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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.

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Events

Friday, November 6, 2026 1:30 pm - 2:30 pm EST (GMT -05:00)

Geometry and Topology Seminar | Jesse Madnick | The Morse index of quartic minimal hypersurfaces

Jesse Madnick (Seton Hall University)

The Morse index of quartic minimal hypersurfaces

Given a minimal hypersurface S in a round sphere, its Morse index is the number of variations that are area-decreasing to second order. In practice, computing the Morse index of a given minimal hypersurface is extremely difficult, requiring detailed information about the Laplace spectrum of S. Indeed, even for the simplest case in which S is homogeneous, the Morse index of S is not known in general.
In this talk, we compute the Morse index of two such minimal hypersurfaces. Moreover, we observe that their spectra contain both integer eigenvalues as well as (irrational) eigenvalues that are not expressible in radicals. This is joint work with Gavin Ball (Missouri) and Uwe Semmelmann (Stuttgart).
MC 5403
Monday, November 9, 2026 2:30 pm - 3:30 pm EST (GMT -05:00)

Pure Math Colloquium | Kumar Murty | Motives, periods and Catalan's constant

Kumar Murty (University of Toronto)

Motives, periods and Catalan's constant

There is a fundamental view that the constants that repeatedly arise in number theory should either be special values of L-functions, or periods of algebraic varieties (or more generally, of motives), and usually both.We will describe this view with examples, including recent work with Payman Eskandari and Yusuke Nemoto on Catalan's constant.
MC 5501
Tuesday, November 10, 2026 10:00 am - 11:00 am EST (GMT -05:00)

Number Theory Seminar | Sourabhashis Das | Prime Gaps in Arithmetic Progressions Are Graphic

Sourabhashis Das (University of Lethbridge)

Prime Gaps in Arithmetic Progressions Are Graphic
A sequence of positive integers is called graphic if it arises as the degree sequence of a simple graph. In this talk, we explore a surprising connection between this classical graph-theoretic notion and the distribution of primes.
Let us call a simple graph on \(n \geq 2\) vertices a prime gap graph if its vertex degrees are \(1\) and the first \(n-1\) prime gaps. Growing out of an empirical observation by Toroczkai, he and his collaborators established that a prime gap graph exists for every sufficiently large \(n\), and for every \(n \geq 2\) under the Riemann Hypothesis, and that an infinite sequence of such prime gap graphs can be generated via the degree-preserving growth process---the first naturally occurring infinite sequence of positive integers identified as graphic.
In this talk, we extend these results to prime gaps in arithmetic progressions. Specifically, we show that the gap sequences formed by consecutive primes in a fixed progression \(a \pmod{q}\), with \(\gcd(a,q)=1\), are likewise graphic. The analytical tools required stem from Heath-Brown's work on bounding moments of large prime gaps. We demonstrate these tools in the context of primes in arithmetic progressions and explain how they drive our proof.
This is joint work with Keshav Aggarwal and is a work in progress.
MC 5501
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