Events by date

Yuanhang Zhang, Jilin University

"Connecting invertible analytic Toeplitz operators in $G(\mathcal{T}(\mathcal{P}^{\perp}))$"

We prove that there exists an orthonormal basis $\mathcal{F}$ for classical Hardy space $H^2$, such that each invertible analytic Toeplitz operator $T_\phi$ (i.e. $\phi$ is invertible in $H^\infty$) could be connected to the identity operator via a norm continuous path of invertible elements of the lower triangular operators with respect to $\mathcal{F}$.

Michael Deveau, Department of Pure Mathematics, University of Waterloo

"Generalizing $\omega^k$-c.e. for Relativization"

Just as the arithmetic hierarchy characterizes reductions below various Turing jumps of $\emptyset$, Anderson and Csima showed that the Ershov hierarchy -- related to the notion of $\omega^k$-c.e. -- characterizes reductions of bounded Turing jumps of $\emptyset$. We discuss how to relativize this to reductions below bounded Turing jumps of an arbitrary set.

MC 5413

Patrick Naylor, Department of Pure Mathematics, University of Waterloo

“Is any knot not the unknot?”

Ever wanted to learn something about knots? This is your chance! We'll talk about some basics of knot theory, including how to  prove some intuitively `obvious' but mathematically tricky results.  Along the way, we'll see knot coloring invariants, polynomial invariants, and more. We'll even show how to produce a knotted surface: a  sphere ($S^2$) in $\mathbb{R}^4$ that is `knotted'. This talk will be very accessible and will include many cool pictures.