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Anthony Leverrier
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Anyone who's studied quantum mechanics knows that the subject is largely about pairs of linear operators, a and a⁺, such that:

aa⁺ = a⁺a+1

Solving physics problems often involves rearranging expressions in a and a⁺ so that all of the a⁺ factors are on the left of each monomial and the a factors are on the right. This sort of thing:

= (a⁺a+1)aa⁺a⁺a⁺aa⁺a
= a⁺aaa⁺a⁺a⁺aa⁺a+aa⁺a⁺a⁺aa⁺a
= ...
= a⁺⁵a⁴+10a⁺⁴a³+23a⁺³a²+9a⁺²a

Getting to the last line takes a substantial amount of work and of course it gets worse when you have infinite sums.

But now I've read I see that there's a much easier way of getting those coefficients: 1, 10, 23, 9.

You can translate a monomial in a and a⁺ into a path on a grid by drawing a⁺ as a horizontal line and a as a vertical line, as in the diagram. That defines a region under the path known as a Ferrers board.

1 is the number of ways of placing zero non-attacking rooks on this Ferrers board. 10 is the number of ways of placing 1 rook, 23 is the number of ways of placing 2 rooks and so on.

I can't believe I've gone all these years without coming across this simple interpretation of the coefficients before.

It's worth reading the proof in the paper. The expression aa⁺ = a⁺a+1 corresponds precisely to a single step in a recursive procedure for counting rook placements.

This is just a tiny hint of the richness of the combinatorics of a and a⁺.

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Maltsiniotis' talk on Grothendieck's Lasserre-gribouillis   #Grothendieck

Yesterday, George Maltsiniotis gave a talk at the Gothendieck conference in Montpellier with title "Grothendieck's manuscripts in Lasserre" [1].

This morning, +David Roberts  asked for more information on its content, and earlier i gave a short reply on what i learned [2], but perhaps this matter deserves a more careful write-up.

+Damien Calaque  attended George's talk and all info below is based on his recollections. Damien stresses that he didn't take notes so there might be minor errors in the titles and order of the parts mentioned below.

EDIT: based on info i got from +Pieter Belmans  in the comments below (followed up by the picture he got via +Adeel Khan  taken by Edouard Balzin) i've corrected the order and added additional info.

 The talk was videotaped and should become public soon.

As i mentioned last week [3] Grothendieck's family has handed over all non-family related material to the Bibliotheque Nationale. Two days ago, Le Monde wrote [4] that the legacy consists of some 50.000 pages.

Maltsiniotis insisted that the BNF wants to make these notes available to the academic community, after they made an inventory (which may take some time).

I guess from the blackboard-picture i got from Pieter, the person responsible at the BNF is Isabelle le Masme de Chermont [7].

The Lasserre-griboillis themselves consists of 5 parts:

1. Géométrie élémentaire schématique. (August 1992)
This is about quadratic forms and seems to be really elementary.

2. Structure de la psyché. (12/10/1992-28/09/1993) 3600 pages
This one is about some combinatorics of oriented graphs with extra-structure (part of the structure are successor and predecessor operators on the set of arrows).

3. Psyché et structures (26/03/93-20/06/93) 700 pages
This one is non-mathematical.

4. Maxwell equations.
Maltsiniotis mentioned that he was surprised to see that there was at best one mathematics book in G's home, but plenty of physics books.

5. Le problème du mal. (1993-1998) 
This one is huge (30.000 pages) and is non-mathematical.

Note that also the Mormoiron-gribouillis will be made public by the University of Montpellier, [5] or if you prefer video [6].

Finally, is the photo below what you think it is? Yep!

[1] :
[2] :
[3] :
[4] :
[5] :
[6] :
[7] :

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Bimal Roy was, until a few days ago, the director of the Indian Statistical Institute, a graduate institute based in Kolkata. He is well-known in cryptography for his work on block ciphers. He was also awarded the Padma Shri last year, one of the highest civilian awards in India. 

My interactions with him were limited, but I have generally been impressed by the huge summer internship program for Indian undergraduates that he runs at ISI. 

Roy was just removed from his position by the Ministry of Statistics and Programme Implementation, citing concerns about potential "indiscipline". The reasons are almost comically vague:

"A number of general and specific matters of financial and administrative irregularities which show the direct or supervisory responsibilities for acts of omission or commission on the part of the present Director, Prof. B. Roy are available in the Ministry in the various files on the different subjects. "

Below is an account of the events leading up to his dismissal written by Roy's colleague and former Ph.D. student, Sushmita Ruj. I copy her email here verbatim.

I don't know the facts of the story, but I am inclined to believe Sushmita's account. The lack of transparency should be especially troubling for academics, in India and elsewhere. 


