Past Kinderseminar

30 November 2016
11:30
Adam Keilthy
Abstract
This talk will introduce some arguably trivial results about partition identities, and generating functions for various counts of partitions. We will discuss methods of proving q-series identities via bijections of partitions, and proving partition identities via analytic methods. We will then comment on the Rogers-Ramanujan identities, their combinatorial interpretation, and their various methods of proof.
16 November 2016
11:30
Kieran Calvert
Abstract

I will try to give a brief description of the use of group theory and character theory in chemistry, specifically vibrational spectroscopy. Defining the group associated to a molecule, how one would construct a representation corresponding to such a molecule and the character table associated to this. Then, time permitting, I will go in to the deconstruction of the data from spectroscopy; finding such a group and hence molecule structure. 

9 November 2016
11:30
Alex Margolis
Abstract

Two polyhedra are said to be scissors congruent if they can be subdivided into the same finite number of polyhedra such that each piece in the first polyhedron is congruent to one in the second. In 1900, Hilbert asked if there exist tetrahedra of the same volume which are not scissors congruent. I will give a history of this problem and its proofs, including an incorrect 'proof' by Bricard from 1896 which was only rectified in 2007.

2 November 2016
11:30
Adam Jones
Abstract

The problem of computing the Galois group of an irreducible, rational polynomial has been studied for many years. I will discuss the methods developed over the years to approach this problem, and give some examples of them in practice. These methods mainly involve constructing and factorising resolvent polynomials, and thereby determining better upper bounds for the conjugacy class of the Galois group within the symmetric group, i.e. describe its action on the roots of the polynomial explicitly. I will describe how using approximations to the zeros of the polynomial allows us to construct resolvents, and in particular, how using p-adic approximations can be advantageous over numerical approximations, and how this can yield a direct and systematic method of determining the Galois group.

15 June 2016
11:30
Giles Gardam
Abstract

We will explore the many guises under which groups of 2x2 matrices appear, such as isometries of the hyperbolic plane, mapping class groups and the modular group. Along the way we will learn some interesting and perhaps surprising facts.

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