Talk 1. Jon Herman, Pure Mathematics Department, University of Waterloo
“Noether’s theorem in Lagrangian mechanics”
Albert Einstein referred to Emmy Noether as the most significant and creative female mathematician of all time. In this talk I will discuss the Lagrangian formulation of Noether’s theorem. Her theorem makes precise the relationship between two fundamental properties of nature; symmetry and conserved quantities. That is, the conservation of momentum, angular momentum, energy and so forth can all be seen as consequences of certain symmetries in the physical system under study. Before giving a proof, I will first make precise the notions of ”symmetry” and ”conserved quantity”. I will then show by example how powerful and amazing the consequences of this theorem can be.
Talk 2. Spiro Karigiannis, Pure Mathematics Department, University of Waterloo
“The classification and geometry of normed real division algebras”
This lecture will be a crash course in the fundamental properties of the normed real division algebras, including the quaternions and the octonions. The relation between such algebras and cross product structures will be explored in depth. Finally, the relevance of these ideas to special Riemannian structures (including Calabi-Yau and G2 manifolds) and to calibrated geometry will be explained.