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
Pure Math Department celebrates outstanding Teaching by a Graduate Student and Teaching Assistants at awards ceremony
On November 3, the department of Pure Mathematics held its Graduate Teaching and Teaching Assistant Awards Ceremony, an event that celebrates the accomplishments of its remarkable graduate students
53rd annual COSY conference a success
More than 100 researchers and students from across Canada and around the world attended the 53rd annual Canadian Operator Algebras Symposium (COSY), which took place from May 26-30 at the University of Waterloo.
Pure Math Department celebrates undergraduate achievement at awards tea
On March 24, the department of Pure Mathematics held its annual Undergraduate Awards Tea, an event that celebrates the accomplishments of its remarkable undergraduate students.
Events
PhD Defence
Jennifer Zhu, University of Waterloo
Categorical Limits of Quantum Graphs and Possibilities Induced by QuantumPseudometrics
Quantum graphs and quantum pseudometrics as defined by Kuperberg and Weaver have roots in quantum errorcorrection but have since been developed as subjects in their own right. The motivation for the first half of thisthesis is to build an infinite quantum graph from finite quantum graphs. The latter have been subjected to fargreater scrutiny due to their connections to categorical quantum theory, while the former have been somewhatneglected. To be precise, we define and take the categorical (co)limit of quantum graphs by developing a newnotion of morphism compatible with previous notions but carrying less baggage. The inspiration for the secondhalf follows from the (unpublished) theorem that pure states on a von Neumann algebra \mathcal{M} are givenby maximal filters in the projection lattice of \mathcal{M}. Upon the observation that points in a metric space$(X, d)$ with topology $\tau$ are also given by maximal filters $\tau$ and that quantum pseudometrics provide anotion of distance between projections in $B(\ell^2) \overline{\otimes} \mathcal M$, we are led to a notion ofdistance $f$ between pure states induced by these quantum pseudometrics. Also this function $f$ does not satisfythe triangle inequality, we make some parallels between it and David Lewis's conception of ``possible worlds.''
MC 2009
Analysis Seminar
Paul SkoufranisYork University
Non-Commutative Majorization
The maps that send a self-adjoint matrix $A$ to $U^*AU$ where $U$ is a unitary matrix are essential inQuantum Information Theory as these maps transmit quantum information in a reversible way. When convexcombinations of such maps are taken, one obtains what are known as the mixed unitary quantum channels, whichare essential models for how quantum information can be transmitted when noise is present. Just as the unitaryconjugates of a self-adjoint matrix can be determined via spectral data, so too can the image of a self-adjointmatrix under all possible mixed unitary quantum channels. Since this is equivalent to characterizing the convexhull of the unitary orbit of a self-adjoint matrix, this problem has a well-known solution from operator theoryinvolving the notion of matrix majorization of one self-adjoint operator by another. In this talk, we will examinehow we can extend the notion of matrix majorization to non-commutative contexts. In particular, we will discussa notion of non-commutative majorization that characterizes the potential outputs under all quantum channels ofany non-commutative tuple of matrices. This is based on joint work with Matt Kennedy.
MC 5417 or Join on Zoom