Welcome to the York University Discrete Mathematics seminar. During the Winter 2025 term, the seminar will be on Wednesday every two weeks at 2:00 PM, Ontario time. Location: N501/Ross, York University.

This seminar is organized by Amena Assem (amnassem@yorku.ca) and Sarobidy Razafimahatratra (srazafim@fieldsinstitute.ca). Please email us if you would like to give a talk in this seminar.



Speaker: Gill Barequet (Technion – Israel Inst. of Technology)

Date and time: March 14 at 2:00 PM.

Location: N638/Ross, York University

Title: Polycubes with small perimeter defect

Abstract: Lattice animals are connected sets of cells on a lattice. For example, polyominoes are connected sets of cells on the planar square lattice, where connectivity is through edges (sides of the squares). One of the main problems in this area is finding a formula for the number of animals (or for the number of members of some family of animals) on some lattice.

In this talk, I will explore methods for setting formulae for the number of animals on the \(d\)-dimensional cubical lattice, whose perimeter deviates by a fixed constant from the maximum possible perimeter.

Joint work with Andrei Asinowski (Alpen-Adria-Universität Klagenfurt) and Yufei Zheng (UMass Amherst).



Speaker: Jane Breen (Ontario Tech University)

Date and time: February 12 at 2:00 PM.

Location: N501/Ross, York University

Title: Maximum spread of graphs

Abstract: Given a graph \(G\), let \(\lambda_1\) and \(\lambda_n\) be the maximum and minimum eigenvalues of its adjacency matrix and define the spread of \(G\) to be \(\lambda_1-\lambda_n\). In this talk we discuss solutions to a 20-year-old conjecture of Gregory, Hershkowitz, and Kirkland regarding the spread of graphs. Our proofs use techniques from the theory of graph limits (graphons) and numerical analysis, including a computer-assisted proof of a finite-dimensional eigenvalue problem using both interval arithmetic and symbolic computations.



Speaker: Denys Bulavka (Hebrew University of Jerusalem)

Date and time: January 29 at 3:00 PM.

Location: N638/Ross, York University

Title: A Hilton-Milner theorem for exterior algebras

Abstract: The now-classical theorem of Erdős, Ko and Rado from 1961 says that the largest pairwise-intersecting families of k-sets are the ones where all the members share a fixed element, and with slightly stronger hypothesis these are the only maximal families. These families are called trivial families. Hilton and Milner in 1967 proved the next best upper-bound, that is they provided an upper bound for the size of non-trivial pairwise intersecting families of k-sets. These theorems have been generalized to several scenarios where there is a notion of intersection such as simplicial complexes, permutations, matrices, vector spaces, to name a few. In this talk I will focus on subspaces of the exterior algebra where the analog of being pairwise-intersecting is called self-annihilating. Scott and Wilmer ‘21, and Woodroofe ‘22 proved an upper-bound on the dimension of self-annihilating subspaces of the exterior algebra and conjectured that the characterization part of the Erdős, Ko and Rado theorem should hold as well. We proved this conjecture. Moreover, we prove a Hilton-Milner type upper-bound for non-trivial self-annihilating subspaces.This is a joint work with Francesca Gandini and Russ Woodroofe.

Future talks