Research Area: Geometry & Topology

Research Profile: Topology and geometry
Topology and geometry Geometry is the study of shapes and spaces. Most people are aware of the standard objects of Euclidean geometry: lines, circles, polygons, and of familiar notions such as angles, parallel lines, and congruent figures. In its modern form geometry has a much wider scope, reaching into higher dimensions and encompassing a broad range of current ideas. The subject of Topology is concerned with those features of geometry which remain unchanged after twisting, stretching or other deformations of a geometrical space. It includes such problems as colouring maps, distinguishing knots, classifying surfaces and their higher dimensional analogs. The influence of topology is also important in other mathematical disciplines such as dynamical systems, algebraic geometry (the study of polynomial equations in many variables) and certain aspects of analysis and combinatorics.

My research in recent years has focused on the study of the topology of manifolds and cell complexes by means of algebraic K-theory, pseudoisotopy theory, gauge theory, and representation theory.

Geometry & Topology

2020/2021
On Research Leave

2019/2020
Math 1AA3
Math 2X03
Math 732

2018/2019
Math 1AA3
Math 4BT3
Math 4E03/6E03
Math 761

2017/2018
Math 1AA3
Math 4TT3
Math 732

2016/2017
Math 1AA3
Math 4E03/6E03
Math 761

2015/2016
Math 1AA3
Math 4E03/6E03
Math 732

2014/2015
Math 1AA3
Math 3T03
Math 761

2013/2014
Math 2R03
Math 3B03
Math 731