There are many great examples of algebras which arise as tensor power
centralizer algebras, algebras of operators which preserve symmetries
in a tensor space. The most familiar example is the connection between
the general linear group and the symmetric group, studied by Frobenius
and Schur around 1900. The key is that these mutually centralizing
algebras have linked representation theory, so the combinatorial tools
used to study one algebra can be harnessed to study the other. In this
talk, I will introduce some of these combinatorial tools, and talk
about how to apply them to the representation theory of many favorite
examples of diagram algebras.
August 21:
Anthony Mays, Something about juggling
Juggling is the noblest of pursuits, invented by the ancient king of
Babylon. These facts might be fabrications, but my talk this afternoon
will be full of things with more truth value. Juggling has an
interesting description in terms of integer sequences, as well as being
fun, so it has at least two things in common with mathematics.
I'll look at how some juggling geeks have applied maths to improve their
leet skills, and then how some maths geeks have applied juggling to
prove some sick theorems. Crowd participation invited - you will be
compensated with carbohydrates and trans-fats.
August 28:
Anthony Mays, The joy of juggling (aka yet more stuff about juggling)
There'll be some juggling, and some maths. Then probably some more
juggling. I plan to cover the stuff I didn't get onto last week, plus
some new stuff I've read about in the meantime.
Come for the show and stay for the maths. No prior knowledge required.
And if that's not enough to get you there, then the promise of
artery-hardening treats should do it.
September 4:
Wendy Baratta, Latin Squares
I'll be chatting about Latin squares, particularly mututally orthogonal Latin Squares. Looking at existence and generation - it'll be a mixed bag of
combinatorics and algebra with some discussion at the end of their
applications in the real world - yes, sometimes pure maths does have
applications!
September 11:
Nicholas Beaton, Block Designs
In the same spirit as Wendy's talk on Latin square last week, I'll be doing
a rundown on block designs - what they are, some of their properties, how to
construct them, and the sometimes-quite-tenuous applications that
combinatorialists claim in order to justify more funding
September 18:
Nicholas Stevenson, Invariant Theory
A branch of algebra, was one of the major areas of
mathematics in the 19th century and remains of interest today - David
Mumford won a Fields medal for his application of David Hilbert's work on
invariant theory to algebraic geometry. In this talk, I will sketch
Hilbert's proof that the invariant ring of a linearly reductive group is
finitely generated and discuss its significance.
October 9:
Sandy Clarke, Statistics
If you want breadth in your mathematical education, you really ought to
know some stats. The plan is to discuss a few simple but important
results, look at some examples of ways in which these can be expanded to
make things more interesting and visit a couple of amusing historical
applications (and misapplications). You will leave wanting to be a
statistian or, at the very least, a better person.
October 16:
Anthony Mays, Random Matrices, What they are and where's it at
"Random" is a word that the youth of today have distorted out of all
meaning. With their pants practically hanging off and their hair in all
manner of disorder, they scornfully strut about butchering the language
with impunity. We can't let this continue, and we'll start by taking
back the word "random". Join me as we explore the workings of Random
Matrix Theory, which has a respectably proper randomness about it.
Cowabunga.
October 23:
Ellie Button, Fluid Dynamics
Have you ever wondered what those dirty applied mathematicians do? I will
introduce the equations governing basic fluid flow, and discuss the very
crude assumptions we make in order to solve them. Some simple examples
will be given. No knowledge of fluid dynamics is assumed, and you should
expect very little maths (this is about the biscuits!).