Pawel Rudnicki- Title: Bio- Sensor Modelling.
Abstract: Using a small lab-on-chip type technology, available to a broad medical community, would allow a cheap and reliable early disease detection directly from bodily fluids such as saliva. The recent advances in micro- and nano-technology provide such an opportunity by using micro-cantilevers, suitably modified to specifically interact with the MNPs of interest. The change in cantilever vibration frequency depends on the added mass of such MNPs, and, as a result, provides a way of measuring their concentration in the fluid.

Rachel Gaffney- Title: Connections between Coding Theory and the Theory of Modular Forms.
Abstract: An error-correcting code is an algorithm for expressing a sequence of numbers such that any errors which occur can be detected and corrected based on the remaining numbers. The study of error-correcting codes is known as coding theory, and is an area of discrete mathematics. A modular form is a complex analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, also satisfying a growth condition. Modular forms are of interest in many areas of mathematics, but particularly in number theory. Although they may appear very different, there are many interesting connections between error-correcting codes and the study of modular forms.

Dylan Johnston- Title: On the representation theory of GL3(Fp) and the decomposition of its representations into irreducibles.
Abstract: Group representation theory involves the study of groups by representing their elements as linear transformations of vector spaces. There is a common trend in mathematics to take an object and ask about smaller sub-objects (for example; subspaces of vector spaces, subgroups of groups) and with representations this is no different - a very important question to ask of any representation is how/if it decomposes into smaller so-called irreducible representations.

Ben Sinclair- Title: Self-Similar Substitution Tilings and Strange Loops.
Abstract: This presentation will bring together two distinct mathematical topics, namely the study of aperiodic tilings and the mathematics underlying in the lithograph 'Print Gallery' by M.C. Escher. This link will be demonstrated by formalising a method to represent self-similar substitution tilings that contain different hierarchy levels, such that a strange loop is produced when this tiling is mapped onto Escher's Grid.