Symmetry and Space
Unlocking the mysteries of the global shape of space has fascinated scientists for centuries.
The study of higher dimensional spaces, or spaces "in the large," is aided by the presence of symmetry. The collection of all symmetries of a space has a simple algebraic structure: Two symmetries can be composed to yield a third, and to any symmetry there is an inverse symmetry. The fundamental mathematical concept behind this algebraic structure is the notion of a group, and the unchanging characteristic of a group that captures the essence of symmetry is group cohomology.
Dr. Alejandro Adem is an expert in the computation and application of the cohomology of groups.
Scientists classified the basic building blocks of finite group theory - the simple groups - in the latter part of the 20th century. The next step is to understand how they arise as groups of symmetries and how they can be used to construct key geometric objects, a context where group cohomology plays a central role.
As the Canada Research Chair in Algebraic Topology and Group Cohomology, Dr. Adem is leading a group of scientists whose research focuses on fundamental questions related to geometry and symmetry, topics that underlie the mathematical structure of the natural sciences. This basic research is serving as a cornerstone on which applications can be developed for a wide array of disciplines, including theoretical physics, computer science, robotics, and mathematical biology.