Last night, on our way to the fireworks in Antwerp, we walked by this definition of prime numbers:
“The numbers, only divisible by $1$ and itself are: $2,3$ and every number before or after a multiple of $6$, without their squares or products.” (Peter Wynen)
True enough.
And a lot more user-friendly than: the generators of the multiplicative monoid of all natural numbers which are $\pm 1$ modulo $6$ are the prime numbers, except for $2$ and $3$.
I wish you a 2018 full of math (and artistic) pleasures.
It features the work by number-theorist Minhyong Kim of Oxford University.
In it, Minhyong Kim comes out of the closet, revealing that many of his results on rational points of algebraic curves were inspired by analogies he sees between number theory and physics.
So far he refrained from mentioning this inspiration in papers because “Number theorists are a pretty tough-minded group of people,” he said.
Yesterday, Peter Woit had a post on this on his blog ‘Not Even Wrong’, stuffed with interesting links to recent talks and papers by Minhyong Kim.
Minhyong Kim’s ideas grew out the topic of arithmetic topology, that is, the analogy between number rings and $3$-dimensional compact manifolds and between their prime ideals and embedded knots.
In this analogy, which is based on the similarity between finite connected covers of manifolds on the one hand and connected etale extensions of rings on the other, the prime spectrum of $\mathbb{Z}$ should correspond (due to Minkowski’s result on discriminants and Perelman’s proof of the Poincare-conjecture) to the $3$-sphere $S^3$.
Inevitably, they had to suffer through a photoshoot and give their university’s PR-people some soundbites.
CAPTION
In the simplest terms, an elliptic curve is a doughnut shape with carefully placed points, explain Emory University mathematicians Ken Ono, left, and John Duncan, right. “The whole game in the math of elliptic curves is determining whether the doughnut has sprinkles and, if so, where exactly the sprinkles are placed,” Duncan says.
CAPTION
“Imagine you are holding a doughnut in the dark,” Emory University mathematician Ken Ono says. “You wouldn’t even be able to decide whether it has any sprinkles. But the information in our O’Nan moonshine allows us to ‘see’ our mathematical doughnuts clearly by giving us a wealth of information about the points on elliptic curves.”
(Photos by Stephen Nowland, Emory University. See here and here.)
Some may find this kind of sad, or a bad example of over-popularisation.
I think they do a pretty good job of getting the notion of rational points on elliptic curves across.
That’s what the arithmetic of elliptic curves is all about, finding structure in patterns of sprinkles on special doughnuts. And hey, you can get rich and famous if you’re good at it.
Their Nature-paper Pariah moonshine is a must-read for anyone aspiring to write a math-book aiming at a larger audience.
“Strictly speaking the article was published in Nature Communications (https://www.nature.com/ncomms/). We were also rejected by Nature. But Nature forwarded our submission to Nature Communications, and we had a great experience. Specifically, the review period was very fast (compared to most math journals), and the editors offered very good advice.
My understanding is that Nature Communications is interested in publishing more pure mathematics. If someone reading this has a great mathematical story to tell, I (humbly) recommend to them this option. Perhaps the work of Mumford–Tate would be more agreeably received here.
By the way, our Nature Communications article is open access, available at https://www.nature.com/articles/s41467-017-00660-y.”
There will be one talk a month, on a tuesday evening from 18hr-20hr. Among the lecturers are the ‘usual suspects’:
Pierre Cartier (October 24th) will discuss the state of functional analysis before Grothendieck entered the scene in 1948 and effectively ‘killed the subject’ (said Dieudonné).
Alain Connes (November 7th) will talk on the origins of Grothendieck’s introduction of toposes.
In fact, toposes will likely be a recurrent topic of the seminar.
Laurant Lafforgue‘s title will be ‘La notion de vérité selon Grothendieck'(January 9th) and on March 6th there will be a lecture by Olivia Caramello.
