Sage Days 130.5 – April 27 – May 8, 2026, Montréal

A two-week SageMath Festival in Montréal

École de Technologie Supérieure (ÉTS) and Université du Québec à Montréal (UQAM), Montréal, Canada

Topics: Introduction to SageMath for Teaching and Research • Teaching with SageMath • SageMath Research and Development

Overview

As partner institutions within the Université du Québec network, UQAM and ÉTS will host a two-week Sage Days event in Montréal. This will be the 8th Sage Days held in Montréal and the first Sage Days hosted at the École de Technologie Supérieure.

The festival is structured in two complementary weeks:

• Week 1 (ÉTS) focuses on introductions to Python and SageMath for students, instructors, and researchers.

  • It is open to participants from all institutions and levels, with a particular emphasis on:

    learning Python, using SageMath for teaching, basic mathematical applications, and collaborative development tools.

• Week 2 (UQAM) takes the form of a Research Summer School.

  • It will feature a mini-course (with exercise sessions), research talks, and collaborative SageMath working sessions. The emphasis will be on geometric and algebraic combinatorics, computational experimentation, and contributing to the SageMath ecosystem.

This Sage Days is organized within the framework of an NSERC Discovery Grant entitled: “Geometric Combinatorics of Symmetric and Infinite Structures.”

Dates and Venue

Dates

• Week 1: April 27 – May 1, 2026 (ÉTS)

• Week 2: May 4 – May 8, 2026 (UQAM)

Venue

• Week 1: ÉTS Pavillon B (1111 rue Notre Dame Ouest, Montréal, H3C 6M8), B-1516 and B-1518

• Week 2: UQAM Pavillon PK (201 avenue du Président-Kennedy, Montréal, H2X 3Y7), PK-5115

Registration

Registration is required to attend Sage Days 130.5.

• Participation is possible for either week or both weeks.

• Registration is free of charge.

• The registration form is available at https://framaforms.org/inscription-sage-days-ets-uqam-1770393973

Target Audience

Sage Days 130.5 is intended for:

• undergraduate and graduate students
• lecturers and professors
• researchers using computational tools

• SageMath users at all levels

• developers interested in contributing to SageMath

Beginners are welcome, especially during Week 1. Week 2 is particularly suitable for participants with some prior exposure to Python or SageMath.

Prerequisites

• Week 1: No prior knowledge of Python or SageMath is required.

• Week 2: Basic familiarity with Python and/or SageMath is recommended.

Participants are expected to bring a laptop with a working SageMath installation (or the ability to use SageMath via online platforms). If you do not have Sage installed: not a problem! Installation instructions will be provided during the event.

Organizers

• Jose Bastidas (ÉTS - LACIM)

• Jean-Philippe Labbé (ÉTS)

• Nadia Lafrenière (Concordia)

• Alejandro Morales (UQAM)

• Xavier Provençal (ÉTS)

• Franco Saliola (UQAM)

Program

Week 1

Learning Python and SageMath

• Iannick Gagnon (ÉTS) — Introduction to python workflow

• Iannick Gagnon (ÉTS) — More on Python: debugging, call stack, spys

• Iannick Gagnon (ÉTS) — What is git? The basics

• Nadia Lafrenière (Concordia) — Introduction to Sagemath

• TBA — More on Sage

• Jean-Philippe Labbé (ÉTS) — How to contribute to Sage in 2026

• Blaec Bejarano (Cocalc Inc.) — Introduction to Cocalc

• Blaec Bejarano (Cocalc Inc.) — Cocalc for teaching

Tutorials

• TBA — Migrate your material to python/Jupyter

• Jean-Philippe Labbé (ÉTS) — Tutorial Jupyter

• TBA — Tutorial on a desired Sage topic

Interactive Activities

• Lightning Talks — “This is who I am, this is what I wish I could do”

• Notebook Challenge — Learn to create a jupyter notebook, fast!

• Easy bug fixing Challenge — Learn to contribute to Sage, en direct!

• Work hacks — Have/want an efficient life hack? Share and learn!

Week 2

Lectures

• Federico Castillo (Pontificia Universidad Católica, Santiago, Chile) — Crash course on polyhedra

  • This mini course explores the geometry and combinatorics of polyhedra through the lens of SageMath, beginning with classical foundations. The Weyl-Minkowski theorem characterizes polyhedra as intersections of halfspaces and as Minkowski sums of polytopes with cones, providing the structural backbone for everything that follows. From there we move into the arithmetic setting of lattice polytopes, rational cones, and their associated semigroups, where normality and Hilbert bases become central objects of study.

