Atlantic GR Seminar: Nicholas Layden (Dalhousie) and Sharmin Akhter (MUN)
2020-08-26 13:00 - 14:00 (America/Halifax) | Zoom seminar
Geometric Horizons in the Szekeres Spacetime
Nicholas Layden (Dalhousie University)
A new conjecture for geometric horizons has been introduced which may provide a potential alternative to using apparent horizons and related surfaces for analyzing the dynamics of black hole spacetimes. In particular, using two examples of black hole formation in a collapsing universe in the Szekeres spacetime, the formation, evolution, and detection of geometric horizons are shown. In addition, a function for detecting apparent horizons in the Szekeres spacetime is also considered, and it is shown that the apparent horizon in the Szekeres model, is in fact, a geometric horizon. The Cartan-Karlhede algorithm for determining local equivalences of spacetimes is used to compute an invariant frame in the Newman Penrose frame formalism, and Cartan invariants derived from the spacetime in this frame are shown to detect the geometric horizons under various conditions on the curvature tensors of the spacetime. One model for primordial black hole formation and another for galactic black hole formation are considered with non-zero cosmological constants, generalizing work published previously on these models with zero cosmological constant. Future work utilizing geometric horizons may provide benefits in gravitational wave research involving black hole mergers.
Rigidity of Marginally Outer Trapped Surfaces in RNdS Spacetime
Sharmin Akhter (Memorial University of Newfoundland)
We investigate the rigidity of MOTS in four dimensional Reissner-Nordstrom-de Sitter spacetime. This is connected to the study of the first order derivative of stability operator (and hence the second derivative of outgoing null expansion). Since the stability operator has a zero eigenvalue in our case, we use the Lyapunov-Schmidt reduction to establish rigidity.
The Atlantic General Relativity 2020 online postdoc/student seminar series is in the tradition of the annual AGR meetings, providing a forum not only for students and postdocs to present their research and make professional contacts but also to facilitate connections and collaborations between all Atlantic Canadian relativists. The series is student-organized and includes all areas of classical and quantum gravity. Talks will occur on the last Wednesday of every month, with each session consisting of two 30 minute talks. If you would like to attend, please email the organizers for connection details.

AARMS COVID-19 Seminar: Amy Hurford (MUN)
2020-08-26 15:00 - 16:30 (America/Halifax)
Modelling the impact of travel restrictions on COVID-19 cases in Newfoundland and Labrador
Imported infections disproportionally contribute to coronavirus disease 2019 (COVID-19) outbreaks in regions where infection prevalence is low. On May 4th, Newfoundland and Labrador implemented travel restrictions whereby non-residents could enter NL only with exemptions. As the prevalence of COVID-19 was low at the time, it is likely that the travel restrictions substantially reduced the COVID-19 epidemic in NL. We fit a stochastic epidemic model to data describing the number of active COVID-19 cases in NL from March 14th – May 4th. We then forecast the distribution of outbreak sizes over the 9 weeks subsequent to May 4th, with and without the travel restrictions, and for physical distancing scenarios ranging from a 40% to 70% reduction in the daily contact rate relative to pre-pandemic levels. The implementation of travel restrictions in NL resulted in a 20-fold decrease in the number of cases over the subsequent 9 weeks. Assuming that physical distancing reduced the contact rate to 55% of its pre-pandemic level, the median number of cases without the travel restrictions was 19 and with the travel restrictions was 1. Using epidemic modelling, we show how the NL outbreak would have unfolded had travel restrictions not been implemented. The few COVID-19 cases reported following the implementation of travel restrictions is not evidence that the travel restrictions were unnecessary; rather our modelling shows that the travel restrictions are a plausible reason why there were few reported cases in NL in the 9-weeks after May 4th.
This is a virtual zoom seminar. If you would like to attend, please email the organizers for connection details.

