TBA

• Andrew Sutherland (Massachusetts Institute of Technology)

Room: Amphithéâtre Hermite

TBA

• Arnaud Chéritat (CNRS/Institut de Mathéamtiques de Toulouse)

Room: Amphithéâtre Hermite

What Color Should This Pixel Be?

• Roice Nelson

Room: Amphithéâtre Hermite Often mathematical illustration boils down to drawing digital images, which itself is ultimately setting colors of individual pixels. I'm going to share escapades in the context of this reductionistic perspective. We'll discuss how the particular color choice for a pixel can have big effects, how much image sizes limit us, and weirder questions like choosing pixel shapes. Technology really wants pixels to be Gaussian integers!

TBA

• Iván Rasskin (Aix-Marseille Université)

Room: Amphithéâtre Hermite

TBA

• Cruz Godar (Yale University)

Room: Amphithéâtre Hermite

TBA

• Stephen Trettel (University of San Francisco)

Room: Amphithéâtre Hermite

TBA

• Jonathan Love (Leiden University)

Room: Amphithéâtre Hermite

Rational points on the sphere

• Claire Burrin

Room: Amphithéâtre Hermite I will discuss some recent work on the distribution of rational points on the unit sphere and related conjectures.

TBA

• Daniel Martin (Clemson University)

Room: Amphithéâtre Hermite

Dots and Laurent Series

• Jayadev Athreya (University of Washington)

Room: Amphithéâtre Hermite We'll describe some ongoing discussions and visuals around a beautiful example of Francois Ledrappier, known as the 3-dots example. We'll explain the connection between this example and Laurent series over finite fields, which we learned from Doug Lind, and explain some ongoing work on understanding periodic objects with Aaron Abrams, Edmund Harriss, and Glen Whitney.

TBA

• Edmund Harriss

Room: Amphithéâtre Hermite

A dichotomy in the tail behaviour of quadratic Weyl sums

• Francesco Cellarosi (Queen's University)
• Francesco Cellarosi (Queen's University)

Room: Amphithéâtre Hermite Jointly with Tariq Osman, we completed the classification of the tail behaviour of the limiting distributions of all quadratic Weyl sums of the form 1/\sqrt{N} \sum_{n=1}^N e( ((1/2)n^2+\beta n)x+\alpha n). When \alpha and \beta are both rational, while trying to understand the contribution of certain orbits to the heavy tails, we discovered that some pairs actually lead to a compactly supported limiting distribution. I will especially emphasise the role of mathematical illustration in our understanding of the geometry of the relevant orbits, as well the importance of numerical simulations to validate our results and prompt new questions.

A Few Attempts at Visualizing Shimura Varieties

• Sean Gonzales (UC Berkeley)

Room: Amphithéâtre Hermite Shimura varieties are notoriously complex objects; the very definition of a Shimura variety is typically avoided in a research presentation, lest the entire talk is eaten up by the details. In this talk, I will share some of my attempts at visualizing Shimura varieties, ranging from the modular curve to higher dimensional Shimura varieties in characteristic p. Prior exposure to Shimura varieties is not required.

TBA

• PIERRE ARNOUX (Université d'Aix-Marseille)

Room: Amphithéâtre Hermite

TBA

• Robert Corless (Western University)

Room: Amphithéâtre Hermite

TBA

• Sébastien Labbé

Room: Amphithéâtre Hermite

Classifying integer hypertilings

• Ian Short (The Open University)

Room: Amphithéâtre Hermite In 2018 Demonet et al observed that there is essentially only one three-dimensional positive integer tiling with the property that each cross-section is an SL2-tiling (in which all squares have determinant 1). Inspired by Bhargava’s work on binary quadratic forms, we describe a model for the more general class of three-dimensional integer tilings, which we call hypertilings, with the property that each cross-section is a two-dimensional integer tiling (in which all squares have the same determinant). This model comprises a Bhargava cube and a triple of paths in the weighted Farey graph. The hypertiling entries are encoded geometrically by lambda lengths between horocycles or arithmetically by data from the weighted Farey graph. This is joint work with Oleg Karpenkov, Matty van Son, and Andrei Zabolotskii.

TBA

• Sally Koutsoliotas (Bucknell University)

Room: Amphithéâtre Hermite

TBA

• Claire Frechette

Room: Amphithéâtre Hermite

TBA

• Bernat Espigule (Universitat de Girona)

Room: Amphithéâtre Hermite

Unintentional illustration

• Anna Felikson (Durham University)

Room: Amphithéâtre Hermite I will report on two stories when illustration happened without my conscious participation. The first story is elementary and concerns tilings on the plane. The second one is about friezes on surfaces (a generalization of Conway-Coxeter's frieze patterns) and hyperbolic geometry. This second story is based on the joined work with Pavel Tumarkin (see arXiv:2410.13511).

TBA

• Gabriel Dorfsman-Hopkins (St. Lawrence University)

Room: Amphithéâtre Hermite