One of the perks of working in mathematics is that I get to travel the world as part of my job. This time it was Cape Town, South Africa; I flew down there to participate in a workshop on maths `outreach' activities in Africa. The workshop was held at the African Institute for Mathematical Sciences (AIMS) and was organised in partnership with IMAGINARY. Will introduce the organisers in a bit but let me focus on the idea of mathematics outreach for now.

For me, mathematics outreach is an attempt to share mathematical ideas with non-experts in the field. The term non-expert includes a broad spectrum of people stretching from school children to senior citizens. Math-outreach is usually done through exhibitions and the written media but the definition allows for many more forms of communication. Why one would care about such efforts varies from person to person and may change depending on the audience. There is always the diplomatic, politically correct cause, that is, getting more elements of society involved in the mathematics reaps rewards. I guess one can dig up statistics to that support an argument of the form: a mathematically savvy population is a route to economic growth. However, the reason why I am interested in this are a little more selfish. I love mathematics! As with most things we enjoy, we get a warm fuzzy feeling from sharing them with others. It is especially amazing when you strike a chord with somebody. Mathematics outreach gives me a chance to share this passion of mine with the world.

Back to the organisers of the workshop. The AIMS centre in South Africa is part of an expanding network of AIMS centres operating under the Next Einstein Initiative. There are currently five such centres. Each centre has a teaching arm which runs a master's degree programme, as well as a section devoted to research. They also have a division devoted to community development which, at the moment, focuses on in-job teacher training. IMAGINARY, the other organisers, are a very cool institution; they define themselves as "a platform for open and interactive mathematics". Their activities range from setting up maths exhibitions around the world to developing fun mathematics software applications. I would highly recommend visiting their website and playing with some of their programs. Better still, if you are at the ICTP, you could mess around with software by IMAGINARY on our maths section touch-screen. Until very recently, IMAGINARY have not organised any events in Africa. This workshop was an attempt to fix this.

Both of these institutions share common goals with our ICTP. Carlo Fonda, from our SciFabLab, and I were meant to represent the ICTP at the workshop. The plan was to run a session in which we give an introduction to 3D-printing mathematical objects at a low cost. We would demonstrate the techniques live using one our 3D-printers. Unfortunately, we had to cancel our part of the workshop because Carlo had some last minute passport related complications.

Fortunately for me, the workshop was very interactive so I didn't feel left out. It was very different from your standard mathematics conference where the focus is usually on talks; where some people spoke, the others listened and interaction was mainly reserved for coffee breaks and meal times. Here everybody got their hands dirty. We drew up plans for a mathematics exhibition at the, soon to become, AIMS building in Bagamoyo, Tanzania. A web-forum was created to communicate all aspects of mathematics in Africa, including jobs, exhibitions, blog posts. My favourite thing about it is its name, it is called mathemafrica.org. We pooled our mutual knowledge about the status quo of mathematics outreach in Africa and shared tips on writing funding proposals. There was also a session where Marcos Cherinda, a researcher in ethnomathematics based in Mozambique, spoke to us about the mathematics involved in twill weaving. We all had a go at weaving a sphere, with varying degrees of success I must add. A more comprehensive review of these workshops and the others I failed to mention will hopefully be available at the IMAGINARY website (excuse the pun) soon.

All the positive energy coming out of this meeting is all well and good. However, its success can only be measured through the actions stemming from it. Will this exhibition in Tanzania ever happen? Will mathemadrica.org take-off? Only time will tell. We scheduled another AIMS-IMAGINARY workshop to be held in Senegal in October of next year to examine the various outcomes of this meeting. For now, our duty is to make sure that by then these questions have positive answers.

*The photo is Prof. Diane Wilcox of Wits University with her weaved sphere.*

His first slide includes the surprising list:

* theorems, laws, social norms and practices, art and culture, *

all examples of what he called "public knowledge", words I never expected to appear together in the same phrase.

He also described the Fields medal (which were going to be awarded the day after) and similar prizes as an "amazingly cheap way to produce knowledge".

Overall a remarkable and thought-provoking lecture.

