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.
Congratulations to Clement Wan, MMath and Eric Boulter, PhD, who convocated in Spring 2023. Best of luck in your future endeavours!
On July 1st, 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 4th. We’re happy to have you with us, Jo-Ann! Welcome to Pure Math!
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.
Xujia Chen, Harvard University
"Why can Kontsevich's invariants detect exotic phenomena?"
In topology, the difference between the category of smooth manifolds and the category of topological manifolds has always been a delicate and intriguing problem, called the "exotic phenomena". The recent work of Watanabe (2018) uses the tool "Kontsevich's invariants" to show that the group of diffeomorphisms of the 4-dimensional ball, as a topological group, has non-trivial homotopy type. In contrast, the group of homeomorphisms of the 4-dimensional ball is contractible. Kontsevich's invariants, defined by Kontsevich in the early 1990s from perturbative Chern-Simons theory, are invariants of (certain) 3-manifolds / fiber bundles / knots and links (it is the same argument in different settings). Watanabe's work implies that these invariants detect exotic phenomena, and, since then, they have become an important tool in studying the topology of diffeomorphism groups. It is thus natural to ask: how to understand the role smooth structure plays in Kontsevich's invariants? My recent work provides a perspective on this question: the real blow-up operation essentially depends on the smooth structure, therefore, given a manifold / fiber bundle X, the topology of some manifolds / bundles obtained by doing some real blow-ups on X can be different for different smooth structures on X.
Rahim Moosa, Department of Pure Mathematics, University of Waterloo
We continue to read through Pierre Simon's "A Guide to NIP Theories".
Junichiro Matsuda, Kyoto University
"Algebraic connectedness and bipartiteness of quantum graphs"
Quantum graphs are a non-commutative analogue of classical graphs related to operator algebras, quantum information, quantum groups, etc. In this talk, I will give a brief introduction to quantum graphs and talk about spectral characterizations of properties of quantum graphs. We introduce the notion of connectedness and bipartiteness of quantum graphs in terms of graph homomorphisms, and these properties have algebraic characterizations in the same way as classical cases. We also show the equivalence between bipartiteness and two-colorability of quantum graphs defined by two notions of graph homomorphisms: one respects adjacency matrices, and the other respects edge spaces. This talk is based on arXiv:2310.09500.
This seminar will be held both online and in person:
- Room: MC 5479
- Zoom link: https://uwaterloo.zoom.us/j/94186354814?pwd=NGpLM3B4eWNZckd1aTROcmRreW96QT09