This is Sushmita Ruj, writing from the Cryptology group of Indian Statistical Institute, Kolkata.

Professor Bimal Roy, the leader of our group, has been removed from the post of Director of the Indian Statistical Institute with a special emergency order issued by out governing Ministry (MoS&PI) on 10 June 2015. He was about to complete his five year term as Director on 31 July 2015.

The Ministry has expressed its apprehension that Prof. Bimal Roy may indulge in "propagation of indiscipline and mischief, including acts of financial and administrative impropriety" if he continues as the Director. However, neither has it put forward any formal charge against Prof. Roy, nor has it offered him the basic courtesy to defend himself before the decision was taken. There was no show-cause served to Prof. Roy at all, and the grounds for the decision seem quite fragile:

As we understand, this drastic decision from the Ministry is orchestrated by the Chairman of our Institute, Mr. Arun Shourie, who allegedly tried to coerce Prof. Bimal Roy into signing the proceedings of our last Council Meeting, in which the selection of the new Director of the Institute was considered. Allegedly, the drafted proceedings of the meeting was substantially different from the actual incidents at the meeting, especially on the issue of the selection of the new Director, and hence Prof. Roy refused to sign the proceedings. This is the only issue that may have been considered as "indiscipline" on Prof. Roy's part, as far as we know.

To verify the truth in this matter, a senior Professor of our Institute filed a written petition (RTI) to obtain the audio recording of the meeting, and the hearing of the RTI was due on 11 June 2015. It is quite an amazing coincidence that the Ministry took the decision of stripping Prof. Bimal Roy of all his powers as the Director just the night before, in the afternoon of 10 June 2015. Not to mention, the RTI hearing has been postponed at once. This raises a strong suspicion that the Ministry, supporting the Chairman of the Institute, is aiming at suppressing the audio recording of the meeting to avoid a transparent investigation into the matters at hand.

Professor Bimal Roy has dedicated his life for services to the Nation, and this is not what he deserves from the Institute which has gained from his leadership in the last five years more than it probably has under the leadership of any other Director in the recent times. Prof. Roy, and our Institute, deserves a transparent independent public investigation. The audio recording and proceedings of the Council meeting should be released and investigated by independent authorities. Prof. Roy should be offered a chance for a fair trial, independent of the actions by the Ministry, and till the investigation is over, Prof. Roy should be reinstated as the Director of our Institute, till 31 July 2015, the end of his rightful term. At the end of his term, Prof. Bimal Roy deserves a vote of thanks from the Council for his services to the Institute during the last five years, and not a humiliating send-off. This is simply unacceptable!

If you support the cause, and want justice for Prof. Bimal Roy, please convey your thoughts to the Hon'ble President of India at the following email IDs.     
Public Grievance Cell : Mr. Purushottam Dass   
Private Secretary to the President : Mr. Rajneesh   
Private Secretary to the President : Mr. Pradeep Gupta

You may also write directly to the Hon'ble Prime Minister of India through the online portal at :

I request you to propagate the news in the concerned academic community, government organizations and public media that you deem suitable, and sign-and-share the online petition supporting the cause.

It will be nice to have the community support Prof. Bimal Roy in these dire times. Please feel free to write to him directly as well.


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Lost World. A pristine wilderness in the island of New Guinea first investigated as recently as 2005, turns out to be a “megadiverse hotspot” of strange new creatures.

The Pinocchio frog male sports a protuberance on his nose that points up when he is energetically calling out, but deflates when he is less excited :) "Exactly what it is for, no one really knows for sure", says Paul Oliver.

The smallest living vertebrate has just been found! As reported in yesterday’s issue of PLoS ONE , it is a frog that measures only 7.7 mm long, just beating out a previously known small fish that measured 8 mm. To compensate for its diminutive size, it has been given a long name: Paedophryne amanuensis is one species. The male’s call resembles the chirping of a cricket,extending only 50 cm to the neighboring frog living under the leaf litter of the forest.

Other strange animals include the smallest wallaby (described as “a gentle creature”), a huge wooly rat (“rather tame”), an unusually colorful pigeon that was caught gawking at the mating ritual of bower-birds (“voyeuristic behavior”; I am not making this up), and a “gargoyle-faced” gecko (I disagree; it looks just as handsome as any other gecko, IMO).

Something to think about : vertebrate sizes vary by 3000 fold, from these tiny <10 mm frogs to the blue whale that averages 26 m. Scientists had assumed that only aquatic habitats supported extreme sizes, but this turns out not to be true. Extreme miniaturization means that all sorts of developmental compromises have to be made. For example, these frogs have fewer toes. Researchers are thrilled by their new find because “such discoveries are increasingly critical in this time of global amphibian declines and extinctions” .

PLoS ONE paper (open access):

Lost World story:
4 Photos - View album

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