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
Viktor Majewski, University of Waterloo
Filling Holes in the Spin(7)-Teichmüller Space and String Cohomology
In this talk, I apply the analytic results from the first talk to study the boundary of the Spin(7) Teichmüller space.Using compactness results for Ricci-flat metrics together with known examples of Spin(7) manifolds, it is knownthat Spin(7) orbifolds with SU(N) isotropy arise as boundary points of the moduli space. Building on theresolution scheme for Spin(7) orbifolds that I discussed in 2024, and which I will briefly review, we show howthis boundary can be removed by requiring Spin(7) orbifolds to encode information about their resolutions. Inthis way, the Teichmüller space is enlarged to include orbifold limits together with their compatible resolutions,thereby filling in the boundary. Finally, we explain how this perspective is related to a Spin(7) analogue of thecrepant resolution conjecture from string cohomology, providing a geometric interpretation of the obstructioncomplex discussed in the linear gluing analysis in the first talk.
MC 5403
Geometry and Topology Seminar
Siyuan Lu, McMaster University
Interior C^2 estimate for Hessian quotient equation
In this talk, we will first review the history of interior C^2 estimates for fully nonlinear equations. As a matter offact, very few equations admit this property, not even the Monge-Ampère equation in dimension three or above.We will then present our recent work on interior C^2 estimate for Hessian quotient equation. We will discuss themain idea behind the proof. If time permits, we will also discuss the Pogorelov-type interior C^2 estimate forHessian quotient equation and its applications.
MC 5417
Computability Learning Seminar
William Dan, University of Waterloo
Solovay Reducibility and Relative Randomness
Having completed our characterization of left-c.e. random reals, we return to the concept of Solovay reducibilityto study it more deeply. We will see that beyond the characterizations we have seen so far, Solovay reducibilitycan be viewed as a measure of relative randomness, and connect this perspective back to the Kucera-Slamantheorem. We will also relate it to the reducibilities we have studied previously, and give a final, possiblysimplest, characterization of Solovay reducibility. This seminar follows sections 9.1 and 9.2 from the Downeyand Hirschfeldt book.
MC 5403