**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