Talk #1 (1:00pm - 2:15pm)
Jacques van Wyk, Department of Pure Mathematics, University of Waterloo
"Fundamentals of Elliptic Partial Differential Operators"
In differential geometry, there is a very nice class of operators taking sections of one bundle to another known as elliptic partial differential operators. In this talk, I will prove some fundamental results about these operators, intending to give some idea for why these operators are so nice. This will come in two parts: first I will give a brief overview of the theory of (elliptic) pseudodifferential operators on ordinary multivariate functions from the perspective of Fourier analysis; then, I will show how this theory can be extended to elliptic operators between bundles. If time permits, I will show how these results can be used to prove a strong generalisation of the Hodge Decomposition Theorem.
Talk #2 (2:30pm - 4:00pm)
Christopher Lang, Department of Pure Mathematics, University of Waterloo
"Revisiting Symmetric Hyperbolic Monopoles"
In this talk, I will present a new derivation of the symmetry equations for spherically symmetric hyperbolic monopoles. This new proof sidesteps previously needed hypotheses and also provides a new constraint on the structure group. It is also easy to modify for other gauge-theoretic objects like Euclidean monopoles and instantons.
MC 5403