Events

Rui Philip Xiao, Department of Pure Mathematics, University of Waterloo

“Universal enveloping algebras”

Any associative algebra can be made into a Lie algebra by introducing the commutator bracket [a,b] = ab-ba, a Lie algebra arising in this way is called a commutator algebra.

“Free probability for pairs of faces”

The talk will deal with the recent extension of free probability to systems with two faces, one face of left variables and another face of right variables.

Talk 1. Justin Shaw, Pure Mathematics Department, University of Waterloo

“Spheres, the quaternions, and rotations”

The ideas developed in last week’s lecture on division algebras will be used to show which spheres are groups and to define the Hopf fibrations.

Talk 1.

Billy Lee, Department of Pure Mathematics, University of Waterloo

“Commutativity Theorems”

This week, we will explore numerous conditions a ring may have that forces it to be a commutative ring.

Adam Dor On, Department of Pure Mathematics, University of Waterloo

”Differential forms, exterior derivative and the ∂-operator”

We continue to develop the tangent space theory of real and complex manifolds by introducing the co-tangent space and Grassmann algebras for them.

Michael Baker, Department of Pure Mathematics, University of Waterloo

“Schur functors, Young tableaux, and representation theory”

In this talk, we give an introduction to tensor symmetry and the beautiful role played by Young tableaux (which are combinatorial objects) in the representation theory of Lie groups and Lie algebras.

Talk 1. Jon Herman, Pure Mathematics Department, University of Waterloo

“Noether’s Theorem under the Legendre transform”

First I will give a proof of Noether’s theorem as stated in Hamiltonian mechanics. I will then show how the Legendre transform, Φ, gives a one-to-one correspondence between the Hamiltonian and Lagrangian statements of Noether’s theorem.

Talk 1. Ehsaan Hossain, Pure Mathematics Department, University of Waterloo

“Extensions of line bundles, mk.

Susan Sierra, University of Edinburgh

“The universal enveloping algebra of the Virasoro algebra is not noetherian.”

The Virasoro algebra is an infinite-dimensional Lie algebra of great importance in physics and representation theory. We answer a long-standing question and show that its universal enveloping algebra is not noetherian.