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Dr I Grojnowski - Algebraic Curves


Yes! Yes! Yes! Grojnowski rides again! ...See also [my page of Grojnowski Part III quotes] and [my page of Grojnowski Part II quotes] --AlexChurchill

This lecture is brought to you by the following polynomial

Image: 46 I've made two cuts in the complex plane. Think of it as a nasty paper cut. <shudders> Eugh!

You take the equation y^2-x^3-x, and out pops a doughnut!
<sup> doesn't work! Waah!

That concludes the introduction. Now I get to burble for a bit.

Image: 46 This subject is both easy and hard, because some of the easy bits are confusing

I can't be trusted with indices.

This is a very round space - it's a sphere.

~The reason these notions seem complicated is because they are.

Well, here's a funky way of spelling that.


Dr A Thomason - Combinatorics


See also AlexChurchill's quotes from Dr Thomason in [Part III] and [Part II]

Image: 46 Image: 46 ...a book by Bollobas called "Combinatorics". It's an infinitely long title, but if you look at the front, it just says "Combinatorics".

Unfortunately, this course has Aleph-naught definitions to get through.
Waah! Neither does <font>

I want to be a tree.
This is quite entertaining.  AlexChurchill remembers Dr Thomason giving both this quote and the one below when AC was in Combinatorics lectures 3 years ago...
YupYup? - Is he trying to make himself unquotable, do you think?  --Vitenka

This is Hall's Theorem... it was known much earlier, so though much of Europe it's called König's Theorem, because it was proved first by Agavar.

We could assume it's true, that'd save us proving it.

<in exasperation>Ach, Shangrila!

What you have here is a normal curve, if you like normal curves. Well, you've got one anyway.

Image: 46 I'm going to try to prove this without my hands leaving my arms.

I had an example earlier... Oh, I've eaten it.

There's always that life-saving life-belt underneath you in case of tragedy.

Your intuition to stand on your head and look at the cube is right, but you also need to look in a mirror.

Image: 46 So one can forgive Katona for having the most ridiculous hairpiece on the planet - it's a beautiful proof.

I'm ready now, nurse!

I'm thinking about what I'm writing, which is a sure way of making it wrong.

<with respect to a theorem proved by Ramsey before 1930, then by Erdös-Szekeres in 1935> They were working in parallel, in an Einsteinian way.

Image: 46 I don't think you can drink too much coffee.

~ Here's another finite theorem.

Image: 46 Given two numbers m and k and r, so that's three numbers. Given three numbers m,k and r...
Reminds one of the SpanishInquisition... well, they're not that different from MathsLecturers? anyway... --AlexChurchill

There exists a number "FFUH", in a sort of Greek sense.

This is the end of the infinite excursion.

This is a rather seductive observation - one must resist the seduction.

Image: 46 Is anything more known? Well, yes, by an infinite amount of work, we know that...

~ By Markov's inequality, or just by obviousness.

~ Look at the puce coloured vertices.

There are worse things in life, and in maths. Well, perhaps not in life, but definitely in maths.


Prof. C B Thomas - Representation Theory


Image: 46 Image: 46 Ich könnte natürlich auch Eigenwert sagen, aber ich glaube nicht, daß das hier nötig ist.

Which, by general nonsense, is...

How do we define a definition?

Image: 46 From our past discussion, or indeed our future discussion, of tensor products.

~ This proof is by careful looking.

It leads nicely into the infinite part of the course.
...
[The course] could be made infinite, but it's probably not a good idea.

How big is the infinite-dimensional subspace?

This is the Peter-Weyl Theorem. I put it that way because Herr Peter and Herr Weyl were two separate people.

That's an extremely deep piece, verging between Part III and Part IV-and-a-half.

At this point there's a quote from Bilbo's birthday party at the start of Lord of the Rings.

This may please some of the audience, but the tangent bundle for a Lie group is trivial.
-[voice from back of lecture]: Yaaaaay!

Candidate 0 is sheer inspiration. Let's leave that to one side. Candidate 2 is...
<We always knew mathematicians couldn't count>
But Charles Thomas in particular is known for [splitting things into three halves]... :)



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