The math club offers a pleasant place to take a break in busy exam weeks. Floyd Williams gives a talk for us. For the abstract, see below:
A tractroid ( or pseudosphere ) is a surface generated by revolving a special curve ( a tractrix ) about an axis. By a clever change of variables one can find a nice realization of this surface as a certain “vaccum space”, which mathematicians call an orbifold -the latter being defined by a simple relation between points. This vaccum space is similar in nature to a 2-dimensional black hole with mass degenerating to zero. Thankfully however these objects are “not” the same (otherwise there’s no life on earth ), and thankfully no knowledge of black holes is needed for the talk-which mainly involves calculus.
We will meet in LGRT 1634 at 5 pm just as usual.
The abstract of the talk is as follows:
The Radon transform is a way of transforming one function into another which has applications in mathematics and image processing. I will define the Radon transform as well as the closely related X-ray transform. I will recall the more famous Fourier transform, and then discuss the connection between these operators (which seems to have given rise to the popularity of the Radon transform in medical imaging)
It was really unfortunate that we had to cancel the math club last week due to the snow. We will reschedule GaYee’s talk at some time this semester, so don’t miss it!
This week, we are happy to have Eric Sommers as a speaker. He will talk about “An Introduction to Representation Theory”.
Here is his abstract:
I’ll give a survey of the main ideas behind the representation theory of finite groups. Representation theory is the study of the ways in which a group can be represented by a set of matrices. Knowing some linear algebra (Math 235) is helpful, but not required. It is not necessary to know what a group is– I will give the definition. This is a beautiful subject, accessible to all math majors, but not something that shows up in our undergraduate curriculum (although our friends in chemistry do see it).
We appreciated the nice opening math club talk given by Pat Dragon. Here is his abstract.
A de Bruijn sequence is a binary string of length $2^n$ which, when viewed cyclically, contains every binary string of length $n$ exactly once as a substring. For example, 00010111 suffices for $n = 3$. Knuth refers to the lexicographically least de Bruijn sequence for each $n$ as the “Granddaddy” sequence due to its venerable origin. In 1934 Martin originally constructed these sequences and later it was shown by Fredericksen et al that they can also be constructed by concatenating the aperiodic prefixes of the binary necklaces of length $n$ in lexicographic order. In a recent publication, we proved that the Granddaddy has a lexicographic partner. The “Grandmama” sequence is constructed by concatenating the aperiodic prefixes of necklaces in co-lexicographic order. This talk will introduce de Bruijn sequences, the FKM algorithm, and some applications.