Also, Colin McLarty will speak about them on May 3rd: “Nonetheless one should learn the language of topos: Grothendieck on building houses”.
Further Grothendieck news, there’s the exhibition of a sculpture by Nina Douglas, the wife of Michael Douglas, at the Simons Center for Geometry and Physics (h/t Jason Starr).
It depicts Grothendieck as shepherd. The lambs in front of him have Riemann surfaces inserted into them and on the staff is Grothendieck’s ‘Hexenkuche’ (his proof of the Riemann-Roch theorem).
Either this is horribly wrong, or it must be well-known. So I guess I’m asking for either a rebuttal or a reference.
Take a ‘smallish’ category $\mathbf{C}$. By this I mean that for every object $C$ the collection of all maps ending in $C$ must be a set. On this set, let’s call it $y(C)$ for Yoneda’s sake, we can define a pre-order $f \leq g$ if there is a commuting diagram
$\xymatrix{D \ar[rr]^f \ar[rd]_h & & C \\ & E \ar[ru]_g &}$
A sieve $S$ on $C$ is the same thing as a downset in $y(C)$ with respect to this pre-order. Composition with $h : D \rightarrow C$ gives a map $h : y(D) \rightarrow y(C)$ such that $h^{-1}(S)$ is a downset (or, sieve) in $y(D)$ whenever $S$ is a downset in $y(C)$.
A Grothendieck topology on $\mathbf{C}$ is a function $J$ which assigns to every object $C$ a collection $J(C)$ of sieves on $C$ satisfying:
$y(C) \in J(C)$,
if $S \in J(C)$ then $h^{-1}(S) \in J(D)$ for every morphism $h : D \rightarrow C$,
a sieve $R$ on $C$ is in $J(C)$ if there is a sieve $S \in J(C)$ such that $h^{-1}(R) \in J(D)$ for all morphisms $h : D \rightarrow C$ in $S$.
From this it follows for all downsets $S$ and $T$ in $y(C)$ that if $S \subset T$ and $S \in J(C)$ then $T \in J(C)$ and if both $S,T \in J(C)$ then also $S \cap T \in J(C)$.
In other words, the collection $\mathcal{J}_C = \{ \emptyset \} \cup J(C)$ defines an ordinary topology on $y(C)$, and the second condition implies that we have a covariant functor
Some weeks ago I did register to be a participant of NaNoWriMo 2016. It’s a belated new-year’s resolution.
When PS (pseudonymous sister), always eager to fill a 10 second silence at family dinners, asked
(PS) And Lieven, what are your resolutions for 2016?
she didn’t really expect an answer (for decades my generic reply has been: “I’m not into that kinda nonsense”)
(Me) I want to write a bit …
stunned silence
(PS) … Oh … good … you mean for work, more papers perhaps?
(Me) Not really, I hope to write a book for a larger audience.
(PS) Really? … Ok … fine … (appropriate silence) … Now, POB (pseudonymous other brother), what are your plans for 2016?
If you don’t know what NaNoWriMo is all about: the idea is to write a “book” (more like a ‘shitty first draft’ of half a book) consisting of 50.000 words in November.
We’re 5 days into the challenge, and I haven’t written a single word…
Part of the problem is that I’m in the French mountains, and believe me, there always more urgent or fun things to do here than to find a place of my own and start writing.
A more fundamental problem is that I cannot choose between possible book-projects.
Here’s one I will definitely not pursue:
“The Grothendieck heist”
“A group of hackers uses a weapon of Math destruction to convince Parisian police that a terrorist attack is imminent in the 6th arrondissement. By a cunning strategy they are then able to enter the police station and get to the white building behind it to obtain some of Grothendieck’s writings.
A few weeks later three lengthy articles hit the arXiv, claiming to contain a proof of the Riemann hypothesis, by partially dismantling topos theory.
Bi-annual conferences are organised around the globe aimed at understanding this weird new theory, etc. etc. (you get the general idea).
