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Thursday, October 8, 2026 2:30 pm - 3:30 pm EDT (GMT -04:00)

Intro to My Research | Jason Bell

Jason Bell (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, October 8, 2026 3:00 pm - 4:00 pm EDT (GMT -04:00)

Logic/Model Theory Seminar | Daniel Max Hoffmann | Amenable tame flows: Theorems motivated by model-theoretic dynamics

Daniel Max Hoffmann (University of Warsaw)
Amenable tame flows: Theorems motivated by model-theoretic dynamics
There is an interesting interplay between model theory and topological dynamics. Newelski suggested using the machinery of topological dynamics to study definable groups and the related dynamics on spaces of types. For example, he proposed a conjecture stating that, under suitable model-theoretic assumptions, the Ellis group of a flow should be isomorphic to the compact group (G/G^{00}). This conjecture was confirmed for definably amenable groups in NIP by Chernikov and Simon (2018), but was also refuted in NIP for SL(2,R) by Gismatullin, Penazzi and Pillay (2015). Krupiński and Pillay formulated a weaker version, the so-called revised Newelski conjecture, stating that, under NIP, the Ellis group associated with definable group dynamics has a Hausdorff (\tau)-topology. This revised conjecture was confirmed by Chernikov, Gannon and Krupiński for definable group dynamics in a metrizable setting. Basso and Zucker then extended this result to the non-metrizable setting via forcing; in fact, they generalized some parts of Glasner’s structural results.
Krupiński and I observed that an abstract variant of Newelski’s original conjecture follows from Glasner’s results for amenable, tame, minimal and metrizable flows. Our goal was then to remove the metrizability assumption, as had been done in the case of the revised conjecture. This led to results on the amenability of the Ellis semigroup and on the measurable structure of amenable minimal tame flows. These results will be presented in two papers.
The first is already available on arXiv: https://arxiv.org/abs/2607.24381.
MC 5403
Friday, October 9, 2026 9:30 am - 11:00 am EDT (GMT -04:00)

Algebraic Geometry Working Seminar | Francisco Villacis | Linear Amoebas and their Combinatorial Properties

Francisco Villacis (University of Waterloo)
Linear Amoebas and their Combinatorial Properties
A projective toric variety \(X\Sigma\) comes with a moment map \(\mu\), whose image is a convex polytope that encodes a lot of the geometry of \(X\Sigma\). These moment maps and their associated polytopes have played a fundamental role in quantization programs and mirror symmetry. One natural question when studying these maps is whether the image \(\mu(X)\) also encodes geometric information of a subvariety \(X\subset X_\Sigma\). In this talk, we introduce combinatorial objects that let us study this image, called the (compactified) amoeba of \(X\), in the case where \(X\) is a linear subspace of projective space.
MC 5403
Tuesday, October 20, 2026 10:00 am - 11:00 am EDT (GMT -04:00)

Number Theory Seminar | Xingchi Ruan | The Hilbert-Kamke Problem in Number Fields

Xingchi Ruan (University of Waterloo)
The Hilbert-Kamke Problem in Number Fields
The Hilbert-Kamke problem is a generalization of Waring’s problem to a system of equations, in which the sums of the first n powers of the same variables are given. By the circle method, the existence of solutions depends on a positive lower bound for the singular series. In this talk, we study this problem over a number field. We set up the circle method, following Siegel and Wang, and write the singular series as a product of local densities. Under a necessary arithmetic condition, and with enough variables, we prove that the singular series is bounded below by a positive constant depending only on the number of equations and the degree of the field. The proof is given first for quadratic fields and then for every number field.
MC 5501
Thursday, October 22, 2026 1:00 pm - 2:00 pm EDT (GMT -04:00)

Student Number Theory Seminar | AJ Fong | Galois actions on the Picard groups of K3 surfaces of rank 2

AJ Fong (University of Waterloo)

Galois actions on the Picard groups of K3 surfaces of rank 2

We are interested in studying the actions of the absolute Galois group on curves on surfaces. As surfaces of intermediate type, K3 surfaces can be considered geometric analogues of elliptic curves. In this talk I will describe the combinatorial data controlling the possible actions of the Galois group, and ongoing work on constructing (more) explicit examples of surfaces with the desired actions.

MC 5479

Thursday, October 22, 2026 2:30 pm - 3:30 pm EDT (GMT -04:00)

Pure Math Colloquium | Nigel Hitchin | Geometry and Physics in two dimensions

Nigel Hitchin (University of Oxford)
Geometry and Physics in two dimensions
Fifty years ago, gauge theory in four dimensions brought new techniques into play in geometry and established a dialogue between physicists and mathematicians which has persisted. The talk will discuss ways in which these aspects have been adopted in studying quite concrete problems in two dimensions of interest to both communities. They reveal both the benefits and limitations of having alternative viewpoints.
DC 1302
Friday, October 23, 2026 9:30 am - 11:00 am EDT (GMT -04:00)

Algebraic Geometry Working Seminar | Abdullah Zubair | Fantastacks

Abdullah Zubair (University of Waterloo)

Fantastacks

In this talk, we will discuss fantastacks which are a special family of toric stacks whose construction parallels the Cox construction of toric varieties. We will compute the Picard group of any fantastack and give an idea of how to compute the cohomology of line bundles.

In the pre-seminar period, I will give a brief overview of toric stacks.

MC 5403

Thursday, October 29, 2026 1:00 pm - 2:00 pm EDT (GMT -04:00)

Student Number Theory Seminar | Gian Cordana Sanjaya | Multiplicatively dependent integer vectors on a hyperplane

Gian Cordana Sanjaya, University of Waterloo

Multiplicatively dependent integer vectors on a hyperplane

In 2018, Pappalardi, Sha, Shparlinski, and Stewart counted the number of multiplicatively dependent n-tuples of algebraic integers in a fixed number field, ordered by pointwise Weil height. Extending this work, in a joint with with Afifurrahman and Iverson in 2026, we count the number of multiplicatively dependent n-tuples of rational integers lying on a hyperplane, ordered by maximum absolute value. In this talk, we will discuss about the multiplicatively dependent tuples, some motivations behind them, and how to count these tuples, leading to the main results of both papers.

MC 5479