    The second part of the course focuses on unimodular triangulations, which provide a bridge between the combinatorial structure of a polytope and the smoothness of the corresponding toric variety. This naturally sets the stage for a polyhedral treatment of the Nash blowup of a toric variety, where the geometry of the blowup is encoded in an explicit fan construction that can be explored concretely and computationally throughout using SageMath.

• Rafael S. González D'León (Loyola University Chicago) — Permutation Flows

  • The flow polytope \mathcal{F}_G(\mathbf{a})\subset \mathbb{R}^{E(G)} is defined as the collection of nonnegative flows on an (acyclic directed) graph G whose total net flow at vertices is \mathbf{a}\in \mathbb{R}^{V(G)}. Flow polytopes arise as the feasible regions of many optimization problems and exhibit rich combinatorial, algebraic, and geometric structure: the study of their faces, volumes, and lattice points reveals deep connections to a wide range of familiar mathematical objects.

    Danilov, Karzanov, and Koshevoy introduced a combinatorial method, based on the notion of a framed graph (G,F), that produces regular unimodular triangulations of flow polytopes with a unique source, a unique sink, and unit netflow. It was conjectured by Benedetti, González D'León, Hanusa, Harris, Morales, and Yip, that the dual graph of this triangulation has the structure of a lattice—a conjecture recently proved by Bell and Ceballos. The original description of the simplices in terms of collections of coherent routes, however, is unwieldy in practice.

    We introduce a new broadly unifying family of combinatorial objects associated to a framed graph (G,F), which we call permutation flows. This model yields a transparent combinatorial description of these lattices and extends the construction to triangulations of \mathcal{F}_G(\mathbf{a}) for more general netflows \mathbf{a}.

    As applications, we compute the h^*-polynomial of the flow polytope in the unit-flow case and give a new geometric proof of the generalized Lidskii volume formula originally due to Baldoni and Vergne.

Plenary talk

• Amy Wiebe (University of British Columbia) — Nonnegative Integer Matrix Factorization via Lattice Points in Polyhedral Cones

  • Nonnegative matrix factorization is a well-studied problem with many applications, which is nonetheless hard to compute. In this talk, we look at a discrete version of the problem and show how it can be interpreted as a problem of lattice points in polyhedral cones. Using this interpretation, we find geometric inspiration for an algorithm that solves the problem in the case of rank 2 matrices. We also show how the geometry also allows us to reduce the problem efficiently in the case when the matrices are large.

Posters

• Félix Gelinas (York University) - Ornamentation lattices and intreeval hypergraphic lattices

  • Given a directed graph D with transitive closure \text{tc}(D) and path hypergraph \mathbb{P}(D), we study the connections between the (acyclic) reorientation poset of \text{tc}(D), the (acyclic) sourcing poset of \mathbb{P}(D), and the (acyclic) ornamentation poset of D.

    Geometrically, the acyclic reorientation poset of \text{tc}(D) (resp. the acyclic sourcing poset of \mathbb{P}(D)) is the transitive closure of the skeleton of the graphical zonotope of \text{tc}(D) (resp. of the hypergraphic polytope of \mathbb{P}(D)) oriented in a linear direction.

    When D is a rooted (or even unstarred) increasing tree, we show that the acyclic sourcing poset of \mathbb{P}(D) is isomorphic to the ornamentation lattice of D, and that they form a lattice quotient of the acyclic reorientation lattice of \text{tc}(D). As a consequence, we obtain polytopal realizations of the ornamentation lattices of rooted (or even unstarred) increasing trees, answering an open question of C. Defant and A. Sack.

    When D is an increasing tree, we show that the ornamentation lattice of D is the MacNeille completion of the acyclic sourcing poset of \mathbb{P}(D).

    Finally, still when D is an increasing tree, we use the ornamentation lattice of D to characterize the subhypergraphs of the path hypergraph \mathbb{P}(D) whose acyclic sourcing poset is a lattice. This is a joint work with Antoine Abram, Jose Bastidas, Vincent Pilaud and Andrew Sack.

• Shousen Lu (McGill University) - Using Sage to Verify Kolyvagin’s Conjecture for Higher Rank Elliptic Curves

  • In the late 1980s, Kolyvagin used Heegner point on elliptic curve to construct some Galois cohomology class and proved that if those classes are non trivial, we will get an upper bound of the rank of the elliptic curve. We will follow William Stein’s algorithm to use Sage to verify Kolyvagin’s conjecture for more higher rank elliptic curves and point out a potential relation between Mazur-Tate’s refined BSD conjecture and Kolyvagin’s conjecture.