The papers are believed to have resulted from the Grothendieck heist. But then, similar raids are carried out in Princeton and in Cambridge UK and a sinister plan emerges… “
Funny as it may be to (ab)use a story to comment on the current state of affairs in mathematics, I’m not known to be the world’s most entertaining story teller, so I’d better leave the subject of math-thrillers to others.
Here’s another book-idea:
“The Bourbaki travel guide”
The idea is to hunt down places in Paris and in the rest of France which were important to Bourbaki, from his birth in 1934 until his death in 1968.
This includes institutions (IHP, ENS, …), residences, cafes they frequented, venues of Bourbaki meetings, references in La Tribu notices, etc.
This should lead to some nice Parisian walks (in and around the fifth arrondissement) and a couple of car-journeys through la France profonde.
Here the advantage is that I have already a good part of the raw material. Of course it still has to be followed up by in-situ research, unless I want to turn it into a ‘virtual math traveler ’s guide’ so that anyone can check out the places on G-maps rather than having to go to France.
I’m still undecided about this project. Is there a potential readership for this? Is it worth the effort? Can’t it wait until I retire and will spend even more time in France?
Here’s yet another idea:
“Mr. Yoneda takes the Tokyo-subway”
This is just a working title, others are “the shape of prime numbers”, or “schemes for hipsters”, or “toposes for fashionistas”, or …
This should be a work-out of the sga4hipsters meme. Is it really possible to explain schemes, stacks, Grothendieck topologies and toposes to a ‘general’ public?
At the moment I’m re-reading Eugenia Cheng’s “Cakes, custard and category theory”. As much as I admire her fluent writing style it is difficult for me to believe that someone who didn’t knew the basics of it before would get an adequate understanding of category theory after reading it.
It is often frustrating how few of mathematics there is in most popular maths books. Can’t one do better? Or is it just inherent in the format? Can one write a Cheng-style book replacing the recipes by more mathematics?
The main problem here is to find good ‘real-life’ analogies for standard mathematical concepts such as topological spaces, categories, sheaves etc.
The tentative working title is based on a trial text I wrote trying to explain Yoneda’s lemma by taking a subway-network as an example of a category. I’m thinking along similar lines to explain topological spaces via urban-wide wifi-networks, and so on.
But al this is just the beginning. I’ll consider this a success only if I can get as far as explaining the analogy between prime numbers and knots via etale fundamental groups…
If doable, I have no doubt it will be time well invested. My main problem here is finding an appropriate ‘voice’.
At first I wanted to go along with the hipster-gimmick and even learned some the appropriate lingo (you know, deck, fin, liquid etc.) but I don’t think it will work for me, and besides it would restrict the potential readers.
Then, I thought of writing it as a series of children’s stories. It might be fun to try to explain SGA4 to a (as yet virtual) grandchild. A bit like David Spivak’s short but funny text “Presheaf the cobbler”.
Once again, all suggestions or advice are welcome, either as a comment here or privately over email.
Perhaps, I’ll keep you informed while stumbling along NaNoWriMo.
A fun way to teach first year students the different methods of proof is to play a game with chocolate bars, Chomp.
The players take turns to choose one chocolate block and “eat it”, together with all other blocks that are below it and to its right. There is a catch: the top left block contains poison, so the first player forced to eat it dies, that is, looses the game.
Let’s prove some results about Chomp illustrating the strengths and weaknesses of different methods of proof.
[section_title text=”Direct proof”]
By far the most satisfying method is the ‘direct proof’. Once you understand it, the truth of the statement is unescapable.
Theorem 1: The first player to move has a winning strategy for a $2 \times n$ chocolate bar.
Here’s the winning move: you take the lower right block!
What can the other player do? She can bring the bar again in rectangular shape of strictly smaller size (in which case you eat again the lower right block), or she can eat more blocks from the lower row (but then, after her move, you eat as many blocks from the top row bringing the bar again in a shape in which the top row has exactly one more block than the lower one. You’re bound to win!
