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
Differential Geometry Working Seminar
Amanda Petcu, University of Waterloo
Some results on hypersymplectic structures
A conjecture of Simon Donaldson is that on a compact 4-manifold X^4 one can flow from a hypersymplectic structure to a hyperkahler structure while remaining in the same cohomology class. To this end the hypersymplectic flow was introduced by Fine-Yao. In this thesis the notion of a positive triple on X^4 is used to define a hypersymplectic and hyperkahler structure. Given a closed positive triple one can define either a closed G2 structure or a coclosed G2 structure on T^3 x X^4. The coclosed G2 structure is evolved under the G2 Laplacian coflow. This descends to a flow of the positive triple on X^4, which is again the Fine-Yao hypersymplectic flow. In the second part of this thesis we let X^4 = R^4 \0 with a particular cohomogeneity one action. A hypersymplectic structure invariant under this action is introduced. The Riemann and Ricci curvature tensors are computed and we verify in a particular case that this hypersymplectic structure can be transformed to a hyperkahler structure. The notion of a soliton for the hypersymplectic flow in this particular case is introduced and it is found that steady solitons give rise to hypersymplectic structures that can be transformed to hyperkahler structures. Some other soliton solutions are also discussed.
MC 5403
Analysis Seminar
Elisabeth Werner, Case Western Reserve University
The $L_p$-Floating Area and Isoperimetric Inequalities on the Sphere
Euclidean convex bodies in spaces of constant positive curvature. We introduce the family of $L_p$-floatingareas for spherical convex bodies, as an analog to $L_p$-affine surface area measures from Euclidean geometry.We investigate a duality formula, monotonicity and isoperimetric inequalities for this new family of curvaturemeasures on spherical convex bodies. Based on joint works with Florian Besau.
MC 5417
Logic Seminar
Nathaniel Bannister, Carnegie Mellon University
Condensed Sets and the Solovay Model
We exhibit a geometric morphism from the Grothendieck topos representing the Solovay model to the κ-pyknotic sets of Barwick--Haine and Clausen--Scholze. We then use the properties of this morphism andautomatic continuity in the Solovay model to outline a proof of Clausen--Scholze's resolution of the Whiteheadproblem for discrete condensed abelian groups. Joint work with Dianthe Basak.
MC 5417