Abdul Zreika is a second-year student at the University of Sydney, currently studying a degree in Advanced Mathematics and Software Engineering. He is interested in a variety of mathematical fields, in particular algebra and discrete mathematics, and is hoping to pursue an Honours degree in Pure Mathematics in the near future.
The Space Of Closed Essential Normal Surfaces In Knot Complements
This project will undertake the first systematic study of the set of all essential normal surfaces in the space of all normal surfaces, with the aim of finding answers to questions such as: Is a simplest essential surface always amongst the vertex surfaces? What is the dimension of a top-dimensional subpolytope that entirely carries essential surfaces? Does the set of essential vertex surfaces span a connected graph in the boundary of the normal surface polytope?