Research

Ongoing Projects

• Gélinas, F. : “Source Characterization of the Hypergraphic Posets”.
• Abram, A.; Bastidas, J.; Gélinas, F.; Pilaud, V.; Sack, A.; Tzanaki, E.: “Hypergraphic Polytopes”.
• Gélinas, F.; Poullot, G.: “Hypergraphic Polytopes Diameter”.

Preprints:

• Andrews, N.; Gagnon, L.; Gélinas, F. ; Schlums, E.; and Zabrocki, M.: “When are Hopf Algebras Determined by Integer Sequences?”. arxiv.2505.06941
• Gélinas, F.; Segovia, A.; and Thomas, H.: “Proof of a conjecture of Matherne, Morales, and Selover on encodings of unit interval orders”. arxiv.2212.12171 – Accepted in The Electronic Journal of Combinatorics.

Publications:

• Frieden, G.; Gélinas, F.; and Soucy, É.: “Cones and ping-pong in three dimensions”. In: Involve, a Journal of Mathematics 17.1 (Mar. 2024), pp. 11–28. issn: 1944-4176. doi: 10.2140/involve.2024.17.11. Journal version. arxiv.2111.14692

Upcoming Talks:

Talks:

• Source Characterization of the Hypergraphic Posets, Canadian Discrete and Algorithmic Mathematics Conference (CanaDAM), University of Ottawa, Ottawa, Ontario, Canada, May, 2025.
• Source Characterization of the Hypergraphic Posets, Algebraic and enumerative combinatorics seminar, University of Waterloo, Waterloo, Ontario, Canada, May, 2025.
• Source Characterization of the Hypergraphic Posets, Winter School and Workshop on Polytopes 2025, Universität Osnabrück, Osnabrück, Lower Saxony, Germany, February, 2025.
• Caractérisation du poset hypergraphique à partir des sources d'orientations acycliques, LACIM seminar, Université du Québec à Montréal (UQAM), Montréal, Québec, Canada, February, 2025.
• Source Characterization of the Hypergraphic Posets, Combinatorial Algebra meets Algebraic Combinatorics (CAAC), The Fields Institute, Toronto, Ontario, Canada, January, 2025.
• Hypergraphic polytopes | Part 2, The Algebraic Combinatorics Workgroup, The Fields Institute, Toronto, Ontario, Canada, November, 2024.
• Hypergraphic polytopes | Part 1, The Algebraic Combinatorics Workgroup, The Fields Institute, Toronto, Ontario, Canada, October, 2024.
• Gently Discovering Gentle Algebras, The Algebraic Combinatorics Workgroup, The Fields Institute, Toronto, Ontario, Canada, May, 2024.
• Permutrees, Graduate student Group, The Fields Institute, Toronto, Ontario, Canada, May, 2024.
• The volume polynomial of a Matroid, The Algebraic Combinatorics Workgroup, The Fields Institute, Toronto, Ontario, Canada, September, 2023.
• Proof of a conjecture of Matherne, Morales, and Selover on encodings of unit interval orders, The Graduate Student Seminar UofT, University of Toronto, Toronto, Ontario, Canada, March, 2023.
• Cones and ping-pong in three dimensions, The Algebraic Combinatorics Workgroup, The Fields Institute, Toronto, Ontario, Canada, March, 2023.
• Proof of a conjecture of Matherne, Morales, and Selover on encodings of unit interval orders, Applied Algebra Seminar, York University, Toronto, Ontario, Canada, March, 2023.
• Cones and ping-pong in three dimensions, The Graduate Students Seminar (UQAM), Université du Québec à Montréal, Montréal, Québec, Canada, August, 2022.
• Cones and ping-pong in three dimensions, Pan-Québec colloquium for students of the ISM, Université Laval, Québec, Québec, Canada, June, 2022.

Poster:

• Source Characterization of the Hypergraphic Posets, AlCoVE: an Algebraic Combinatorics Virtual Expedition, Online, May, 2025.
• Proof of a conjecture of Matherne, Morales, and Selover on encodings of unit interval orders, VIII Encuentro Colombiano de Combinatoria (ECCO), Universidad del Cauca, Popayàn, Cauca, Colombia, June, 2024.
• The volume polynomial of a Matroid, Combinatorial Algebra meets Algebraic Combinatorics (CAAC), Université du Québec à Montréal, Montréal, Québec, Canada, January, 2024. Poster.
• Proof of a conjecture of Matherne, Morales, and Selover on encodings of unit interval orders, Combinatorial Algebra meets Algebraic Combinatorics (CAAC), University of Waterloo, Waterloo, Ontario, Canada, January, 2023. Poster