## April 26, 2012

### The Mathematics of Biodiversity

#### Posted by Tom Leinster

Interested in biological diversity? Want to know more about how diversity can be quantified? Maybe diversity comes up in your work. Maybe you’ve heard rumours that there’s serious mathematics involved, and you want to know more. Or maybe you’re just curious.

If so, come to a meeting in Barcelona! It’s running 2-6 July, and there are grants to cover attendance expenses. (If you want one, please apply as soon as possible.) We also have free slots for contributed talks.

We’ve assembled what is already a head-spinningly varied group of people, from livestock breeding experts to ostensibly pure mathematicians to evolutionary ecologists. Two or three of your Café hosts will be there. Details follow.

## April 25, 2012

### PSSL 93 trip report

#### Posted by Mike Shulman

I just got back from an excellent trip to the U.K., which started with my first visit ever to Wales, continued with my second PSSL, and concluded with my first ever visit to Scotland (thanks Tom!). Homotopy type theorists may be interested to have a look at my slides from Swansea (and also the slides from a seminar we had at UCSD last quarter), but I won’t say any more about that now. Instead I want to discuss briefly several of the PSSL talks.

## April 23, 2012

### Principal ∞-Bundles

#### Posted by Urs Schreiber

I have been speaking about *principal ∞-bundles* in an $\infty$-topos for a while now, in print starting around the article

- Hisham Sati, Urs Schreiber, Jim Stasheff,
*Twisted differential String- and Fivebrane structures*.

Last year Thomas Nikolaus and myself visited Danny Stevenson in Glasgow. We labored day and night for two weeks with the aim to compile an article with a comprehensive account of the matter. As it goes with these glorious plans, they don’t fit the intended time schedule, and so we find ourselves still working on the article these days, always almost finished. At least Danny has meanwhile put a major piece of his on the arXiv, which we are making use of:

Danny Stevenson,

*Classifying theory for simplicial parametrized groups*David Roberts, Danny Stevenson,

*Simplicial principal bundles in parametrized spaces*.

See below the fold for an abstract of what we are after now.

While we are not done yet with typing, next week I will speak about the subject (to an audience of topologists). I decided to prepare something like a first-order talk script, possibly usable as a pdf-handout, which gives a concise overview of what it’s all about, what the main theorems are and what the impact on applications is. I still have a bit of time to fine-tune this, but since some feedback can be useful for this, I am hereby posting these notes:

*Principal $\infty$-bundles – Theory and applications*, pdf-handout notes.

I’d be interested in hearing whatever comments you might have.

There is a little table on page 5, which indicates something that I am fond of, and which I have been talking about here on the $n$Café in various guises every now and then. It tabulates examples of $\infty$-bundles of smooth moduli $\infty$-stacks and indicates what happens when you interpret these as universal associated coefficient bundles for nonabelian cohomology. Due to size limitations of a “handout”, this table is a small piece of a more extensive table, which is discussed in section 4.4

- Urs Schreiber,
*differential cohomology in a cohesive topos*.

Along the lines of such a “table of twists” I will probably also give the lectures at ESI in a few weeks.

### 10,000

#### Posted by Tom Leinster

Ten thousand people have joined The Cost of Knowledge boycott.

## April 20, 2012

*Higher Structures in Topology and Geometry VI*

#### Posted by Urs Schreiber

This July takes place in Göttingen the next *Higher Structures* meeting

Courant Research Centre workshop
**Higher Structures in Topology and Geometry VI**

July 9-11

Göttingen, Germany.

www.crcg.de/wiki/HSTG6

The invited speakers are

The workshop will consist of mini-courses given by the invited speakers plus a small number of shorter talks given by participants. Limited funds are available, in particular for phd students and postdocs. The deadline for registration is June 15.

### Teleparallel Gravity as a Higher Gauge Theory

#### Posted by John Baez

It’s finally done! Let me say a bit about it:

- John Baez and Derek Wise, Teleparallel gravity as a higher gauge theory.