Dalhousie-AARMS AAMP Seminar: Michael Ward (UBC)
2020-09-25 16:00 - 17:00 (America/Halifax)
Synchrony and Oscillatory Dynamics for a 2-D PDE-ODE Model of Diffusion-Sensing with Small Signaling Compartments
We analyze a class of cell-bulk coupled PDE-ODE models, motivated by quorum and diffusion sensing phenomena in microbial systems, that characterize communication between localized spatially segregated dynamically active signaling compartments or “cells” that have a permeable boundary. In this model, the cells are disks of a common radius and they are spatially coupled through a passive extracellular bulk diffusion field with diffusivity in a bounded 2-D domain. Each cell secretes a signaling chemical into the bulk region at a constant rate and receives a feedback of the bulk chemical from the entire collection of cells. This global feedback, which activates signaling pathways within the cells, modifies the intracellular dynamics according to the external environment. The cell secretion and global feedback are regulated by permeability parameters across the cell membrane. For arbitrary reaction-kinetics within each cell, the method of matched asymptotic expansions is used in the limit of small cell radius to construct steady-state solutions of the PDE-ODE model, and to derive a globally coupled nonlinear matrix eigenvalue problem (GCEP) that characterizes the linear stability properties of the steady-states. The analysis and computation of the nullspace of the GCEP as parameters are varied is central to the linear stability analysis. In the limit of large bulk diffusivity, an asymptotic analysis of the PDE-ODE model leads to a limiting ODE system for the spatial average of the concentration in the bulk region that is coupled to the intracellular dynamics within the cells. Results from the linear stability theory and ODE dynamics are llustrated for Sel’kov reaction-kinetics, where the kinetic parameters are chosen so that each cell is quiescent when uncoupled from the bulk medium. For various specific spatial configurations of cells, the linear stability theory is used to construct phase diagrams in parameter space characterizing where a switch-like emergence of intracellular oscillations can occur through a Hopf bifurcation. The effect of the membrane permeability parameters, the reaction-kinetic parameters, the bulk diffusivity, and the spatial configuration of cells on both the emergence and synchronization of the oscillatory intracellular dynamics, as mediated by the bulk diffusion field, is analyzed in detail. The linear stability theory is validated from full numerical simulations of the PDE-ODE system, and from the reduced ODE model when is large.
Joint work with Sarafa Iyaniwura (UBC) and Jia Gou (UC Riverside).
The Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over Zoom. If you would like to attend, please email the organizers for connection details.

Atlantic GR Seminar: Kam To Billy Chan (MUN)
2020-09-30 13:00 - 14:00 (America/Halifax)
The Reissner-Nordstrom Near Horizon Geometry is a Tangent Spacetime
The near horizon geometry (NHG) of an extremal Reissner-Nordstrom black hole is obtained in conventional global AdS coordinates and in the coordinates of the parent spacetime. Geometrical objects, specifically Killing vectors and spacetime points, are mapped from the boundary and horizon of the NHG into the parent spacetime coordinates. The outcome is that the NHG is a tangent spacetime to the extremal Reissner-Nordstrom black hole’s degenerate horizon and that the degenerate horizon does not bifurcate. A generalization is made for N-dimensional Reissner-Nordstrom black holes. This work is an extension of Sean Stotyn’s A Tale of Two Horizons.
The Atlantic General Relativity 2020 online postdoc/student seminar series is in the tradition of the annual AGR meetings, providing a forum not only for students and postdocs to present their research and make professional contacts but also to facilitate connections and collaborations between all Atlantic Canadian relativists. The series is student-organized and includes all areas of classical and quantum gravity. Talks will occur on the last Wednesday of every month, with each session consisting of two 30 minute talks. If you would like to attend, please email the organizers for connection details.

AARMS COVID-19 Seminar: Karen Phillips (Dept of Health and Wellness, PEI) and Javier Sanchez (Atlantic Veterinary College, UPEI)
2020-09-30 15:00 - 16:30 (America/Halifax)
The Covid-19 modeling experience in Prince Edward Island
Since the beginning of the COVID-19 pandemic, Atlantic Canada and particularly PEI, has experienced a low number of cases with limited community spread. This epidemiological situation has created some unique and challenging opportunities for the modelers to address the questions of interest posed by public health officers.
A simple SEIR model was developed to assess the magnitude of the consequences in terms of hospitalizations, PPE, and bed requirements under a set of scenarios that could potentially happen if community spread starts to occur in the region. The model was based on differential equations and included features such as reduction of contact rates, self isolation, contact tracing, and quarantine. It also allows assessing the impact on different testing strategies and test requirements to control the outbreak.
Also, a Bayesian model was also developed to assess the probability that the province was free of virus circulation given the testing carried out by the government.
During this seminar will discuss how the model and modeling team addressed some of the questions of interest and describe in [some] details the mathematical models developed by the team.

