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Events
11 / 24
Start: 12:00
If you've taken a look at any recently published book or mathematical paper, chances are you've already seen what LaTeX can do. LaTeX is, simply put, an elegant and convenient way of typing mathematics on a computer and particularly useful if you would like to typeset any type of mathematical essay or project (second year essays in particular). Unlike word processors such as Microsoft Word and Open Office Writer, you do not work directly on something which looks like the finished document. Instead, it is much more similar to a programming language (albeit a very simple one): you have to type in text along with a series of commands which determine the mathematical equations, alignment, font size and almost everything else. This may sound daunting at first but is in fact much easier than it sounds and, as usual, the WMS is here to help you: we will be running two LaTeX classes per week during the final three weeks of term, Tuesdays 12-1 and Wednesdays 11-12 (the two classes will have exactly the same content). By the end of these, you should be able to write mathematics much better and faster than you would on a conventional word processor and be able to typeset a professional looking second year essay. | ||
11 / 25
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11 / 26
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11 / 27
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11 / 28
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11 / 29
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11 / 30
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12 / 1
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12 / 2
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12 / 3
Start: 19:30
End: 21:00
Classification of manifolds up to diffeomorphism is a hard problem (deciding whether two given 4-manifolds are diffeomorphic is at least as hard as the word problem for groups). Thom's brilliant idea (which had been considered, before him, by Poincaré and Pontryagin) was to introduce a weaker equivalence relation than diffeomorphism: the equivalence relation of cobordism. Two There are other types of cobordism, that arise by putting structure on our manifolds and requiring that the cobordisms preserve this, for example oriented cobordism: we only study oriented manifolds, and the oriented boundary of the Pontryagin's success was to realise that certain cobordism groups end up being equal to stable homotopy groups of spheres, helping the calculation of the latter. Thom largely reversed the process and generalised Pontryagin's idea, making an explicit correspondence between cobordism groups and homotopy groups of certain spaces, now called Thom spaces. Another useful way to study cobordism is through characteristic classes. Many cobordism theories have particular characteristic classes associated to them, and it turns out that two manifolds are cobordant if and only if all the characteristic numbers of these two manifolds agree. This lead to great insights into the theory of characteristic classes, for example the idea of a generalised genus (a topological invariant) as a homomorphism from the cobordism ring to some other ring, for example the rationals. This is then of great interest in classifying manifolds, and allowed things such as Milnor's construction of exotic If you're already impatient to hear more, then you should come to MS.05 this thursday at 7:30 pm; you'll hear about all this and then much more (such as topological quantum field theories!). After which we realise that we are cobordant to our future selves that are in the pub. | ||
12 / 4
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12 / 5
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12 / 6
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12 / 7
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12 / 8
Start: 19:30
End: 21:00
To all our friends in the Warwick Maths Society, we cordially invite you to join us for our annual Christmas get together this Tuesday. We will be going out for a meal at The City Arms, in Earlsdon (Coventry), where we will be making the best use of Wetherspoons' steak night offer! The plan is to gather in the pub at around 7.30, if you are on campus and are not sure how to get to Earlsdon then there will be a crew of helpers around the bus stop at 7pm. The 12 bus goes at 7.05, so don't be late! We look forward to seeing you on Tuesday. The WMS Exec. | ||
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12 / 24
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-manifolds are (unoriented) cobordant if their disjoint union is the boundary of an 
-manifold with boundary. We can see that we can compose cobordisms end to end, and every manifold is cobordant to itself as we have 
, so it is easy to check it is indeed an equivalence relation. In each dimension we can form an abelian group, with operation disjoint union, the 
-spheres.