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October 2020
Dalhousie-AARMS AAMP Seminar: Jean-Pierre Garbardo (McMaster University)
Title: Factorization of positive definite functions through convolution and the Turàn problem Abstract: If $G$ is a finite abelian group, we call a subset $S\subset G$ symmetric if $0\in G$ and $-x\in S$ whenever $x\in S$. We also let $S^*=(G\setminus S)\cup\{0\}$. We consider the problem of expressing an arbitrary positive definite function $F$ on $G$ as the convolution product of two positive definite functions, one supported on $S$ and the other one supported on $S^*$. We show that, in the…
Find out more »November 2020
Atlantic Graph Theory Seminar: Dr Andrea Burgess (University of New Brunswick, Saint John)
Equitably colourable cycle decompositions A $c$-colouring of a decomposition of a graph $G$ is an assignment of $c$ colours to the vertices of $G$. A colouring is equitable if each colour is represented (as closely as possible) an equal number of times on each block, i.e. for any two colours $i$ and $j$, the number of vertices of colour $i$ and $j$ in any given block differ by at most 1. In this talk, we give an overview of colourings…
Find out more »Dalhousie-AARMS AAMP Seminar: Reem Yassawi (Open University, London)
Title: Some tame or wild Cantor dynamical systems Abstract: A topological dynamical system is a pair $(X,T)$ where $X$ is a compact metric spaces and $T$ is a group or semigroup acting continuously on $X$. One algebraic invariant of a such a dynamical system is the Ellis semigroup. The Ellis semigroup $E(X,T)$ of a topological dynamical system is defined to be the compactification of the action $T$ in the topology of pointwise convergence on the space of all function $X^X$. …
Find out more »AARMS COVID-19 Seminar: Shannon LeBlanc (Dept of Health NB)
Importation Risk under the Northern Lights To understand the risk that an infectious traveler from other Canadian provinces and territories will enter the Northwest Territories the Government of the Northwest Territories has fitted jurisdictional reported COVID-19 transmission data to a simple SEIR model. Using the most recent epidemiological parameters for transmission we estimate the likelihood that a pre-symptomatic or asymptomatic/unreported COVID-19 case will travel to the NWT at time t. We have mapped territorial travel data collected since May 2020…
Find out more »Atlantic Graph Theory Seminar: Kyle MacKeigan (PhD Candidate, Dalhousie University)
Orthogonal Colourings of Graphs Two colourings of a graph are orthogonal if they have the property that when two vertices receive the same colour in one colouring, then those vertices receive distinct colours in the other colouring. In this talk, the importance of perfect orthogonal colourings is demonstrated. Then, perfect orthogonal colourings of Cayley graphs and tree graphs are constructed. To conclude, it is shown how the Cartesian, tensor, and strong graph product can be used to generate perfect orthogonal…
Find out more »Atlantic GR Seminar: Jinzhao Wang (ETH Zurich) and Saikat Mondal (MUN)
Outer entropy equals Bartnik-Bray inner mass, and the gravitational ant conjecture Jinzhao Wang (ETH Zurich) Entropy and energy are found to be closely tied on our quest for quantum gravity. We point out an interesting connection between the recently proposed outer entropy, a coarse-grained entropy defined for a compact spacetime domain motivated by the holographic duality, and the Bartnik-Bray quasilocal mass long known in the mathematics community. In both scenarios, one seeks an optimal spacetime fill-in of a given closed,…
Find out more »Atlantic Graph Theory Seminar: Dr Jared Howell (Memorial University of Newfoundland, Grenfell Campus)
Gracefully labelling windmills using Skolem-like sequences To gracefully label a graph G, assign each vertex v ∊ V(G) a distinct label l(v) from {0,1,2,...,|E(G)|}, such that {|l(u)-l(v)| : uv ∊ E(G)}={1,2,3,...,|E(G)|}. In this talk we will examine constructive techniques using Skolem-like sequences to gracefully label windmills of cycles. This includes new constructive techniques for known results as well as new results on windmills with vanes of mixed cycle length. The Atlantic Graph Theory Seminar series will take place every Wednesday…
Find out more »Dalhousie-AARMS AAMP Seminar: Graham Cox (Memorial University)
Title: Nodal deficiency via equipartition energy functionals and the Dirichlet-to-Neumann map Abstract: A classic result in differential equations is that the nth eigenfunction of a Sturm-Liouville boundary value problem has precisely n-1 zeros. Courant’s nodal domain theorem provides a natural generalization of this result to higher dimensions, but it is generally not sharp. The lack of sharpness is measured by the “nodal deficiency” of an eigenfunction. Despite over a century of intensive study, this quantity is still not very well…
Find out more »December 2020
Atlantic Graph Theory Seminar: Dr Melissa Huggan (Ryerson University)
The Cheating Robot and Insider Information Throughout this talk, we explore a deterministic model as an alternative approach to studying simultaneous play combinatorial games. We call this the Cheating Robot model. This model forces both players to move at the same time, but one player has extra information about where their opponent is going to move and can react accordingly. We discuss some general theory and explore a case study to get some insight into this model. This is joint…
Find out more »Dalhousie-AARMS AAMP Seminar: Peter Hintz (MIT)
Title: Linear stability of slowly rotating Kerr spacetimes Abstract: I will describe joint work with Dietrich Häfner and András Vasy in which we study the asymptotic behavior of linearized gravitational perturbations of Schwarzschild or slowly rotating Kerr black hole spacetimes. We show that solutions of the linearized Einstein equation decay at an inverse polynomial rate to a stationary solution (given by an infinitesimal variation of the mass and angular momentum of the black hole), plus a pure gauge term. The proof uses…
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