Dr. Karen Phillips is an Epidemiologist at the Chief Public Health Office, Prince Edward Island Department of Health and Wellness
Dr. Javier Sanchez is a Professor of Epidemiology at the Atlantic Veterinary College, University of Prince Edward Island

This is a virtual zoom seminar. If you would like to attend, please email the organizers for connection details.

Dalhousie-AARMS AAMP Seminar: John Toth (McGill University)
2020-10-02 16:00 - 17:00 (America/Halifax)
Title: Pointwise bounds for joint eigenfunctions of quantum completely integrable (QCI) systems
Abstract: I will discuss some recent results on improvements in supremum bounds for joint eigenfunctions of QCI systems together with sharp exponential decay estimates away from the projections of invariant Lagrangian tori (ie. in the microlocally forbidden region). This is joint work with Jeff Galkowski.
The Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over Zoom. If you would like to attend, please email the organizers for connection details.

Atlantic Graph Theory Seminar: David Pike (Memorial)
2020-10-14 15:30 - 16:30 (America/Halifax)
Perfect 1-Factorisations
A matching in a graph is a subset of the edge set of such that no two edges of share a vertex. A 1-factor of a graph is a matching in which every vertex of is in one of the edges of . If is a -regular graph of even order then we can ask whether admits a 1-factorisation, namely a partition of its edge set into 1-factors.
Suppose that are the 1-factors of a 1-factorisation of a -regular graph . If, for each , the union yields a Hamilton cycle in , then we say that is a perfect 1-factorisation. We will discuss some of the history and properties of 1-factorisations, including the recent discovery of a perfect 1-factorisation of .
The Atlantic Graph Theory Seminar series will take place every Wednesday from 3:30-4:30 ADT online via zoom. The talks, provided by researchers, postdocs and graduate students, will be on a variety of current topics in graph theory. If you would like to give a talk or attend, please email one of the organizers (Jason Brown and Danielle Cox).

Dalhousie-AARMS AAMP Seminar: Julie Rowlett (Chalmers, Sweden)
2020-10-16 16:00 - 17:00 (America/Halifax)
Decisions and Disease
Do you usually get a flu shot every year? Do you usually take preventive measures to avoid contracting sexually transmitted infections? It is reasonable to expect that while many people may answer `no‘ to the first question, they may answer `yes‘ to the second question. In recent joint work with my PhD student, Carl-Joar Karlsson, we have discovered a mathematical explanation for these different choices. Here I will explain mathematical models we have developed that combine the spread of different types of diseases together with the evolution of human behavioral choices. These models create dynamical systems, and the stable equilibrium points provide insights into both the spread of disease as well as the evolution of human behaviors. These insights may be relevant for both the current pandemic as well as any new diseases we may encounter in the future.
The Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over Zoom. If you would like to attend, please email the organizers for connection details.

Atlantic Graph Theory Seminar: Dr. Ben Cameron (University of Guelph)
2020-10-21 15:30 - 16:30 UTC
Title: Families of graphs containing only finitely many vertex-critical graphs.
In this talk, motivated by algorithmic aspects of graph colouring, we will consider the problem of classifying vertex-critical graphs in families of graphs. We will complete a dichotomy theorem for the number of k-vertex-critical H-free graphs when H is a graph of order four. Our results also reduce the remaining open problem for graphs of all orders to two families of graphs. Toward implementing the corresponding graph colouring algorithms, we then improve upon previous research to show tight upper bounds on the order and independence number of k-vertex-critical graphs in another family of graphs, allowing for exhaustive generation of these graphs for k at most 7 . Joint work with Chính Hoàng and Joe Sawada

Dalhousie-AARMS AAMP Seminar: Hari Kunduri (Memorial University)
2020-10-23 16:00 - 17:00 (America/Halifax)
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 equations. I will discuss recent work on extending this class of inequalities to higher dimensions, where a number of qualitative differences arise (e.g. black holes can have non-spherical horizon topology). In particular, I will discuss how a lower bound for the mass, in terms of a (regularized) harmonic energy functional is obtained.
The Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over Zoom. If you would like to attend, please email the organizers for connection details.