]]>* The rumours are true: the editors which in 2007 resigned from the journal K-Theory have now resigned from the splinter journal they helped set up, Journal of K-Theory, to start a third journal, Annals of K-Theory. What a headache!*

Have a look at the whole post. Interesting times indeed.

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Read all about it!]]>
*"The Misfortunes of a Trio of Mathematicians Using Computer Algebra Systems. Can We Trust in Them?"* linked in the article.

Determinants? Really?

]]>It doesn't take much to suspect an e-mail addressed to a number theorist that claims:

*
given your expertise in the area of supply chain dynamics, disruption
management, resilience, and control, we cordially invite to submit a paper
to a Special Issue on Supply Chain Dynamics, Control and Disruption
Management in IJPR with the NEW submission deadline by JULY 15, 2014.
*

I typically just took it as yet more spam to have to deal with.

As it happens things can be nastier than that. I quote from the Wikipedia page on predatory publishing

*
"In academic publishing, some publishers and journals have attempted to exploit the business model of open-access publishing by charging publication fees to authors without providing the editorial and publishing services associated with more established and legitimate journals (open access or not)."*

*
*
As if things were not already hard enough for researchers struggling to have their work published in reputable journals.

I heartily recommend the Wikipedia article as well as the editorial by B. Teissier in the EMS newsletter discussing the issue further.

]]>"The existence of a contact structure is proved in any homotopy class of almost contact structures on a closed 5-dimensional manifold." The work, a substantial 47 pages long, underwent a long and rigorous refereeing process, and is regarded as a major milestone. Dishant Pancholi was with ICTP as a postdoc during 2008 and 2009, and is now Associate Professor at the Chennai Mathematical Institute. He is also a Simons Associate of ICTP.

We invited Dishant to tell us more, and here is what he wrote:

A contact structure on a manifold M is a maximally non-integrable codimension one distribution. (A distribution is a sub-bundle of the tangent bundle; a distribution is integrable if given any two vector fields that are sections of the sub-bundle, their Lie bracket is also a section of the sub-bundle. We will not define the notion of "maximally nonintegrable".)

Contact geometry is closely related to symplectic geometry. The study of contact structures is at the forefront of current research in geometric topology because of the intimate relationship with subjects like complex and Kaehler geometry. In 1966, S.S. Chern posed the question: under which condition(s) does a manifold M admit a contact structure? A necessary condition is that the manifold should admit a codimension one distribution that has a structure of a complex vector bundle. (In particular the dimension of M must be odd.)

Such manifolds are now known as almost contact manifolds. M. Gromov showed (using his h-principle philosophy) that any open (that is, non-compact) almost contact manifold is in fact contact.

As for closed (that is, compact and without boundary) manifolds, the first breakthrough came in the seventies and was due to R. Lutz and J. Martinet. They established that any orientable three manifold admits a contact structure. At around the same time, D. Bennequin discovered invariants that distinguished contact structures.

In late eighties and early nineties Y. Eliashberg greatly generalized these constructions to show that every homotopy class of codimension one distribution on a closed 3-manifold admits a unique "overtwisted" contact structure.

Despite the complete answer to Chern's question in dimension three, not much was known in higher dimensions. The most notable advance was due to H. Geiges who showed that a simply connected manifold admits a contact structure if and only if the Stieffel-Whitney class W_3 with integral coefficient is zero.

After joining ICTP as a post-doc (in January 2008) I started working on the problem of constructing contact structure on closed manifolds of dimension higher than three. John Etnyre (whom I visited using my travel grant as ICTP post-doc) and I generalized the Lutz's construction to higher dimension. This enabled us to construct new contact structures out of existing ones.

On the other hand, Fran Presas and others generalized a technique due to S. Donaldson (who was interested in invariants of symplectic manifolds) to establish a Lefschetz-pencil type structure on an almost contact manifold. Fran Presas, his student Roger Casals, and I combined these results and the classification of overtwisted contact structures on 3-manifolds due to Eliashberg to establish that on a five-dimensional manifold, there exists a contact structure in every homotopy class of almost contact distributions. This collaboration was also made possible by support from ICTP.

Ramadas Ramakrishnan Trivandrum
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Best wishes for the New Year! Auguri!

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