# Welcome to Pure Mathematics

We are home to 30 faculty, four staff, approximately 60 graduate students, several research visitors, and numerous undergraduate students. We offer exciting and challenging programs leading to BMath, MMath and PhD degrees. We nurture a very active research environment and are intensely devoted to both ground-breaking research and excellent teaching.

## News

## Spring 2023 Graduands

Congratulations to Clement Wan, MMath and Eric Boulter, PhD, who convocated in Spring 2023. Best of luck in your future endeavours!

## Grad Coordinator Staff Change

On July 1^{st}, we sadly had to say "so long" and "thank you" to Nancy Maloney who retired from the Pure Math grad coordinator position. Nancy had been with Pure Math for over 16 years and will definitely be missed. We wish you all the best for a long, healthy, and restful retirement, Nancy!

And we say "welcome" to Jo-Ann Hardy who has taken over the grad coordinator role as of July 4^{th}. We’re happy to have you with us, Jo-Ann! Welcome to Pure Math!

## Alexandru Nica wins Faculty of Math Distinction in Teaching Award

Pure Math Professor Alexandru (Andu) Nica is a recipient of this year's Faculty of Mathematics Distinction in Teaching Award. Up to two awards are given each year to teachers who have “consistently demonstrated outstanding pedagogical skills and a deep commitment to our students’ education.” Congratulations, Andu!

Read more about Andu's award here.

## Events

## Geometry & Topology Seminar

**Ákos Nagy, BEIT Canada**

**"On the hyperbolic Bloch transform"**

Motivated by recent theoretical and experimental developments in the physics of hyperbolic crystals, I will introduce the noncommutative Bloch transform for Fuchsian groups which I will call the hyperbolic Bloch transform (HBT). The HBT transforms wave functions on the hyperbolic plane to sections of irreducible, flat, Hermitian vector bundles over the orbit space and transforms the hyperbolic Laplacian into the covariant Laplacian. I will prove that the HBT is injective and “asymptotically unitary”. If time permits, I will talk about potential applications to hyperbolic band theory. This is a joint work with Steve Rayan (arXiv:2208.02749).

MC 5417

## Analysis Seminar

**Matthijs Vernooij, TU Delft**

**"Derivations for symmetric quantum Markov semigroups"**

Quantum Markov semigroups describe the time evolution of the operators in a von Neumann algebra corresponding to an open quantum system. Of particular interest are so-called symmetric semigroups. Given a faithful state, one can define the GNS- and KMS-inner product on the von Neumann algebra, and a semigroup is GNS- or KMS-symmetric if it is self-adjoint w.r.t. the inner product. GNS-symmetry implies KMS-symmetry, and both coincide if the state is a trace. It was shown in 2003 that the generator of a tracially symmetric quantum Markov semigroup can be written as the 'square' of a derivation, i.e. d* after d, where d is a derivation to a Hilbert bimodule. This result has proven to be very influential in many different directions. In this talk, we will look at this problem in the case that our state is not tracial. We will start by discussing how a computer can be used to decide whether such a derivation exists in finite dimensions, and work our way up to a general result on KMS-symmetric quantum Markov semigroups. This is joint work with Melchior Wirth.

This seminar will be held both online and in person:

- Room: MC 5479
- Zoom link: https://uwaterloo.zoom.us/j/94186354814?pwd=NGpLM3B4eWNZckd1aTROcmRreW96QT09

## Grad Student Colloquium

**Kieran Mastel, Department of Pure Mathematics, University of Waterloo**

**"An Aperiodic Monotile"**

Last year, David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss found the first example of an aperiodic monotile (or ‘einstein’), solving a longstanding open problem. We will look at the ‘hat’ tile they define and try to visually understand why it tiles the plane and why none of its tilings are periodic.

MC 5501