Vishnu Mangalath is a Bachelor of Philosophy student from the University of Western Australia majoring in Mathematics and Physics. He has a wide range of interests in pure mathematics and physics, particularly, algebraic topology and geometry, statistical mechanics and quantum mechanics. He will be completing his honours in mathematics in 2018 in pure mathematics.
Simplicial homology and computation from nerves
This project will start by investigating the basics of simplicial homology theory, a well-established feild of algebraic topology, up to and including the Mayer-Vietoris exact sequence. During this investigation, the student will gain the required back- ground for further investigation, such as constructing simplicial complexes from the nerve of an open cover of a topological space.
The research component will predominantly involve calculating the homology groups of the nerve of an open cover found from experimental data. For example, this data may be points from the state space of some unknown dynamical system. From this we can take an open cover of this data and therefore construct a simplicial complex via the nerve. Calculating the homology groups of these simplicial complexes will give insight into the shape of the underlying state space.