Atlantic GR Seminar: Turkuler Durgut (MUN)
2020-10-28 13:00 - 14:00 (America/Halifax)
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 as an example of a solution where stable trapping occurs. This project is joint work with Dr. Hari K. Kunduri and Dr. Robie A. Hennigar.
The Atlantic General Relativity 2020 online postdoc/student seminar series is in the tradition of the annual AGR meetings, providing a forum not only for students and postdocs to present their research and make professional contacts but also to facilitate connections and collaborations between all Atlantic Canadian relativists. The series is student-organized and includes all areas of classical and quantum gravity. Talks will occur on the last Wednesday of every month, with each session consisting of two 30 minute talks. If you would like to attend, please email the organizers for connection details.
Note: all times are Atlantic Time

Atlantic Graph Theory Seminar: Iain Beaton (PhD Candidate, Dalhousie University)
2020-10-28 15:30 - 16:30 UTC
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 2n/3. Finally, we show that the normalized average, while dense in [1/2,1], tends to 1/2 for almost all graphs.
The Atlantic Graph Theory Seminar series will take place every Wednesday from 3:30-4:30 ADT online via zoom. The talks, provided by researchers, postdocs and graduate students, will be on a variety of current topics in graph theory. If you would like to give a talk or attend, please email one of the organizers (Jason Brown and Danielle Cox).

Dalhousie-AARMS AAMP Seminar: Jean-Pierre Garbardo (McMaster University)
2020-10-30 16:00 - 17:00 (America/Halifax)
Title: Factorization of positive definite functions through convolution and the Turàn problem
Abstract: If is a finite abelian group, we call a subset symmetric if and whenever . We also let . We consider the problem of expressing an arbitrary positive definite function on as the convolution product of two positive definite functions, one supported on and the other one supported on . We show that, in the particular case where is the constant function , this problem is related to the Tur’an problem for positive definite functions. In the particular case of a finite abelian group, this last problem asks the following question. Given a symmetric set , find the maximum value of the sum if and is a positive definite function on supported on . We introduce the notion of {it dual Tur’an problem for }, which is essentially the Tur’an problem for the set , and show how the Tur’an problem for and its dual are related, and how the factorization mentioned above plays a role is solving both those problems. We will then give an overview of how these results can be extended to other abelian groups such as .
The Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over Zoom. If you would like to attend, please email the organizers for connection details.

Atlantic Graph Theory Seminar: Dr Andrea Burgess (University of New Brunswick, Saint John)
2020-11-04 15:30 - 16:30 UTC
Equitably colourable cycle decompositions
A -colouring of a decomposition of a graph is an assignment of colours to the vertices of . 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 and , the number of vertices of colour and in any given block differ by at most 1. In this talk, we give an overview of colourings of designs and cycle decompositions, and present some recent joint results with Francesca Merola on the existence of equitably 2-colourable cycle decompositions of the cocktail party graph. In particular, we give a complete existence result for equitably 2-colourable -cycle decompositions of in various cases, including that or (mod ); is a power of 2; for a prime power; or .
The Atlantic Graph Theory Seminar series will take place every Wednesday from 3:30-4:30 ADT online via zoom. The talks, provided by researchers, postdocs and graduate students, will be on a variety of current topics in graph theory. If you would like to give a talk or attend, please email one of the organizers (Jason Brown and Danielle Cox).

