Research Focus
Symmetry is fundamental to our understanding of nature. It is modeled by the mathematical notion of a group. Such groups are difficult to understand and classify. My research program concerns the ways mathematical groups can be understood as geometrically. This geometric study of mathematical groups finds applications in theoretical physics. I approach this subject experimentally, visually, and collaboratively; often including undergraduate and graduate students in projects.
Current Projects
■ Understanding how persistent properties in spaces of geometric avatars of a group tells the nature of the group.
■ Understanding how non-commutative algebraic structures control the geometry of a group’s space of geometric avatars.
■ Experimentally/computationally discovering and verifying conjectures about geometric objects associated to groups.
Select Publications
