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.
]]>Read all about it!]]>
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 ]]>
Best wishes for the New Year! Auguri!
]]>One could argue that though the world used to look like the former it progressively looks more and more like the latter. Algebra is quintessentially the science of the discrete and its relevance for the real world will only increase with time. (Unfortunately due to some technical problems there is no video of my talk in Guanajuato but you can watch a short interview where I discuss some of this.)
One of the places we visited in Panama was the Universidad Tecnológica de Panamá. You can find some details of our visit here (in Spanish).
In Costa Rica we visited the Instituto Tecnológico de Costa Rica as well as the Universidad de Costa Rica. At the end of our stay in San José, Claudio and I also participated in a meeting with many representatives of Universities from around Central America on an ongoing discussion to open a regional Doctorate in Physics and Mathematics. The rectors from 22 Universities from 6 countries in the region met to continue to hammer out the details of this important project.
]]>