New paper here.

Well boys and girls, I will now live for ever.

Well, what I shall do, actually. This requires a fairly liberal interpretation of “holidays”, encompassing anything that is done away from ones home city. The first thing is the Postnikov Memorial Conference, 17th - 24th of June, in Bedlewo, Poland. The first thing to notice about Bedlewo is how it’s never even heard of the beaten track, nevermind been on it. Consequently planes, trains and automobiles all need to be involved. Luckily I’m going with my office chum Liz, so I won’t be entirely alone in the enterprise. Compare and contrast with the Strasbourg conference.

Secondly, for 8th - 14th of July I’m off to sunny Southampton (see right) for a week-long Homological algebra bonanza. Here the meaning of “holiday” becomes hazy, as i) we are doing algebra, and ii) we are not even crossing borders for the pleasure of it. Nontheless, ever optimistic, I will call it a holiday. On this sojourn another office-mate will be my companion, this time George.

Thirdly, an honest holiday: Istanbul with Parminder (of com leite frio fame, the jet-setting bon viveur) for 6th - 13th of August. It seems like a fantastic place, and I fully intend to return laden with outrageous Turkish objets d’art, worthy of a fin de siecle orientalist. Enough with the italics.
Fourthly, Marbella at some point. Which point, exactly, remains unknown. I will try to coincide it with those points belonging to friends of mine. Promise.

And now for something completely different. Strasbourg was as indicated on your left. In fact, that’s not very representative of my time there, as mostly it was spent in rooms with blackboards and writing things down as quickly as you could before the effervescent lecturer lost you entirely.

In other news, the paper that Johannes Ebert and I wrote, about characteristic classes of bundles of non-orientable surfaces, has been sent to the Bulletin of the London Mathematical Society to se if they like it. Unfortunately their rather stringent requirements mean I can’t post a preprint online, nor on the ArXiV. If, however, you are somebody who is interested, just ask me and I’ll send you a copy.

More recently, I’ve been working on understanding the space of d-dimensional submanifolds of a fixed n-dimensional manifold M. This is related to the concept of cobordism in the background space M (which, if you like, is what string theory sort of does: M is some 3-manifold called “the universe”, and cobordisms run in the time direction). I don’t want to mention too much as it might be a fruitful area for me to research…

It’s quite tricksy writing things for this, you know? So, what’s been going on? I notice that in my last post I was hopeful I’d be getting started on something concrete. Well, I have done, and finished it as well, so anything you would like to know about the divisibility of characteristic classes of bundles of non-orientable surfaces, I’m the person to ask. I would elaborate, but there’s a short note about it in the pipeline and I wouldn’t want to spoil the surprise. Probably appearing on the ArXiV before long.

This of course occupied much of the preceeding few months, but I’ve been doing a few other things too. In particular, I’m getting quite interested in hardcore stable homotopy theory, with formal groups, MU, and all that story. Not things that are obviously or immediately applicable to problems I’ll be working on, but very interesting and clever stuff. It’s best to do this broad learning now I think, because when I’m stuck into a problem I have little mind-space for anything else.

So I’m not going back to Marbella this Easter, as I’m saving up my precious scraps of holiday for the summer, as all the world assures me Oxford is a dull place of a summer. I’ll be going to Marbella for a while, possibly accompanied by this child and this man:

So I’m definitely going to Strasbourg in May now, so do let me know anyone else who is.

Not very good and the old regular updates, it seems. The things you learn about yourself, eh? Although I’ve been back for ages now (it is, after all, fourth week of term already) there haven’t really been any grand breakthroughs. I’m not quite sure why I expect there ought, but it would certainly be nice. Perhaps I’ll first give a plan for the future, in no particular order, especially not chronological:

• Stable homotopy theory: classical calculations and modern structures, Strasbourg, May 7th - 11th. Self and one or perhaps more office mates will probably be attending. If anyone else is do drop me a line, it would be nice to know at least a few of those going! Here the link.
• Junior Geometry & Topology Seminar, Thursday of 8th week. I’ll be giving a talk, tentatively titled “The Classification of Smooth Manifolds”, cunningly not mentioning up to what sort of equivalence to trick some geometers into attending. Unable to resist he continues: it’s up to unoriented cobordism. Thom showed (in the 50s?) that the cobordism ring of unoriented manifolds is polynomials with mod 2 coefficients on a system of generators, on in each dimension not one less that a power of two. Try here.
• Soonish (the precision of mathematicians!) I ought to be getting started on something concrete, though I don’t know what yet. It’s very hard to have any idea of what directions are worth looking in, especially when you know you could spend ages getting nowhere.

And now, what I have done lately:

• Got very excited thinking I had shown something that had evaded the experts, to wit, a sentence in an arxiv paper of my supervisor, Ulrike Tillmann, saying something was unknown. Today I find that that is an old draft and it is now known, proved in the same sort of way. For the curious, all free loop spaces on the circle have nonunique loop structures, and you can easily build an inequivalent delooping.
• Some work in cobordism in preparation for the second item above.

And of course other stuff, to minute to mention. Ta ta.