The Mathematical and Computational Sciences at Western are represented by four separate departments: Applied Mathematics, Computer Science, Mathematics, and Statistical & Actuarial Sciences. The Department of Mathematics has established research groups in several areas of contemporary mathematics including algebra, analysis and analytic geometry, homotopy theory, and noncommutative geometry.
Each week the Department of Mathematics hosts a wide variety of seminars and events. For a comprehensive list of events, please consult our departmental calendar.
In this session I will talk about rationality of algebraic tori. We will first define the notion of rational algebraic variety and then some relaxed notions of rationality. Algebraic tori are important objects in studying algebraic groups.
The rationality problem for an arbitrary group is difficult. Hence it makes sense to study the problem for algebraic groups which have a simple structure.
In order to talk about rationality of algebraic tori we will take a look at the duality between the category of split algebraic tori and the category of G-lattices. We will end the session with the main results about birational classification of tori in small dimensions.