# Engineering graduates 'taking unskilled jobs'

Nearly a quarter of UK engineering graduates are working in non-graduate jobs or unskilled work such as waiting and shop work, a report suggests.

–BBC News Reporter Katherine Sellgren

A study by researchers Birmingham University seems to go against what people in business are always telling us;

“The shortage of science, technology, engineering and maths graduates is an issue for businesses”

–Susan Anderson

I do not understand what people are talking about when they claim there is a shortage of engineers, scientist, mathematicians, computer scientists, and so on.  This is just not true. What is true is that a large proportion of these highly skilled people have to work in “non-scientific” jobs as there is a shortage of jobs relevant to their degrees.

In Physics World (February 2011,  20p ) Jim Grozier basically  complained that banking and finance was taking too many PhD qualified scientists away from science while not directly paying for their training. I agree with the sentiment,  but the point he misses is that there are not enough jobs in science, at Universities or other Labs, to keep these people working in science. Jim himself is one of the lucky ones, he is now based at UCL working in experimental particle physics.  (I vaguely knew Jim when he was PhD student and I a masters student at Sussex. )

It is astonishing, in the light of claims of science graduate shortages, that so few new graduates go into related employment”

–Professor Emma Smith

This is why we must all support the Science is Vital campaign.  Much of what the report says also applies to scientists and mathematicians.

To read more about the report by the University of Birmingham have a look at the BBC news report.

# Science is Vital

From the Science is Vital campaign.

Science Careers: final call for evidence

Following the meeting with Minister of State for Universities and Science, David Willetts, about the ailing state of science careers in the UK, we want to solicit your feedback for the report he requested from us.

I urge everyone in the UK who has anything to do with science to add their evidence. This means undergraduate students, spouses  and people who have been forced to leave science as well as postdocs, lecturers and professors.

# A simple QS and odd Jacobi manifold

Let us quickly recall what I mean by a QS and an odd Jacobi manifold.

Definition A supermanifold equipped with a Schouten structure S and a homological vector field Q such that

$$\{ S, \mathcal{Q} \} =0$$,

where $$\mathcal{Q}$$ is the symbol of the homological vector field is said to be a QS-manifold.

This definition allows us to write everything in terms of an odd function quadratic in momenta and an odd function linear in momenta, ie. functions on the total space of the cotangent bundle of our supermanifold. The bracket in the above is the canonical Poisson bracket.  (The example I will give will make this clearer.)

Definition A supermanifold equipped with an almost Schouten structure  S and a homological vector field Q such that

$$\{ S, S \} ={-} 2 \mathcal{Q} S$$,

$$\{ S,\mathcal{Q} \} =0$$,

where $$\mathcal{Q}$$ is the symbol of the homological vector field is said to be an  odd Jacobi manifold.

Both these species of supermanifold are very similar.  QS-manifolds have a genuine Schouten structure, that is an odd function quadratic in momenta such that it Poisson self-commutes and Poisson commutes with the symbol of the homological vector field.  An  odd Jacobi manifold consists of an almost Schouten structure that has a very specific Poisson self-commutator and Poisson commutes with the symbol of the homological vector field.

On to our example…

Consider the supermanifold $$\mathbb{R}^{1|1}$$, which we equip with local coordinates $$(t, \xi)$$. Here $$t$$  is the commuting coordinate and  $$\xi$$ is the anticommuting coordinate. This supermanifold comes equipped with a canonical Schouten structure

$$S = {-}\pi p$$,

where we employ fibre coordinates $$(p, \pi)$$ on the cotangent bundle.  As the above structure does not contain conjugate variables is it cleat that

$$\{S,S \}=0$$.

We can go a little further than this as we also have a canonical homological vector field, which indeed gives rise to a symbol that Poisson commutes with the Schouten structure:

$$\mathcal{Q} = {-}\pi$$.

So $$\mathbb{R}^{1|1}$$ is a QS-manifold, canonically.  The associated Schouten bracket is given by

$$[f,g]_{S} = ({-}1)^{\widetilde{f}}\frac{\partial f}{\partial \xi} \frac{\partial g}{\partial t} {-} \frac{\partial f}{\partial t}\frac{\partial g}{\partial \xi}$$,

for all $$f,g \in C^{\infty}(\mathbb{R}^{1|1})$$.

Interestingly, we can also consider these structures as being odd Jacobi. Explicitly one can calculate the Poisson self-commutator of the Schouten structure and arrive at

$$\{ S, S\} = {-} 2 \left( {-} \pi\right)\left( {-}\pi p\right)$$,

which is of course zero as $$\pi^{2}=0$$. But also notice that this defines an odd Jacobi structure! We then can assign an odd Jacobi bracket as

$$[f,g]_{J} = ({-}1)^{\widetilde{f}}\frac{\partial f}{\partial \xi} \frac{\partial g}{\partial t} {-} \frac{\partial f}{\partial t}\frac{\partial g}{\partial \xi}{-}({-}1)^{\widetilde{f}}\left( \frac{\partial f}{\partial \xi}\right)g {-}f\left( \frac{\partial g}{\partial \xi}\right)$$.

The Schouten bracket satisfies a strict Leibniz rule as where the odd Jacobi bracket does not, we have an “anomaly” term in the derivation property. Both satisfy the appropriate graded version of the Jacobi identity.

Interestingly, the Schouten structure on $$\mathbb{R}^{1|1}$$ is in fact non-degenerate so we have an odd symplectic supermanifold. One can also consider $$\mathbb{R}^{1|1}$$ as an even contact manifold, but I will delay talking about that for now.

One could of course “compactify” $$\mathbb{R}$$ and consider the supercircle $$\mathbb{S}^{1|1}$$, and this naturally also can be considered as QS and odd Jacobi. Again we have a natural contact structure here and this has been studied in relation to super versions of the Schwarzian derivative. This is really another story…

More details can be found in an older post of mine here. A preprint about odd Jacobi structures can be found on the arXiv here.