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Michi’s blog » archive for March, 2006

 This is me losing all faith in Non-Linear Analysis

  • March 28th, 2006
  • 12:30 pm

A paper recently up on arXiv details the errors committed by an author of a paper in Non-Linear Analysis, who, by ignoring basic conditions of theorems manages to prove most of mathematics and substantial parts of physics inconsistent.

This is the second insufficiently reviewed paper at that Journal causing some sort of waves spreading as far as to me so far. The blogospheric and medial storm around the infamous “proof” by Elin Oxenhielm of the 16th Hilbertian problem a few years ago was, at the core, sparked from her getting the paper accepted at … right, Non-Linear Analysis … and taking this publication as a token that her results were in fact true and anyone critizising here were out to steal her credit.

Needless to say, with the density displayed thus far of crackpotism and sloppy publishing, I don’t think I’ll trust NLA for anything at all in the future.

 Report from Villars (5 in a series)

  • March 12th, 2006
  • 12:12 pm

For the last two half-days of the conference, I managed to take a break in skiing precisely when the conditions were at their very worst; with sight down to a few meters and angry winds. Miles Gould and Arne Weiner, however, managed to sit in a chair lift that kept stopping every 5 meters – AND they managed to break a T-bar lift. Suddenly the rope broke, they told me, and they had to ski down to the warden with the T-bar in the hand.

First out in this mathematical expose, though, is André Henriques, talking about

An operad coming from representation theory

There is a way to connect to a finite Lie algebra \mathfrac g first it’s universal enveloping algebra U\mathfrac g and quantum groups U_q\mathfrac g. From representations of U_q\mathfrac g, one path leads on over braided tensor products to braided tensor categories. Such categories are described by E_2 operads, which occur in the study of Gerstenhaber algebras and their homology.

 Report from Villars (4 in a series)

  • March 8th, 2006
  • 2:09 pm

I haven’t been able to get around to skiing since the last update – I may, or may not, go out in the slopes after this updates. The weather is growing warmer and wetter; and doesn’t really invite to skiing as it previously did.

However, we have had more talks. First out, yesterday evening, was Pascal Lambrechts

Coformality of the little ball operad and rational homotopy types of spaces of long knots

The theme of interest for this talk was long knots; i.e. embeddings of \mathbb R into \mathbb R^d such that outside some finite region in the middle, the embedding agrees with the trivial embedding t\mapsto(t,0,0,\dots,0). The space of all such is denote \mathcal L, and the item of study is more precisely the rational homology and rational homotopy of the fiber of the inclusion of \mathcal L into the space of all immersions of \mathbb R into \mathbb R^d.

 Report from Villars (3 in a series)

  • March 7th, 2006
  • 4:29 pm

This post will concern tuesday morning. Tuesday evening will be in a later post.

With the morning thus came, again, the pain in the legs. However, I’m told it’ll be better if I keep on skiing.

The mathematics in this report will come sooner than in the last; mainly because the lectures start at 8.30 and not at 17.00. :)

First out is Bênoit Fresse with

Little cubes operad actions on the bar construction of algebras

The reduced bar construcion of augmented associative algebras is given by fixing a field F, and for an augmented associative algebra A giving a chain complex B(A) such that B_n(A)=\hat A^{\otimes n} where \hat A denotes the augmentation ideal of A with the differential \partial(a_1\otimes\dots\otimes_n)=\sum_{i=1}^{n-1}a_\otimes\dots\otimes a_ia_{i+1}\otimes\dots\otimes a_n

If the product of A is commutative, then the shuffle product of tensors provides B(A) with the structure of a differential commutative algebra. In the talk, Fresse starts looking at the algebraic structure of B(A) for algebras with a homotopy commutative algebra:

 Report from Villars (2 in a series)

  • March 6th, 2006
  • 11:07 pm

So we hit the pistes during monday morning, those of us who actually already are here. Me, Bruno Vallette (Hi Stockholm!), Arne Weiner, Miles Gould, Paul Eugene Parents and Jonathan Scott, Dev Sinha and Muriel Livernet. Skiing was MARVELOUS. Me, Arne and Miles shot off on our own, and damn did we have a good time.

As I’m writing this, they’re still out there – I went back when the pain in my legs caused tears in my eyes for just turning on the skis. The techniques were solid as concrete. The muscles not so much. It took half an hour in the sauna to get to the point where I actually was able to walk again.

 Report from Villars (1 in a series)

  • March 5th, 2006
  • 8:37 pm

So, I’ve arrived in Villars sur Ollon for the Alpine Operad Workshop. The travel was long and at times annoying, mainly because the heavy snowfall over München and Zürich and some other places in the region triggered extreme delays. As we were supposed to board, the poor attendant at Nürnberg airport told us that the plane had not yet departed from Zürich.

Except for that, though, the travel went fine, and after being treated to some immensely beautiful views (glittering lake of Genéve with rows and rows of snowcovered grapevines in front, anyone?) and reminded of just how much I miss the deep-snow winters, I got up on this mountain in southwestern (very much frenchspeaking) Switzerland to the Hotel du Golf. The receptionist told me, straight off, that a number of my colleagues had already arrived, and then I went to eat (Crêpes – expensive and not even correctly delivered…) and started wrestling the connector dance. Y’see, half of the connectors used in civilized Europe work here. The other half don’t. And those who do work, only do work if they’re impeccably straight. So I had to work for quite a while to actually, y’know, get my laptop, my mp3player, my loudspeakers (I sleep with music, mmmkay? Headphones are NOT very nice to sleep in, mmmkay?) and my cell phone all connected. I think I disconnected 75% of the room lights in the process.