Speaker: Andrew Beveridge, Macalester College Title: Approval Ballot Triangles Time: Wednesday, February 14, 3.30pm Atlantic time Live viewing for local participants in Chase 227, Dalhousie University Bertrand's Ballot Problem enumerates the number of ways to count ballots so that candidate 1 never trails candidate 2. We generalize this problem by considering an approval ballot election between $n$ candidates. In an approval ballot election, each voter endorses a subset of candidates, rather than voting for just one person. The general approval…

Speaker: Ada Chan, York University Title: Polygamy in state transferAbstract:Let $X$ be a graph and $H$ be a Hermitian matrix associated with $X$.   The continuous-time quantum walk with Hamiltonian $H$ isdefined by the time-dependent unitary matrix\begin{equation*}U(t)=e^{i t H}.\end{equation*}Perfect state transfer occurs from vertex $a$ to vertex $b$ at time $\tau$ is $\vert U(\tau)_{b,a}\vert = 1$.   This phenomenon is relevant for information transmission in a quantum spin network.   For real and symmetric Hamiltonians, it is known that perfect state transfer can…

Pursuit-evasion on Graphs Trent Marbach, Toronto Metropolitan University The study of pursuit-evasion on graphs looks at games played between two adversaries, with one player tasked with alluding capture from the other on the graph. We will describe these types of games in general, although we will take a particular focus on two games: the Cops and Robber game, and the Localization game. A famous open conjecture for the Cops and Robber game has spurred recent work in the area, and…

Induced subgraphs and treewidth Speaker: Sophie Spirkl, University of Waterloo Abstract: Treewidth is a measure of the complexity of a graph and has both structural and algorithmic consequences. While results of Robertson and Seymour characterize which minors appear in graphs of large treewidth, the same question is still open for induced subgraphs. I will present some recent results towards an answer to this question, in particular, about when excluding a finite set of induced subgraphs leads to the answer being…

Title: How do we use graphs to transmit quantum information? Time: 3.30pm, Atlantic time, (1:30, CDT) Wednesday Sept. 18 Speaker: Hermie Monterde, University of Manitoba Abstract: In this talk, a graph $G$ represents a quantum spin network (a networking of interacting subatomic particles). The vertices and edges of $G$ represent the particles and their interactions in the network. Consider the complex unitary matrix $U(t)=\exp(itA)$, where $A$ is the adjacency matrix of $G$, $i^2=-1$ and $t$ is a real number. The propagation of quantum…

The Martin Invariant and Other Results on the Interlace Polynomials Josephine Reynes, University of Waterloo There are many well studied graph polynomials, but this talk will focus on the Martin polynomial and the interlace polynomial. Specifically, this talk will look at how these two polynomials are related and how results on the Martin polynomial can be extended to the interlace polynomial. The Martin invariant, a specific evaluation of the Martin polynomial, obeys the symmetries of the Feynman period. The Feynman…

Speaker #1: Peter Collier, Dalhousie University Title #1: Zero Forcing on Twisted Hypercubes Abstract #1: The hypercube stands out as a compelling and versatile structure that extends the geometric notion of a cube into higher dimensions. We study the twisted hypercube variant in an attempt to optimize processes on similarly degree-regular, highly connected graphs. The particular process we optimize is zero forcing, a graph infection process in which a particular colour change rule is iteratively applied to the graph and an…