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## October 2020

### Dalhousie-AARMS AAMP Seminar: Hari Kunduri (Memorial University)

Title: Geometric inequalities for axisymmetric black holes Abstract: In general relativity, isolated, dynamical black holes arise from asymptotically flat initial data for the Einstein equations. Such data are characterized by invariants such as the ADM mass and angular momentum. When angular momentum is conserved in the evolution, the standard picture of gravitational collapse suggests an inequality relating the ADM mass and angular momentum. Such geometric inequalities have been rigorously proved for axisymmetric, asymptotically flat maximal initial data for the vacuum Einstein…

Find out more »### Atlantic GR Seminar: Turkuler Durgut (MUN)

Asymptotically Anti-de Sitter Gravitational Solitons In this talk, I will consider the stability of asymptotically anti-de Sitter gravitational solitons. These are globally stationary, asymptotically (globally) AdS spacetimes with positive energy but without horizons. I will introduce my ongoing project investigating solutions of the linear wave equation in this class of backgrounds. I will provide analytical expressions for the behavior of the scalar field near the soliton bubble and at spatial infinity. The special BPS (supersymmetric) case will then be examined…

Find out more »### Atlantic Graph Theory Seminar: Iain Beaton (PhD Candidate, Dalhousie University)

The Average Order of Dominating Sets of a Graph This talk focuses on the average order of dominating sets of a graph. We find the extremal graphs for the maximum and minimum value over all graphs on n vertices, while for trees we prove that the star minimizes the average order of dominating sets. We prove the average order of dominating sets in graphs without isolated vertices is at most 3n/4, but provide evidence that the actual upper bound is…

Find out more »### 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 »### 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…

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