Dalhousie-AARMS AAMP Seminar: Reem Yassawi (Open University, London)
2020-11-06 16:00 - 17:00 (America/Halifax)
Title: Some tame or wild Cantor dynamical systems
Abstract: A topological dynamical system is a pair where is a compact metric spaces and is a group or semigroup acting continuously on . One algebraic invariant of a such a dynamical system is the Ellis semigroup. The Ellis semigroup of a topological dynamical system is defined to be the compactification of the action in the topology of pointwise convergence on the space of all function . Tameness is a concept whose roots date back to Rosenthal’s embedding theorem, which says that if a sequence in does not have a weakly Cauchy subsequence, then it must be a sequence on unit vectors in . Köhler linked the concept of tameness to the Ellis semigroup. A system is tame if its Ellis semigroup has size at most the continuum. Non-tame systems are very far from tame, as they must contain a copy of , the Stone-Cech compactification of .
In this talk, I will briefly survey the properties of the Ellis semigroup that make it an interesting object to study, and discuss recent developments concerning tameness. I will then discuss Toeplitz shifts, which themselves have been studied extensively in this context and is the subject of some joint work with G. Fuhrmann and J. Kellendonk.
The Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over Zoom. If you would like to attend, please email the organizers for connection details.

AARMS COVID-19 Seminar: Shannon LeBlanc (Dept of Health NB)
2020-11-18 15:00 - 16:30 (America/Halifax)
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 to identify the points in time that our importation risk was highest. Using the output of the importation risk model we have developed a Markov tree to assist public health decision makers in understanding the risk that these travelers pose to the public based on the testing and quarantine strategies that they choose to apply.
Shannon LeBlanc is currently an Epidemiologist at the New Brunswick Department of Health who has recently worked with the government of the Northwest Territories
This is a virtual zoom seminar. If you would like to attend, please email the organizers for connection details.

Atlantic Graph Theory Seminar: Kyle MacKeigan (PhD Candidate, Dalhousie University)
2020-11-18 15:30 - 16:30 UTC
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 colourings.
The Atlantic Graph Theory Seminar series will take place every Wednesday from 3:30-4:30 ADT online via zoom. The talks, provided by researchers, postdocs and graduate students, will be on a variety of current topics in graph theory. If you would like to give a talk or attend, please email one of the organizers (Jason Brown and Danielle Cox).

Atlantic GR Seminar: Jinzhao Wang (ETH Zurich) and Saikat Mondal (MUN)
2020-11-25 13:00 - 14:00 (America/Halifax)
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, connected, spacelike, codimension-two boundary. We show that for an outer-minimizing mean-convex surface, the Bartnik-Bray inner mass matches exactly with the irreducible mass corresponding to the outer entropy. The equivalence implies that the area laws derived from the outer entropy are mathematically equivalent as the monotonicity property of the quasilocal mass. It also gives rise to new bounds between entropy and the gravitational energy, which naturally gives the gravitational counterpart to Wall’s ant conjecture. We also observe that the equality can be achieved in a conformal flow of metrics, which is structurally similar to the Ceyhan-Faulkner proof of the ant conjecture. We compute the small sphere limit of the outer entropy and it is proportional to the bulk stress tensor as one would expect for a quasilocal mass.
Marginally outer trapped (open) surfaces in Schwarzschild geometry and extreme mass ratio merger
Saikat Mondal (MUN)
Black holes are one of the common objects in astrophysics. Some are formed from a dying star, called a stellar black hole. There are also supermassive black holes consisting of mass millions or even billions times that of the sun. Such black holes are thought to lie at the center of almost every galaxy. In this talk we will explore the evolution of horizons of black hole mergers in a special limit called the ” extreme mass ratio” limit. For example, a supermassive black hole merges with a stellar black hole to become a single black hole. In this limit, the merging horizons can be studied with the help of simple numerics. We will discuss mainly about marginally outer trapped surfaces (MOTS). Interestingly, the MOTSs we find in our numerical analysis have an arbitrary number of self-intersections.
The Atlantic General Relativity 2020 online postdoc/student seminar series is in the tradition of the annual AGR meetings, providing a forum not only for students and postdocs to present their research and make professional contacts but also to facilitate connections and collaborations between all Atlantic Canadian relativists. The series is student-organized and includes all areas of classical and quantum gravity. Talks will occur on the last Wednesday of every month, with each session consisting of two 30 minute talks. If you would like to attend, please email the organizers for connection details.

