Asem is a third-year undergraduate student majoring in Pure Mathematics and Physics at the University of Sydney. He is interested in various mathematical areas, including topology and algebra, and areas in physics such as computational neurodynamics. He has previously worked with A/Prof. Tara Murphy on low frequency radio variability, A/Prof. Steve Flammia on quantum error correction, Dr. Stephan Tillmann on knot complements, and Dr. Pulin Gong on computational neuroscience. He intends to continue his studies with Honours next year, and aims to pursue postgraduate research in pure mathematics.
Negatively curved structures in dimensions three and four via discrete geometry
This project examines negatively curved structures on 3-dimensional and 4-dimensional spaces. The 3-dimensional spaces will be built from Euclidean tetrahedra or cubes, such that the negative curvature is concentrated along the edges and at the vertices, and the 4-dimensional spaces are similarly composed of pentachora and hypercubes. This project will give constructions of such negatively curved structures and determine methods to decide whether a given manifold supports such a structure.