Sadly, it is not always possible to prove what you want in such a direct way. That’s why we invented another tactic:
[section_title text=”Proof by induction”]
A proof by induction is less satisfactory because it involves a lot more work, but still everyone considers it as a ‘fair’ method: it shows how to arrive at the solution, if only you had enough time and energy…
Theorem 2: Given any Chomp position, either the first player to move has a winning strategy or the second player has one.
A proof by induction relies on simplifying the situation at hand. Here, each move reduces the number of blocks in the chocolate bar, so we can apply induction on the number of blocks.
If there is just one block, it must contain poison and so the first player has to eat it and looses the game. That is, here the second player has a winning strategy and we indicate this by labelling the position with $0$. This one block position is the ‘basis’ for our induction.
Now, take a position $P$ for which you want to prove the claim. Look at all possible positions $X$ you get after one move. All these positions have strictly less blocks, so ‘by induction’ we may assume that the result is true for each one of them. So we can label each of these positions with $0$ if it is a second player win, or with $\ast$ if it is a first player win.
How to label $P$? Well, if all positions in $X$ are labeled $\ast$ we label $P$ with $0$ because it is a second player win. The first player has to move to a starred position (which is a first player win) and so the second player has a winning strategy from it (by moving to a $0$-position). If there is at least one position in $X$ labeled $0$ then we label $P$ with $\ast$. Indeed, the first player can move to the $0$-position and then has a winning strategy, playing second.
Here’s the chart of the first batch of positions:
But then, it may take your lifetime to work through the strategy for a complicated starting position…
What to do if neither a direct proof is found, nor a reduction argument allowing a proof by induction? Virtually all professional mathematicians have no objection whatsoever to resort to a very drastic tactic: proof by contradiction.
[section_title text=”Proof by contradiction”]
The law of the excluded third (or ‘tertium non datur’) says that for any proposition $P$ either $P$ or not $P$ is true. In 1927 David Hilbert stated that not much of mathematics would remain without the use of this rule:
[quote name=”David Hilbert”]To prohibit existence statements and the principle of excluded middle is tantamount to relinquishing the science of mathematics altogether.[/quote]
Theorem 3: The first player has a winning strategy for a rectangular starting position.
We will prove this by contradiction. That is, we will assume that it is false, that is, the first player has not a winning strategy, and derive a contradiction from it. Therefore $\neg \neg P$ is true which is equivalent to $P$ by the law of the excluded
middle.
If the first player does not have a winning strategy for that rectangular chocolate bar, the second player must have one by Theorem2. That is, for every possible first move the second player has a winning response.
Assume the first player eats the lower right block.
The second player must have some winning response to this. Whatever her move, the resulting position could have been obtained by the first player already after the first move.
So, the second player cannot have a winning strategy.
This strategy stealing argument is a cheap cheat. We have not the slightest idea of what the winning strategy for the first player is or how to find it.
Still, one shouldn’t stress this fact too much to first year students. They’ll have to work through plenty of proofs by contradiction in the years ahead…
Sooner or later in their career they will hear arguments in favour of ‘constructive mathematics’, which does not accept the law of the excluded third.
Andrej Bauer has described was happens next. They will go through the five stages people need to come to terms with life’s traumatising events: denial, anger, bargaining, depression, and finally acceptance.
After 50 years, vivid interest in topos theory seems to have returned to one of the most prestigious research institutes, the IHES. Last november, there was the meeting Topos a l’IHES.
At the meeting, Celine Loozen filmed a documentary which is supposed to have as its title “Unifying Worlds”. Its very classy trailer is now on YouTube (via +David Roberts).
How did topos theory, a topic considered by most to be far too abstract to be useful to main stream mathematics, suddenly return in such force?
It always helps when a couple of world-class mathematicians become interest in the topic, for their own particular reasons. Clearly, the topic gathers considerable momentum if these people are all permanent members of the IHES.
