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
Two Pure Math professors win Outstanding Performance Awards
The awards are given each year to faculty members across the University of Waterloo who demonstrate excellence in teaching and research.
Pure Math PhD student wins Amit and Meena Chakma Award for Exceptional Teaching
The award ($1000), which is given to up to four recipients annually, recognizes excellence in teaching by students, including intellectual vigour, skill in communication and presentation of subject matter, and concern for the needs of students.
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
Algebraic Geometry Working Seminar
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 talk, I will extend this correspondence by providing necessary and sufficient conditions for when a co-Higgs field induces an integrable 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. We will also analyze this correspondence for co-Higgs fields over curves of genus g greater than one. Finally, I will show how stability can be understood geometrically through the zeros of the induced Poisson structure, establishing connections between \Phi-invariant subbundles, Poisson subvarieties, and the spectral curve. As this talk is a preparation for my thesis defense, please ask me many questions!
MC 5403
Differential Geometry Working Seminar
Spiro Karigiannis, University of Waterloo
A tale of two Lie groups
The classical Lie group SO(4) is well-known to possess a very rich structure, relating in several ways to complex Euclidean spaces. This structure can be used to construct the classical twistor space Z over an oriented Riemannian 4-manifold M, which is a 6-dimensional almost Hermitian manifold. Special geometric properties of Z are then related to the curvature of M, an example of which is the celebrated Atiyah-Hitchin-Singer Theorem. The Lie group Spin(7) is a particular subgroup of SO(8) determined by a special 4-form. Intriguingly, Spin(7) has several properties relating to complex Euclidean spaces which are direct analogues of SO(4) properties, but sadly (or interestingly, depending on your point of view) not all of them. I will give a leisurely introduction to both groups in parallel, emphasizing the similarities and differences, and show how we can nevertheless at least partially succeed in constructing a "twistor space" over an 8-dimensional manifold equipped with a torsion-free Spin(7)-structure. (I will define what those are.) This is joint work with Michael Albanese, Lucia Martin-Merchan, and Aleksandar Milivojevic. The talk will be accessible to a broad audience.
MC 5479
Geometry and Topology Seminar
Mingyang Li, UC Berkeley
On 4d Ricci-flat metrics with conformally Kahler geometry.
Ricci-flat metrics are fundamental in differential geometry, and they are easier to study when they have additional structures. I will introduce my recent work on 4d conformally Kahler but non-Kahler Ricci-flat metrics, which is a condition analogous to hyperkahler. This leads to a complete classification of asymptotic geometries of such metrics at infinity and a classification of such gravitational instantons.
MC 5417