• Mario Morán Cañon (Universidad Autónoma de Madrid) - General components of the jet schemes

  • This poster provides an overview of the general components of the jet schemes of an algebraic variety. These form a family of irreducible components of the jet schemes that encode valuable information about the singularities of the base variety. In the poster, we focus on their connection with nilpotency in the arc scheme and discuss effective methods for computing them. We also mention links with differential operators and Rees algebras. This poster is based on results from a collaborative project with Julien Sebag.

• Jerónimo Valencia Porras (University of Waterloo) - Enumerative combinatorics for alcoved triangulations in types A and C

  • We study the alcoved triangulation of the dilations of hypersimplices of type A to recover enumerative identities involving Eulerian numbers. We also generalize these ideas in two ways: First, by considering q-analogs of the identities and the bijections which relate to the definition of q-Eulerian numbers of Carlitz (1954). Second, we develop a parallel construction for dilated hypersimplices in type C to obtain identities for the corresponding type C Eulerian numbers.

Participants

• Sajjad Ahangar (ÉTS)
• Ilani Axelrod-Freed (Massachusetts Institute of Technology)
• Jose Bastidas (ÉTS - LACIM)
• Abdel Kabir Bello (Université de Montréal)
• Anouk Bergeron-Brlek (ÉTS)
• Dieudonné Junior Bikok
• Marc Boulé (ÉTS)
• Loïc Cassista (Université de Moncton)
• Khadija Dhouib (ÉTS)
• Karimatou Djenabou (UQAM - LACIM)
• Myles Dugas (Université de Moncton)
• Ismael El Yassini (Polytechnique Montréal)
• Danielle Ensign (Independent)
• Maxime Fortier Bourque (Université de Montréal)
• Monica Garcia (UQAM - LACIM)
• Félix Gélinas (York University)
• Rafael S. González D'León (Loyola University Chicago)
• Herman Goulet-Ouellet (Université de Moncton)
• Samira Graïne (ÉTS)
• Ben Hersey (Concordia University)
• Jean-Philippe Labbé (ÉTS)
• Sébastien Labbé (IRL CRM-CNRS)
• Nadia Lafrenière (Concordia University)
• Jean-Michel Lemay (ÉTS)
• Antoine Leudière (University of Calgary)

• Shousen Lu (McGill University)

• Vincent Macri (University of Calgary)
• Samy Mekkati (ÉTS)
• Clare Minnerath (University of Washington)
• Yossef Moftah Mohamed
• Mario Morán Cañón (Universidad Autónoma de Madrid)
• Kaveh Mousavand (Okinawa Institute of Science and Technology)
• Scott Neville (UQAM - LACIM)
• Dima Pasechnik (Northwestern University)
• Viraj Patel (Concordia University)
• Kristen Peterson (Concordia University)
• Austin Pham (Carleton University)
• Brigitte Pilon (ÉTS)

• Alice Postovskiy (McGill University)

• Louis-Xavier Proulx (ÉTS)
• Xavier Provençal (ÉTS)
• Tufel Quentin (UQAM - LACIM)
• Catalina Quincosis (UQAM - LACIM)
• Jerome Quintin (ÉTS)
• Sophie Rehberg (UQAM - LACIM)
• Félix Reutenauer (UQAM - LACIM)
• Guillaume Roy-Fortin (ÉTS)
• Mitchell Ryan (University of British Columbia)
• Geneviève Savard (ÉTS)
• Niccolo Turillo (University of Florida)
• Jerónimo Valencia Porras (University of Waterloo)

• Shubkarman Walia (McGill University)

• Alexander Wilson (York University)

• Ziyue Zhou (Université de Bordeaux & Ecole Polytechnique)

• Boris Zupancic (McGill University)

Practical Information

TBA

Getting to ÉTS

From the Bonaventure metro station, search for exit labeled “ÉTS - École de Technologie Supérieure” and follow the map:

1111 rue Notre Dame Ouest, Montréal, H3C 6M8

Getting to UQAM

From the Place-des-arts metro station: search for exit labeled “UQAM”, which will bring you directly to the Pavillon PK

201 avenue du Président-Kennedy, Montréal, H2X 3Y7

Meals near ÉTS and UQAM

TBA

Code of Conduct

All participants are expected to follow the SageMath Code of Conduct.

Accessibility and Inclusion

The organizers are committed to making Sage Days 130.5 an inclusive and accessible event. Participants with accessibility needs or special accommodations are encouraged to contact the organizers in advance.