A lot of geometric information is contained in the category of all sheaves on the geometric object. Topos theory offers a way to construct ‘geometries’ out of nothing, that is, out of arbitrary categories.
Take your favourite category $\mathbf{C}$, then “presheaves” on $\mathbf{C}$ are defined to be contravariant functors $\mathbf{C} \rightarrow \mathbf{Sets}$. For any Grothendieck topology on $\mathbf{C}$ one can then restrict to the sub-category of “sheaves” for this topology, and that’s your typical topos.
Alain Connes got interested in topos theory because he observed that even for the most trivial of categories, such as the monoid category with just one object and endomorphisms the multiplicative semigroup $\mathbb{N}_{\geq 1}^{\times}$, and taking the coarsest of all Grothendieck topologies, one gets interesting objects of baffling complexity.
One of the ‘invariants’ one can associate to a topos is its collection of “points”. Together with Katia Consani, Connes computed in Geometry of the Arithmetic Site that the collection of points of this simple presheaf topos is exactly the set of adele classes $\mathbb{Q}^{\ast}_+ \backslash \mathbb{A}^f_{\mathbb{Q}} / \hat{\mathbb{Z}}^{\ast}$.
Here’s what Connes himself said about this revelation (followed by an attempted translation):
——————————————————
(50.36)
And,in this example, we saw the wonderful notion of a topos, developed by Grothendieck.
It was sufficient for me to open SGA4, a book written at the beginning of the 60ties or the late fifties.
It was sufficient for me to open SGA4 to see that all the things that I needed were there, say, how to construct a cohomology on this site, how to develop things, how to see that the category of sheaves of Abelian groups is an Abelian category, having sufficient injective objects, and so on … all those things were there.
This is really remarkable, because what does it mean?
It means that the average mathematician says: “topos = a generalised topological space and I will never need to use such things. Well, there is the etale cohomology and I can use it to make sense of simply connected spaces and, bon, there’s the chrystaline cohomology, which is already a bit more complicated, but I will never need it, so I can safely ignore it.”
And (s)he puts the notion of a topos in a certain category of things which are generalisations of things, developed only to be generalisations…
But in fact, reality is completely different!
In our work with Katia Consani we saw not only that there is this epicyclic topos, but in fact, this epicyclic topos lies over a site, which we call the arithmetic site, which itself is of a delirious simplicity.
It relies only on the natural numbers, viewed multiplicatively.
That is, one takes a small category consisting of just one object, having this monoid as its endomorphisms, and one considers the corresponding topos.
This appears well … infantile, but nevertheless, this object conceils many wonderful things.
And we would have never discovered those things, if we hadn’t had the general notion of what a topos is, of what a point of a topos is, in terms of flat functors, etc. etc.
(52.27)
——————————————————-
Pierre Cartier has a very wide interest in mathematical theories, the wilder the better: Witt rings, motifs, cosmic Galois groups, toposes…
In this fragment of an interview with Stephane Dugowson and Anatole Khelif in 2014 he plays down his own role in the development of topos theory, compared to his contributions in other fields, such as motifs.
——————————————————-
(46:24)
Well, I didn’t invest much time in topos theory.
Except, I once gave a talk at the Bourbaki seminar on the use of topos theory in logic, such as the independence of the axiom of choice, that is, on the idea of forcing.
But, it was just this talk, I didn’t do anything original in it.
Then there is nonstandard analysis, where one can formulate certain things in terms of topos theory. When I got interested in nonstandard analysis, I had this possible application of topos theory in mind.
At the moment when you have a nonstandard model of the integers or more generally of set theory, then one has two models of set theory, that is two different toposes, and then one obviously tries to compare them.
In that sense, I was completely aware of the fact that everything I was doing could be expressed in the language of toposes,or at least in the philosophy of toposes.
I haven’t made any important contributions in that theory, for me it merely remained a tool.
