Joel Kamnitzer, a mathematician at the University of Toronto, is exploring the link between physics and mathematics, focusing in particular on symmetry.

Picture a sphere floating in the air. It can rotate in any direction, at any angle and in any order. The collection of all these possible rotations is a Lie group. One of the great achievements in mathematics in the late 19th and early 20th century was the classification of all simple Lie groups. Lie groups also appear as symmetries of elementary particles, such as electrons and protons. The different particles and their many states come in patterns that are predicted by representations of Lie groups.

In their attempts to unify gravity and quantum mechanics, physicists are studying physical theories called supersymmetric quantum field theories. These quantum field theories have led to amazing new mathematics. The physics allows us to predict surprising relationships between different geometric objects related to Lie groups.

Kamnitzer's work seeks to understand these predictions and use them to solve important mathematics problems. His work also contributes to finding the correct mathematical framework for theoretical physics.

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