Pure Math Provides Fundamental Answers
In keeping with their mission to encourage intellectual prowess, universities support fundamental academic research that does not easily fit into mainstream studies. Such research areas build on fundamental scientific research that provides the foundation on which important solutions are based. One such area is pure mathematics.
Canada Research Chair Dr. Vladimir Chernousov is an internationally renowned expert in the theory of linear algebraic groups. He conducts research focused on understanding the nature of algebraic groups and their classification. His research has made substantial contributions to the study of linear algebraic groups over non-closed fields. Understanding symmetry, such as how and why it arises, is a fundamental component in both mathematics and physics.
The mathematical objects that measure symmetry are called groups and their study is known as group theory. Classical examples of continuous groups are rotations (e.g., all the different positions that the needle of a compass can assume) and translations (e.g., imagine a train track that runs forever on a straight line in both directions); an example of a discrete group is the symmetry of a square or a snowflake. The first two examples are ones of continuous groups of motions (points in our imaginary track that can arbitrarily be closed to each other), while the symmetries of a snowflake or a square are discrete (you cannot continuously move a square into itself . . . unless you do not move at all)
Though most groups by nature have a geometrical flavour, it has proven crucial for contemporary mathematicians to find the correct kind of group that could be used to deal with purely algebraic or arithmetical questions. These are the so-called algebraic groups. The focus of Dr. Chernousov's present research is on a particular mathematical framework called "non-abelian Galois cohomology" and on the splitting properties of the corresponding algebraic groups.