Atlantic Graph Theory Seminar: Dr Jared Howell (Memorial University of Newfoundland, Grenfell Campus)
2020-11-25 15:30 - 16:30 UTC
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 from 3:30-4:30 ADT online via zoom. The talks, provided by researchers, postdocs and graduate students, will be on a variety of current topics in graph theory. If you would like to give a talk or attend, please email one of the organizers (Jason Brown and Danielle Cox).

Dalhousie-AARMS AAMP Seminar: Graham Cox (Memorial University)
2020-11-27 16:00 - 17:00 (America/Halifax)
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 understood.
The first explicit formula for the nodal deficiency was obtained in 2012
by Berkolaiko, Kuchment and Smilansky, using an energy functional
defined on the space of equipartitions. More recently, with Jones and
Marzuola, I obtained another formula for the nodal deficiency, in terms
of Dirichlet-to-Neumann operators defined on the eigenfunction’s nodal
domains. While originally derived using symplectic methods, this result
can also be understood using the spectral flow generated by a family of
boundary conditions imposed on the nodal set. In this talk I will
describe this flow, and explain how it provides a concrete mechanism by
which low energy eigenfunctions do or do not contribute to the nodal
deficiency. I will also describe recent progress relating these two
formulas for the nodal deficiency, and hint at some applications to the
theory of spectral minimal partitions.
This talk represents joint work with Thomas Beck, Gregory Berkolaiko,
Isabel Bors, Yaiza Canzani, Grace Conte, Christopher Jones and Jeremy
Marzuola.
The Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over Zoom. If you would like to attend, please email the organizers for connection details.

Atlantic Graph Theory Seminar: Dr Melissa Huggan (Ryerson University)
2020-12-02 15:30 - 16:30 UTC
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 work with Richard J. Nowakowski.
The Atlantic Graph Theory Seminar series will take place every Wednesday from 3:30-4:30 ADT online via zoom. The talks, provided by researchers, postdocs and graduate students, will be on a variety of current topics in graph theory. If you would like to give a talk or attend, please email one of the organizers (Jason Brown and Danielle Cox).

Dalhousie-AARMS AAMP Seminar: Peter Hintz (MIT)
2020-12-04 16:00 - 17:00 (America/Halifax)
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 a detailed description of the resolvent of an associated wave equation on symmetric 2-tensors near zero energy.
The Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over Zoom. If you would like to attend, please email the organizers for connection details.

Atlantic Graph Theory Seminar: Dr Erin Meger (Université du Québec à Montréal)
2020-12-09 15:30 - 16:30 UTC
The Iterated Local Model for Social Networks
Complex networks are said to exhibit four key properties: large scale, evolving over time, small world properties, and power law degree distribution. The Preferential Attachment Model (Barab´asi–Albert, 1999) and the ACL Preferential Attachment Model (Aiello, Chung, Lu, 2001) for random networks, evolve over time and rely on the structure of the graph at the previous time step. Further models of complex networks include: the Iterated Local Transitivity Model (Bonato, Hadi, Horn, Pralat, Wang, 2011) and the Iterated Local Anti-Transitivity Model (Bonato, Infeld, Pokhrel, Pralat, 2017). In this talk, we will define and discuss the Iterated Local Model. This is a generalization of the ILT and ILAT models, where at each time step edges are added deterministically according to the structure of the graph at the previous time step.
The Atlantic Graph Theory Seminar series will take place every Wednesday from 3:30-4:30 ADT online via zoom. The talks, provided by researchers, postdocs and graduate students, will be on a variety of current topics in graph theory. If you would like to give a talk or attend, please email one of the organizers (Jason Brown and Danielle Cox).

