surely the single greatest humanitarian achievement of our species.

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  17. proslijedio/la je Tweet
    30. sij

    Hawk’s head stabilization

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  18. proslijedio/la je Tweet
    1. velj

    Vu sur Facebook, via Julia Cassis : "Sur les portes du bâtiment principal de Paris 3"

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  19. proslijedio/la je Tweet
    27. sij

    I had to get a background check for my job, and it turns out the report is a 300+ page pdf of every single tweet I’ve ever liked with the work “fuck” in it. Enjoy your dystopian bs! *waves*

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  20. 31. sij

    Finally, other objects attached to compact Lie groups, like generalised flag varieties, are also algebraic varieties. This is in a way the start of *geometric representation theory* : algebraic geometry in the service of representation theory. [11/n]

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  21. 31. sij

    Surprise! Compact Lie groups are algebraic. More precisely, they can all be realised as subgroups of a matrix group GL_n(C), cut out by polynomial equations with real coefficients. Similarly, all their finite-dimensional representations are algebraic in a precise sense. [10/n]

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