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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

Friday, September 29, 2023

Spring 2023 Graduands

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

Events

Wednesday, December 4, 2024 2:00 pm - 3:30 pm EST (GMT -05:00)

Computability Learning Seminar

Rachael Alvir, University of Waterloo

Conclusion of the Fundamentals of Computability Theory

We will finish presenting results from Soare's book. We will look at Low n and High n sets.

MC 5403

Friday, December 6, 2024 10:00 am - 11:00 am EST (GMT -05:00)

PhD These Defense

Brady Ali Medina, University of Waterloo

Co-Higgs Bundles and Poisson Structures.

There is a correspondence between co-Higgs fields and holomorphic Poisson structures on P(V) established by Polishchuk in the rank 2 case and by Matviichuk in the case where the co-Higgs field is diagonalizable. In this thesis, we extend this correspondence by providing necessary and sufficient conditions for when a co-Higgs field induces a Poisson structure on V and P(V), showing that the co-Higgs field must either be a function multiple of a constant matrix or have only one non-zero column. Furthermore, we analyze this correspondence for co-Higgs fields over curves of genus greater or equal to one.  Finally, we analyze how stability can be interpreted geometrically through the zeros of the induced Poisson structure, establishing connections between \Phi -invariant subbundles, Poisson subvarieties, and the spectral curve.

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Meeting ID: 971 4907 1044

Passcode: 776121

Friday, December 6, 2024 3:30 pm - 4:30 pm EST (GMT -05:00)

Geometry and Topology Seminar

Ruiran Sun, University of Toronto

Rigidity problems on moduli spaces of polarized manifolds.

Motivated by Shafarevich’s conjecture, Arakelov and Parshin established a significant finiteness result: for any curve C, the set of isomorphism classes of non-constant morphisms C → M_g is finite for g≥2. However, for moduli stacks parametrizing higher-dimensional varieties, the Arakelov-Parshin finiteness theorem fails due to the presence of non-rigid families. In this talk, I will review recent advances in rigidity problems for moduli spaces of polarized manifolds, focusing on two main topics: an "one-pointed" version of Shafarevich’s finiteness theorem and the distribution of non-rigid families within moduli spaces.

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