Associate Professor Of Mathematics Thomas Pietraho explains his research as being a study in symmetry.
We are all familiar with symmetry in the geometric and aesthetic sense: the radial symmetry of a starfish or the bilateral symmetry of a leaf.
For mathematicians like Professor Pietraho, questions of symmetry are of great theoretical importance and carry far-reaching ramifications in mathematics and beyond.
Such questions seek to determine what actions can be done to an object while still preserving that object's fundamental qualities (i.e. turning a square by 90 degrees). These actions are known as symmetries.
In Professor Pietraho's work, the concept of symmetry is generalized, placing related symmetries into mathematical objects called groups.
The primary concern in his research is in relating certain qualities of highly specified groups of symmetries, called Lie groups, using techniques from a branch of mathematics known as representation theory.
Non-mathematicians who seek to understand a mathematician's research have a general tendency to nod furiously and absently while attempting to understand what in the world is possibly being said.
Mathematics is a language unto itself, so listening to it or reading it when unfamiliar with the terminology can be much like trying to get directions in France when you only speak Mandarin.
Luckily, Professor Pietraho's research offers us much more than incomprehensible words: a glimpse into why a mathematician would want to study such a distant and austere topic.
On the mathematician's aesthetic, Professor Pietraho says, "In the same way that a chemist would like to be able to describe the elements on the periodic table, a mathematician would like to classify all symmetries possible in the universe."
This reason is hard for most of us, as non-mathematicians (and non-chemists), to understand, but the beauty of working with something that is fundamental and pure is a profound impetus for many mathematicians' work, Professor Pietraho included.
The other reason he gives is grounded in the applicability of his research, despite its ostensible abstraction.
He says, "Representation theory has had many important applications. Understanding symmetries of the circle, a fairly simple geometrical object, has led to the development of .mp3 compression, tide prediction, global temperature patterns...among many others."