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Paul Schwahn

@pschwahn.mathstodon.xyz.ap.brid.gy

8 followers 0 following 151 posts

Sometimes I do differential geometry. [bridged from mathstodon.xyz/@pschwahn on the fediverse by fed.brid.gy ]

Posts Replies Media

Paul Schwahn @pschwahn.mathstodon.xyz.ap.brid.gy · 20/08/2026

Uhh.. what? I already paid a 285 EUR on my visa application. Why does asking questions cost money?

Screenshot from UK Visa and Immigration website. Queries cost 2.74 GBP.

Screenshot from in person appointment booking website. All options (even the "free" ones) cost at least 93 EUR.

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Paul Schwahn @pschwahn.mathstodon.xyz.ap.brid.gy · 16/06/2026

UPDATE: Verbitsky has been released from prison and allowed to leave Armenia! meduza.io/en/news/2026/06/15/russia…

Misha being interviewed by a reporter in a parking lot.

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Paul Schwahn @pschwahn.mathstodon.xyz.ap.brid.gy · 25/05/2026

poor 𝑆²×ℝ 😢

Example S² x R. This is the poorest geometry, since it concerns only two 3-manifolds,
that are S² x S¹ and its quotient by the involution (x, exp(i*t)) mapsto (-x, exp(-i*t)).

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Paul Schwahn @pschwahn.mathstodon.xyz.ap.brid.gy · 02/03/2026

@highergeometer now I can't unsee it myself...

President Bush meme: his advisor is telling him "they made the isospectral drums", while he stares in shock

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Paul Schwahn @pschwahn.mathstodon.xyz.ap.brid.gy · 30/01/2026

Life is going to hell in thousands of ways, but at least I got myself some nice drip from my university.

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Paul Schwahn @pschwahn.mathstodon.xyz.ap.brid.gy · 23/12/2025

This amogus surface in ℝ³ has principal curvatures contained in [-1, 1] and is homeomorphic to a sphere, but its enclosed volume is less than that of the unit ball. arxiv.org/abs/2512.19659

Complicated surface, shaded in red and blue, resembling a character from the videogame "Among Us".

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Paul Schwahn @pschwahn.mathstodon.xyz.ap.brid.gy · 09/12/2025

Wait - am I reading this correctly that firearms are allowed on domestic flights in Brazil? The more you know.

Check-in warning of LATAM airlines, listing items that are not allowed on the flight.

In particular, under hand luggage it says firearms, except on domestic flights in Brazil.

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Paul Schwahn @pschwahn.mathstodon.xyz.ap.brid.gy · 27/11/2025

W from the Chair of Representation Theory at EPFL.

Title: Representation theory studies symmetry
in mathematics, science and engineering

For example, the following is a Al-generated picture of Dynkin
diagrams, a fundamental concept in Lie theory: [AI slop image]

However, the pictures above are not only incorrect, but they make no
sense. As such, the Chair of Representation Theory seeks to unleash
human (underlined!) ingenuity and ambition to tackle problems from fields as
varied as geometry, low-dimensional topology, mathematical physics
and combinatorics

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Paul Schwahn @pschwahn.mathstodon.xyz.ap.brid.gy · 29/09/2025

My passion project (formalizing the basics of synthetic projective geometry in Lean) is now public on Github! github.com/PSchwahn/IncidenceGeomet… Just finished the definition of the projective closure of an affine plane. Now on to proving that it satisfies the projective plane axioms...

Screenshot of VSCode containing Lean code.

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Paul Schwahn @pschwahn.mathstodon.xyz.ap.brid.gy · 24/06/2025

Got my first PR merged into mathlib 🥳

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Paul Schwahn @pschwahn.mathstodon.xyz.ap.brid.gy · 13/05/2025

Alright, I must concur, index notation is better than whatever this is.

Formula in a maths paper that involves the operator Trace_Free_Part_Of, written out including underscores.

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Paul Schwahn @pschwahn.mathstodon.xyz.ap.brid.gy · 13/05/2025

Bell curve meme.
Low IQ regime: "tensor is big matrix"
Mid IQ regime: "Noo! A tensor is something that transforms like a tensor."
High IQ regime: "tensor is big matrix"

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Paul Schwahn @pschwahn.mathstodon.xyz.ap.brid.gy · 26/04/2025

low-effort meme cooked up after collaborating with complex geometers (this is a joke)

Dictionary Complex Algebraic Geometry -- English.

homogeneous space -- (generalized) flag variety.
hyperplane section -- line bundle.
vector bundle -- sheaf of sections.
holomorphic -- holomorphic.
smooth -- holomorphic.
point -- line.
line -- plane.
norm -- quadratic form.
orthogonal group -- complexified orthogonal group.
contact manifold -- complex contact manifold.
real numbers -- complex numbers.

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Paul Schwahn @pschwahn.mathstodon.xyz.ap.brid.gy · 15/04/2025

"A piecewise-linear isometrically immersed flat Klein bottle in Euclidean 3-space", or, in other words, an Origami Klein bottle with self-intersections: arxiv.org/abs/2504.08826

Triangular Origami-like construction resembling a Klein bottle.
Caption: "The image of a piecewise linear local isometric embedding of a flat Klein bottle into R^3."

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Paul Schwahn @pschwahn.mathstodon.xyz.ap.brid.gy · 15/04/2025

Found this on arXiv today, and it evoked imagery of cosmic terror in my mind.

Top: Arxiv preprint titled "Gluing charged black holes into de Sitter space"
Middle: Jeff Goldblum in Jurassic Park, captioned with "Your scientists were so preoccupied with whether or not they could, they didn't stop to think if they should
Bottom: Artistic rendition of spacetime with bright blue glowing orbs in it

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Paul Schwahn @pschwahn.mathstodon.xyz.ap.brid.gy · 13/02/2025

Elsevier... are you trying to tell me something?

Screenshot of the preview of a maths article, titled "Special prehomogeneous vector spaces associated to F4, E6, E7, E8 and simple Jordan algebras of rank 3". The first recommended article is titled "The adult consequences of being bullied in childhood".

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Paul Schwahn @pschwahn.mathstodon.xyz.ap.brid.gy · 08/01/2025

Someone had the questionable idea of using the dreadful ¶ symbol as notation for a function. (I had to google to find out that this thing is called 𝑝𝑖𝑙𝑐𝑟𝑜𝑤).

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