AARMS COVID-19 Seminar: Ali Gharouni (McMaster)
2020-12-16 15:00 - 16:30 (America/Halifax)
COVID-19 Outbreak Dynamics and Testing-Isolation Efficacy; Insights from a Simple Epidemic Model
One of the main challenges in understanding COVID-19 dynamics is to estimate changes in the total level of infection in a population. The daily case count is a highly accessible form of data where observations are driven by two types of processes: (i) epidemic processes and (ii) testing processes. The challenge is then to separate these processes and understand how they interact. We developed a model that incorporates mechanistic processes of epidemic processes and testing. We have used the model to study the potential
effect of testing strategies on disease dynamics. In future work, we will develop improved methods for estimating true incidence by using data from negative as well as positive tests.
In collaboration with: Fady Abdelmalek and Drs Benjamin M Bolker, Jonathan Dushoff, David JD Earn
This is a virtual zoom seminar. If you would like to attend, please email the organizers for connection details. All times are given in the Atlantic timezone.

Atlantic Graph Theory Seminar: Dr Stephen Finbow, Saint Francis Xavier University
2021-01-13 15:30 - 16:30 UTC
The γ-graph of a graph
For a graph G = (V, E), the γ-graph of G, G(γ) = (V (γ), E(γ)), is the reconfiguration graph whose vertex set is the collection of minimum dominating sets, or γ-sets of G, and two γ-sets are adjacent in G(γ) if they differ by a single vertex and the two different vertices are adjacent in G. The γ-graph of G was introduced by Fricke et al. in 2011 where they studied properties of γ-graphs, and raised seven questions. In this seminar we will discuss the study of γ-graphs to date with a focus on the progress of these questions.
The Atlantic Graph Theory Seminar series will take place every Wednesday from 3:30-4:30 ADT online via zoom. The talks, provided by researchers, postdocs and graduate students, will be on a variety of current topics in graph theory. If you would like to give a talk or attend, please email one of the organizers (Jason Brown and Danielle Cox).

Atlantic Graph Theory Seminar: Dr. Hugh Thomas, UQAM
2021-01-20 15:30 - 16:30 UTC
Dynamical algebraic combinatorics and independence sets of graphs
Dynamical algebraic combinatorics is a relatively new (and fun!) topic, which looks at cyclic group actions on objects from algebraic combinatorics, inspired by some questions coming from dynamical systems. I will give an introduction to the area, focusing on an action I have defined with Nathan Williams on the independent sets of a graph (arXiv:1805.00815). We also construct a partial order on the set of independent sets of a graph, which may be of independent interest.
The Atlantic Graph Theory Seminar series will take place every Wednesday from 3:30-4:30 ADT online via zoom. The talks, provided by researchers, postdocs and graduate students, will be on a variety of current topics in graph theory. If you would like to give a talk or attend, please email one of the organizers (Jason Brown and Danielle Cox).

Dalhousie-AARMS AAMP Seminar: Allan Greenleaf (Rochester)
2021-01-22 16:00 - 17:00 (America/Halifax)
The Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over Zoom. If you would like to attend, please email the organizers for connection details.

Atlantic Graph Theory Seminar: Jordan Barrett, PhD Candidate, McGill University
2021-01-27 15:30 - 16:30 UTC
The Atlantic Graph Theory Seminar series will take place every Wednesday from 3:30-4:30 ADT online via zoom. The talks, provided by researchers, postdocs and graduate students, will be on a variety of current topics in graph theory. If you would like to give a talk or attend, please email one of the organizers (Jason Brown and Danielle Cox).

Dalhousie-AARMS AAMP Seminar: Alan Lindsay (Notre Dame)
2021-01-29 16:00 - 17:00 (America/Halifax)

AARMS COVID-19 Seminar: Sanjeev Seahra (UNB)
2021-02-03 10:30 - 11:30 (America/Halifax)
COVID-19 modelling in New Brunswick and elsewhere
We present a simple differential equation based model of the COVID-19 pandemic that allows for time-evolving social distancing. We apply the model to the first 80 days of the pandemic in 24 different jurisdictions to quantify the effectiveness of government lockdowns in March 2020. Using Bayesian methods, we then estimate model parameters relevant to the current outbreak in New Brunswick.
This is a virtual zoom seminar. If you would like to attend, please email the organizers for connection details. All times are given in the Atlantic timezone.
