Shapes

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

Thursday, February 27, 2025 4:00 pm - 5:00 pm EST (GMT -05:00)

Analysis Seminar

Pavlos Kalantzopoulos, UC Irvine

Analysis Seminar: A multiversion of real and complex hypercontractivity

We establish a multiversion of real and complex Gaussian hypercontractivity. More precisely, our result generalizes Nelson’s hypercontractivity in the real setting and the works of Beckner, Weissler, Janson, and Epperson in the complex setting to several functions. The proof relies on heat semigroup methods, where we construct an interpolation map that connects the inequality at the endpoints. As a consequence, we derive sharp multidimensional versions of the Hausdorff-Young inequality, a Noisy Gaussian-Jensen inequality, and the log-Sobolev inequality. This is joint work with Paata Ivanisvili.

MC 5417 or Join on Zoom

Wednesday, March 5, 2025 3:30 pm - 5:00 pm EST (GMT -05:00)

Differential Geometry Working Seminar

Paul Cusson, University of Waterloo

Holomorphic vector bundles over an elliptic curve

We'll go over the classification of holomorphic vector bundles over an elliptic curve, with a focus on the rank 1 and 2 cases. For the case of line bundles, we'll show that the space of degree 0 line bundles is isomorphic to the elliptic curve itself. The classification of rank 2 bundles rests on the existence of two special indecomposable 2-bundles of degree 0 and 1, which we will describe in detail. The general case for higher ranks would then follow essentially inductively

MC 5479

Monday, March 10, 2025 2:30 pm - 3:30 pm EDT (GMT -04:00)

Pure Math Department Colloquium

Elisabeth Werner, Case Western Reserve University

Affine invariants in convex geometry

In analogy to the classical surface area, a notion of affine surface area (invariant under affine transformations) has been defined. The isoperimetric inequality states that the usual surface area is minimized for a ball. Affine isoperimetric inequality states that affine surface area is maximized for ellipsoids. Due to this inequality and its many other remarkable properties, the affine surface area finds applications in many areas of mathematics and applied mathematics. This has led to intense research in recent years and numerous new directions have been developed. We will discuss some of them and we will show how affine surface area is related to a geometric object, that is interesting in its own right, the floating body.

MC 5501