Abstract.We show that general relativity can be viewed as a higher gauge theory involving a categorical group, or 2-group, called the teleparallel 2-group. On any semi-Riemannian manifold $M$, we first construct a principal 2-bundle with the Poincaré 2-group as its structure 2-group. Any flat metric-preserving connection on $M$ gives a flat 2-connection on this 2-bundle, and the key ingredient of this 2-connection is the torsion. Conversely, every flat strict 2-connection on this 2-bundle arises in this way if $M$ is simply connected and has vanishing 2nd deRham cohomology. Extending from the Poincaré 2-group to the teleparallel 2-group, a 2-connection includes an additional piece: a coframe field. Taking advantage of the teleparallel reformulation of general relativity, in which a coframe field, a flat connection and its torsion are the key ingredients, this lets us rewrite general relativity as a theory with a 2-connection for the teleparallel 2-group as its only field.

## April 19, 2012

### Mathematical Cultures

#### Posted by David Corfield

My friend and fellow philosopher Brendan Larvor mentioned an upcoming conference in September 2012 in London. This is the first of a series of three on Mathematical Cultures.

The first conference will gather research that explores and maps the variety of and connections among contemporary mathematical cultures. These can be research cultures, but may also include practitioner cultures (e.g. among engineers, economists, social scientists, etc.) and mathematical cultures among instructor and student groups (e.g. primary/secondary/tertiary teachers, school pupils, mathematics students at all levels). The project will not invite contributions on historically or culturally remote mathematical cultures except as these illuminate contemporary mathematical culture in developed societies.

Confirmed speakers include two professional mathematicians, Alexandre Borovik and Norbert Schappacher. There is a call for papers with a deadline of 1 ~~June~~ May 2012.

Perhaps it’s time to dust down the material I was collecting on the two cultures.

## April 16, 2012

### Research Network *String Geometry*

#### Posted by Urs Schreiber

We had applied with the *DFG* – the *German Research Foundation* – for a research network on *String Geometry*. They have granted it, see:

**Research Network String Geometry**
.

This is about the higher differential geometry of *string structures* and *differential string structures*.

A more detailed project discription is at the above webpage behind the link *Mission*.

The network members are Bas Janssen, Thomas Nikolaus, Ulrich Pennig, Konrad Waldorf, Christoph Wockel and myself.

We’ll now have get-togethers with invited guests and talks and discussion every now and then, which will be listed at the above webpage here. The first meeting is in May, at Hamburg University (probably without invited guests yet) featuring a reading course on index theory and talks on the foundations of String geometry.

I’ll try to report here on whatever report-worthy there may be.

*CATS 4*

#### Posted by Urs Schreiber

This summer at CIRM in Luminy takes place the meeting

**CATS 4**
*Higher Categorical Structures and their Interactions with Algebraic Geometry, Algebraic Topology and Algebra*

at CIRM, Luminy, 2-7 July 2012 .

See the *conference webpage*. (However, besides the list of speakers reproduced below, there is not a whole lot of information there, currently. But at least it does feature a joke about higher stacks.)

## April 9, 2012

### Wellcome Joins In

#### Posted by Tom Leinster

I just looked at the front page of The Guardian, a quality British newspaper that’s especially widely read online… and I was amazed to see that their second-leading story was on The Cost of Knowledge:

The news is that the Wellcome Trust — which Wikipedia says is “the United Kingdom’s largest non-governmental source of funds for biomedical research”, and the Guardian says is “one of the world’s largest funders of science” — is throwing its weight behind the movement. Among other things:

Sir Mark Walport, the director of Wellcome Trust, said that his organisation is in the final stages of launching a high calibre scientific journal called eLife that would compete directly with top-tier publications such as Nature and Science, seen by scientists as the premier locations for publishing. Unlike traditional journals, however, which cost British universities hundreds of millions of pounds a year to access, articles in eLife will be free to view on the web as soon as they are published.

There’s also a story on how Tim Gowers (looking dashing as ever in front of ornate Cambridge architecture) started the current upsurge.