Alejandro Adem

Canada Research Chair in Algebraic Topology and Group Cohomology

Tier 1 - 2017-11-01
Renewed: 2012-03-01
The University of British Columbia
Natural Sciences and Engineering Research Council


Coming to Canada From

University of Wisconsin, Madison, USA

Research involves

Using algebra and topology to study symmetry in mathematics and physics.

Research relevance

The research will result in a more fundamental understanding of higher dimensional spaces.

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.