## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Wednesday, March 20, 2019 — 3:30 PM EDT

**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 $\mathcal{F}$.

Wednesday, March 20, 2019 — 3:30 PM EDT

**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

Wednesday, March 20, 2019 — 4:30 PM EDT

**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.

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.