Events

Title: Oriented Cayley Graphs with all eigenvalues being integer multiples of $\sqrt{\Delta}$

Abstract:

Let $G$ be a finite abelian group. An oriented Cayley graph on $G$ is a Cayley digraph $X(G,C)$ such that $C \cap (-C)=\emptyset$. Consider the $(0,1,-1)$ skew-symmetric adjacency matrix of an oriented Cayley graph $X=X(G,C)$.

Title: Minimal induced subgraphs of two classes of 2-connected non-Hamiltonian graphs

Abstract:

Finding sufficient conditions for a class of graphs to be Hamiltonian is an old problem, with a wide variety of conditions such as Dirac's degree condition and Whitney's theorem on 4-connected planar triangulations. We discuss some past results on sufficient conditions for Hamiltonicity involving the exclusion of fixed induced subgraphs, and some properties of the graphs involved in such results.

Title: Multiplying quantum Schubert polynomials using combinatorics

Abstract:

Schubert polynomials are a very interesting family of polynomials in algebraic geometry due to their relation with the cohomology of the flag variety. Moreover, they are also very interesting from a combinatorial point of view because they can be considered generalizations of Schur functions. 

Title: Yet Another Proof of the Erdős-Ko-Rado Theorem

Abstract:

We give a short new algebraic proof of the Erdős-Ko-Rado theorem, that for k < n/2, the largest families of k-sets of an n-element set such that any two of its members intersect are precisely those families composed of all k-sets that contain some fixed element.

Title: A local version of Hadwiger’s Conjecture

Abstract:

In 1943, Hadwiger famously conjectured that graphs with no $K_t$ minors are $t-1$ colourable. There has also been significant interest in several variants of the problem, such as list colouring or only forbidding certain classes of minors.

Title: Modular relations between chromatic symmetric functions

Abstract:

In 1995, Stanley introduced the chromatic symmetric functions. The study of chromatic symmetric functions of graphs inspired two main research directions.

Title: Deletion-contraction for a unified Laplacian and applications

Abstract:

We define a graph Laplacian with vertex weights in addition to the more classical edge weights, which unifies the combinatorial Laplacian and the normalised Laplacian.

Title: Lattice path matroids, lattice path polymatroids, and excluded minors

Abstract:

We define lattice path matroids, polymatroids, Boolean polymatroids, and lattice path polymatroids, which are a subclass of Boolean polymatroids. 

Title: The one-sided cycle shuffles in the symmetric group algebra

Abstract:

Elements in the group algebra of a symmetric group S_n are known to have an interpretation in terms of card shuffling. I will discuss a new family of such elements, recently constructed by Nadia Lafrenière: Given a positive integer n, we define n elements t_1, t_2, ..., t_n in

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