νεκρική ακαμψία

ήταν ο φόβος και ο τρόμος των διδακτορικών φοιτητών στα σεμινάρια.

mertizable prejudice

Definition: X is a Polish space iff it's drunk at 10am.

comparaisons

les nards c'est un peu comme les cycles: il y a des cycles, des épicycles et des cocycles.

stochastic communist manifesto

Random proletarians have nothing to lose but their Markov chains.

constructive mathematics

Theorem 1: Given a \( C^{\infty }\) compact manifold \( M\) furnished with a smooth volume form \( \mu \), there exists an \( F_{\sigma} \)-set containing all diffeomorphisms which are Cohomology Free in \( C^{\infty}_{\mu} ( M ) \).

The actual statement of this theorem is in fact way more constructive than the one that we just gave. For lack of space we do not give the alternative statement, which would reflect more accurately the content of its proof. The proof actually provides a good description of the \( F_{\sigma} \)-set in terms of the solvability of the cohomological equation, and the condition which is necessary for solvability is obtained in a constructive way (admitting the underlying non-constructivity of the problem and the notions involved).

Therefore, the term constructive is used in the following, quite loose, sense. When one has to prove the existence of a solution to such a difficult equation, the only reasonable way to do it is by constructing one. Thus, they take their screwdriver, go down to the street and, when they have gathered enough cash to live on for some months, come back to their desk and construct a solution using step-by-step approximation.

board diversity

- would you rather give your seminar on projector or blackboard?
- i think it's better if i write things while i talk so no projector, but in fact i would prefer a to give it on a whiteboard.
- you don't say...
- not that there's anything wrong with blackboards... i mean... you know... i have friends who are blackboards.

\( \mathcal{PMS} \, \, \LaTeX \) package

 

$ \varfakis $

$ \fakis $

in other news

the Weinstein conjecture in contact geometry, stating roughly that you can periodically masturbate in front of women without being accused of harassment, has just been disproved in full generality, thus establishing that space-time is of dimension at least \( 4\).

going to group-theoretic work

- man, i just moved to UCL and everybody is obsessed with off-peak hours and shit.
- well, i guess if it saves you half the money and you travel more decently... i mean those guys probably spend three hours in the train every time the go to the office.
- yeah, it's incredible. everybody commutes to UCL
- duh... it's in the centre.

βαρεμάρα

- τι διαβάζεις εκεί;
- τίποτα, μαλακίες, ένα βιβλίο για μερικες διαφορικές είναι.
- σαπίλα;
- κόρτεβεγκ ντε βρίες και λειχήνες.

καρέκλες #3

the beatles on meth

We all live in a yellow sub-Riemannian manifold
Yellow sub-Riemannian manifold, yellow sub-Riemannian manifold
We all live in a yellow sub-Riemannian manifold
Yellow sub-Riemannian manifold, yellow sub-Riemannian manifold

a long time ago in a punctured sphere far, far away

- what's your next exam on, man?
- Riemann surfaces.
- may the ahlfors be with you.

alternative mathematics

Theorem 1 Liouville numbers form a generic subset of the torus \( \mathbb{T}^{1} \).

Proof: We delete the interval of size \( 2 q^{-n} \) centered in \( \frac{p}{q} \), for every \( p \) and every \( q \). \( \square \)

grapes of roth

Klaus Roth tried to make his own wine during the great depression, but his vineyard's growth was very slow. His mathematical legacy was nonetheless quite important.

KAM is like masturbation

For reasons well known in KAM theory, when solving the linear cohomological equation over a Diophantine rotation, one has to introduce an infrared cut-off \( T_{N} \), projecting on frequencies lower than \( N\), and an ultraviolet cut-off \( R_{N} \), projecting on frequencies strictly higher than \( N\).
These operators can be easily estimated in the relevant norm by applying Johnson's cut-off theorem, proved in [Co98].

Since, however, we know by construction that

\( T_{N} + R_{N} = \mathrm{Id} \)

we obtain immediately the following corollary.
Corollary 1. The visible spectrum is empty. If you publish too much in KAM, you will go blind.

math porn

Haar ron añejo, normalized to 1% abv

Theorem: Let \( G\) be a locally compact topological group. Then \( G \times G \times G \) is naturally equipped with a pirate measure.

αδιάφορη ισορροπία στη θεωρία παιγνίων

νά σ' κι εσένα, νά μ' κι εμένα.

classification

- smale spent most of his time in Rio constructing horseshoes.
- what did they look like?
- generically they were transparent with huge heels.
- that's stripper shoes and you just failed Dynamical Systems I.