(47:49)
——————————————————-
Laurent Lafforgue says he spend hundredths and hundredths of hours talking to Olivia Caramello about topos theory.
She must have been quite convincing. The last couple of years Lafforgue is a fierce advocate of Caramello’s work.
Her basic idea is that the same topos can arise from two very different mathematical settings (that is, two different categories with Grothendieck topologies can have equivalent categories of sheaves).
The hope then is to translate results from one theory to the other, or as she expresses it, toposes can be used as “bridges” between different mathematical topics.
At the moment though, is seems a bit far fetched for this idea to be relevant to the Langlands programme.
The paper is based on a lecture Lafforgue gave in April in Nantes. Here’s the video:
In the introduction they write:
“It is our conviction that the theory of toposes and their representations, with its essential and structural ambiguity, is destined to have an impact on mathematics comparable to the impact group theory has had from the moment, some decades after its discovery by Galois, the mathematical community began to understand it.”
Georges Maltsiniotis gave a talk at the Gothendieck conference in Montpellier in june 2015 having as title “Grothendieck’s manuscripts in Lasserre”, raising perhaps even more questions.
In chapter 46 “Que reste-t-il du tresor de Grothendieck?” (what is left of Grothendieck’s treasure?) he recounts what has happened to the ‘Lasserre gribouillis’ and this allows us to piece together some of the jigsaw-puzzle.
Maltsiniotis’ talk
These days you don’t have to be present at a conference to get the gist of a talk you’re interested in. That is, if at least one of the people present is as helpful as Damien Calaque was in this case. A couple of email exchanges later I was able to get this post out on Google+:
Below is the relevant part of the picture taken by Edouard Balzin, mentioned in the post.
The first three texts are given with plenty of details and add up to say 5000 pages. The fifth text is only given the approximate timing 1993-1998, although they present the bulk of the material (30000 pages).
A few questions come to mind:
– Why didn’t Maltsiniotis give more detail on the largest part of the collection?
– There seem to be at least 15000 pages missing in this roundup (previously, the collection was estimates at about 50000 pages). Were they destroyed?
– What happened to the post-1998 writings? We know from a certain movie that Grothendieck kept on writing until the very end.
Douroux’ book
If you have read Scharlau’s biographical texts on Grothendieck’s life, the middle part of Douroux’ book “Alexandre Grothendieck, sur les traces du dernier genie des mathematiques” will not be too surprising.
However, the first 5 and final 3 chapters contain a lot of unknown information (at least to me) about his life in Lasserre. The story of ‘his last friend Michel’ is particularly relevant.
Michel is a “relieur” (book-binder) and Grothendieck used his services to have carton boxes made, giving precise specifications as to their dimensions in mms, to contain his writings.
In the summer of 2000 there’s a clash between the two, details in chapter 4 “la brouille du relieur”. As a result, all writings from 2000-2014 are not as neatly kept as those before.
Each box is given a number, from 1 to the last one: 41.
In chapter 46 we are told that Georges Maltsiniotis spend two days in Lasserre consulting the content of the first 16 boxes, written between 1992 and 1994. He gives also additional information on the content:
Carton box 1 : “Geometrie elementaire schematique” contains 1100 pages of algebra and algebraic geometry which Maltsiniotis classifies as “assez classique” but which Douroux calls ‘this is solid mathematics on which one has to work hard to understand’ and a bit later (apparently quoting Michel Demasure) ‘we will need 50 years to transform these notes into accessible mathematics’.
Carton boxes 2-4 : “Structure de la psyche” (3700 pages) also being (according to Douroux) ‘a mathematical text in good form’.
Carton boxes 5-16 : Philosophical and mystical reflexions, among which “Psyche et structure” and “Probleme du mal” (7500 pages).
