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Thursday, November 5, 2026 3:00 pm - 4:00 pm EST (GMT -05:00)

Model Theory Seminar | Rahim Moosa | Around the wild automorphism conjecture

Rahim Moosa (University of Waterloo)

Around the wild automorphism conjecture

The wild automorphism conjecture, of Reichstein, Rogalski, and Zhang from 2006, proposes that if a projective algebraic variety X (in characteristic zero) admits an automorphism that leaves no proper subvariety invariant then X is an abelian variety. I will discuss recent work with Jason Bell where we use tools from the model theory of difference fields (developed last year by Moshe Kamensky and I) to resolve the “compound fundamental isotrivial” case. I will also give a counterexample to the naive nonautonomous generalisation of the conjecture, exhibiting some of the difficulties in applying a model-theoretic analysis.

MC 5403

Thursday, November 5, 2026 3:30 pm - 4:30 pm EST (GMT -05:00)

Geometry and Topology Seminar | Cameron Krulewski | Invertible Field Theories and the Bott Spiral

Cameron Krulewski (Perimeter Institute)

Invertible Field Theories and the Bott Spiral

Symmetry-protected topological phases of matter (SPTs) admit descriptions in terms of homotopy theory. Freed--Hopkins defined "free-to-interacting maps" to model the physical process of comparing free fermion SPTs (classified by K-theory) with more general, interacting models (classified by certain invertible functorial field theories). With Debray and Stehouwer, we generalized this approach to study the "Bott spiral" of SPTs constructed by Queiroz--Khalaf--Stern. After reviewing the homotopical classification of invertible field theories, I will discuss our construction and some subtleties that arise in defining free-to-interacting maps, such as compatibility with dimensional reduction, continuous versus discrete symmetry types, and the lack of interacting Morita invariance.

MC 5417

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
Thursday, November 12, 2026 2:30 pm - 3:30 pm EST (GMT -05:00)

Intro to My Research | Ty Ghaswala

Ty Ghaswala (University of Waterloo)

Intro to My Research

This is a series of talks by faculty members explaining their research at a level aimed at master's students. All other department members are welcome as well.

MC 5501

Thursday, November 12, 2026 3:30 pm - 4:30 pm EST (GMT -05:00)

Geometry and Topology Seminar | Ergun Yalcin | Free Actions on Products of Real Projective Spaces

Ergun Yalcin (Bilkent University and University of Waterloo)
Free Actions on Products of Real Projective Spaces
There are many conjectures on restrictions on finite groups that can act freely on a topological space with prescribed homotopy type. The most famous of these conjectures is the rank conjecture, which claims that if an elementary abelian p-group of rank r acts freely on a product of k spheres, then r is less than or equal to k. In 1983, Cusick made a similar conjecture for free actions on products of real projective spaces. We recently solved the homotopy-theoretic version of Cusick’s conjecture. I will explain some of the main ideas used in the proof of this conjecture, after introducing the necessary background.
MC 5417
Thursday, November 19, 2026 2:30 pm - 3:30 pm EST (GMT -05:00)

Intro to My Research | Ruxandra Moraru

Ruxandra Moraru (University of Waterloo)

Intro to My Research

This is a series of talks by faculty members explaining their research at a level aimed at master's students. All other department members are welcome as well.

MC 5501