That is, we have an answer to most of the questions raised by Maltsiniotis talk. He only consulted the first 16 boxes, had a quick look at the other boxes and estimated they were ‘more of the same’ and packaged them all together in approximately 30000 pages of ‘Probleme du mal’. Probably he underestimated the number of pages in the 41 boxes containing all writings upto the summer of 2000.
Remains the problem to guess the amount of post 2000 writings. Here’s a picture taken by Leila Schneps days after Grothendieck’s death in Lasserre:
You will notice the expertly Michel-made carton boxes and a quick count of the middle green and rightmost red metallic box reveals that one could easily pack these 41 carton boxes in 3 metallic cases.
So, a moderate guess on the number of post 2000 pages is : 35000.
Why? Read on.
What does this have to do with the Paris attacks?
November 13th 2015 is to the French what 9/11 is to Americans (and 22 March 2016 is to Belgians, I’m sad to add).
It is also precisely one year after Grothendieck passed away in Saint-Girons.
On that particular day, the family decided to hand the Grothendieck-collection over to the Bibliotheque Nationale. (G’s last wishes were that everything he ever wrote was to be transferred to the BNF, thereby revoking his infamous letter of 2010, within 7 months after his death, or else had to be destroyed. So, to the letter of his will everything he left should have been destroyed by now. But fortunately none of it is, because 7 months is underestimating the seriousness with which the French ‘notaires’ carry out their trade, I can testify from personal experience).
While the attacks on the Bataclan and elsewhere were going on, a Mercedes break with on board Alexandre Jr. and Jean-Bernard, a librarian specialised in ancient writings, was approaching Paris from Lasserre. On board: 5 metallic cases, 2 red ones, 1 green and 2 blues (so Leila’s picture missed 1 red).
At about 2 into the night they arrived at the ‘commissariat du Police’ of the 6th arrondissement, and delivered the cases. It is said that the cases weighted around 400 kg (that is 80kg/case). As in all things Grothendieck concerned, this seems a bit over-estimated.
Anyway, that’s the last place we know to hold Grothendieck’s Lasserre gribouillis.
There’s this worrying line in Douroux’ book : ‘Who will get hold of them? The BNF? An american university? A math-obsessed billionaire?’
Let’s just hope for the best. That the initial plan to open up the gribouillis to the mathematical community at large will become a reality.
If I counted correctly, there are at least two of these metallic cases full of un-read post 2000 writings. To be continued…
Michele Audin has written a book on the history of the Julia seminar (hat tip +Chandan Dalawat via Google+).
The “Julia Seminar” was organised between 1933 and 1939, on monday afternoons, in the Darboux lecture hall of the Institut Henri Poincare.
After good German tradition, the talks were followed by tea, “aimablement servi par Mmes Dubreil et Chevalley”.
A perhaps surprising discovery Audin made is that the public was expected to pay an attendance fee of 50 Frs. (approx. 32 Euros, today), per year. Fortunately, this included tea…
The annex of the book contains the lists of all people who have paid their dues, together with their home addresses.
The map above contains most of these people, provided they had a Parisian address. For example, Julia himself lived in Versailles, so is not included.
As are several of the first generation Bourbakis: Dieudonne lived in Rennes, Henri Cartan and Andre Weil in Strasbourg, Delsarte in Nancy, etc.
Still, the lists are a treasure trove of addresses of “les vedettes” (the professors and the people in the Bourbaki-circle) which have green markers on the map, and “les figurants” (often PhD students, or foreign visitors of the IHP), the blue markers.
Several PhD-students gave the Ecole Normale Superieure (btw. note the ‘je suis Charlie’-frontpage of the ENS today jan.9th) in the rue d’Ulm as their address, so after a few of them I gave up adding others.
Further, some people changed houses over this period. I will add these addresses later on.
The southern cluster of markers on Boulevard Jourdan follows from the fact that the university had a number of apartment blocks there for professors and visitors (hat tip Liliane Beaulieu).
A Who’s Who at the Julia seminar can be found in Audin’s book (pages 154-167).
