Mathematical foundations of scientific machine learning
2022-06-01 - 2022-06-03 | Memorial University (St. John’s Campus), St. John's, Newfoundland and Labrador, Canada
Workshop hosted by the AARMS CRG in Scientific Machine Learning. Remote participation via Webex possible. Full program and connection details: Program

Groups, Rings, Lie and Hopf Algebras IV
2022-05-30 - 2022-06-02 | Memorial University (St. John’s Campus), St. John's, Newfoundland and Labrador, Canada
The aim of this workshop is to discuss the current state of research in several interrelated areas of algebra. The first three workshops with the same title were held on the St. John’s campus of Memorial University (MUN) in 2001 and at the Bonne Bay Marine Station of MUN in Gros Morne National Park in 2007 and 2012. The current workshop is organized by the Atlantic Algebra Centre (AAC) of MUN in the framework of the collaborative research group “Groups, Rings, Lie and Hopf Algebras” of the Atlantic Association for Research in the Mathematical Sciences (AARMS). It will immediately precede the summer meeting of Canadian Mathematical Society, which will be held in St. Johns from June 3 to June 6.

Calculus Instruction in Atlantic Canada Conference 2022
2022-05-28 | Online via Zoom
This is a one-day online workshop is an opportunity for high school and university calculus instructors from across Atlantic Canada to come together and engage in discussions regarding calculus instruction.
The theme for 2022 is “Adapting Calculus Instruction in a Changing Educational Climate”
We will have speakers in the morning and in the afternoon there will be a workshop and discussion group based on the theme of the conference.
An optional one day workshop regarding engaging students in mathematical reserach in the high school classroom will take place the day after the teaching conference.

AARMS Geophysical Inverse Problems Discussion
2022-05-27 13:30 - 14:30 UTC | Online via Zoom
Farquharson, 2008, Constructing piecewise-constant models in multidimensional minimum-structure inversions.
Also available on the author’s webpage: https://www.esd.mun.ca/~farq/special.html
Considering the discussion at our previous meeting, it seems natural to next look at methods for recovering sharp/blocky/compact features. This one is a relatively short paper, going back to a time when most inversion work was on rectilinear meshes, and it would be sensible to return to these ideas now that unstructured meshes are seeing more use.

Combinatorial Algebra meets Algebraic Combinatorics 2023
2022-05-26 08:00 - 17:00 UTC | University of Waterloo, 200 University Ave W, Waterloo, Ontario, Canada
Combinatorial algebra and algebraic combinatorics are two highly
active areas of research. Their importance is felt throughout
theoretical and applied mathematics, including algebraic geometry,
representation theory, commutative algebra, and mathematical physics;
they have found numerous practical applications in diverse fields.
The connections between these overlapping subjects are central to
the CAAC workshops’ traditional thematic goals. They were
emphasized in a series of expository lectures which were given by
Tony Geramita and Franc{c}ois Bergeron in January 2004 at
Queen’s University. Through these lectures, it became evident
that interesting special cases of Macaulay’s inverse systems, a
fundamental concept in commutative algebra, are essentially the
coinvariant spaces which arise in algebraic combinatorics. These
connections led to collaborative interdisciplinary research among
two historically disjoint communities of scholars.
The CAAC meeting has been held annually since 2004. It
focuses on the continually evolving interactions between combinatorial
algebra and algebraic combinatorics.

Atlantic General Relativity Meeting 2022
2022-05-16 - 2022-05-19 | Online via Zoom
This series of annual meetings focusses on recent advances in all aspects of classical and quantum gravity. Topics include mathematical general relativity, relativistic astrophysics, gravitational waves, cosmology, gravitational aspects of string theory, loop quantum gravity, and numerical relativity. There is particular focus on the development of graduate students and postdoctoral fellows. As in previous years, there is a two day workshop during which three invited experts (from outside the Atlantic region) give introductory lectures aimed on current topics of high interest. This is followed by two days of contributed research talks, with prizes given to the best student and postdoctoral fellows. While originally aimed to foster collaboration between research groups in Atlantic Canada, in recent years, the conference has attracted participants from both the rest of Canada and abroad.

AARMS Geophysical Inverse Problems Discussion Series
2022-05-13 13:30 - 14:30 (America/Halifax) | Zoom seminar
Zhang et al., 2022, Geophysical inversions on unstructured meshes using non-gradient based regularization
The paper above, the main one we will discuss, seeks to improve upon the method in the paper below, which increases some computational demands. We’d like to better understand how well the paper above improves upon: Lelievre et al., 2013, Gradient and smoothness regularization operators for geophysical inversion on unstructured meshes.

CMS-UPEI-AARMS Regional Math Camp
2022-05-06 - 2022-05-08 | University of Prince Edward Island, Charlottetown, Prince Edward Island, Canada
The School of Mathematical and Computational Science (SMCS) is once again organizing the UPEI-CMS-AARMS Regional Math Camp, to be held at UPEI between May 6 – May 8, 2022. We anticipate hosting some of the most talented grade 10 and grade 11 math students from across the Island. This year, we expect to invite 25-30 students. We offer students an opportunity to participate in challenging, intellectual activities with their peers, guided by the UPEI SMCS faculty members. The students will arrive on the UPEI campus by 9:00 am on Friday (May 6), spend 2 nights in residence, and depart at noon on Sunday (May 8). With the help of several undergraduate math majors, faculty members will conduct several educational, problem-solving and career sessions during the daytime, and recreational sessions during the evenings. The students will be chaperoned at all times
throughout the weekend.

Atlantic Graph Theory Seminar: Aysel Erey (Gebze Technical University, Turkey)
2022-04-13 15:30 - 16:30 UTC | Zoom seminar
Graph polynomials

In this talk, I will discuss various aspects of several graph polynomials such as the location of their roots, their combinatorial properties and extremal questions.

Join Zoom Meeting: link

AARMS Scientific Machine Learning Seminar: Michael W. Dunham (Department of Earth Sciences, Memorial University)
2022-04-12 11:00 - 12:00 UTC | WebEx seminar
Semisupervised machine learning algorithms and their application to geoscience classification problems

In recent years, many disciplines have been challenged with trying to efficiently extract meaning, or value, out of large datasets. Technological advances have improved data storage capabilities as well as how data can be obtained (e.g., real-time data). Manually interpreting data that are exponentially growing in volume has obvious management and analysis challenges. Machine learning is a solution to these challenges. Machine learning algorithms teach computers to recognize patterns in data and assign repetitive patterns to similar categories. This process automates pattern recognition of data and allows meaningful information to be extracted in an efficient manner.

For many machine learning problems, there are sufficient data to train a wide range of algorithms. Some applications, such as image classification and speech recognition, have large training datasets readily available. However, in several geoscience-related problems, labeled data are generally obtained by sampling the earth in some manner (e.g., drilling wells, field sampling, etc.), which is not trivial due to cost and logistical factors. As such, many earth science-related machine learning problems have limited training data. Supervised machine learning algorithms are prone to overfitting in scarce training data situations, but semisupervised approaches are designed for these problems because the unlabelled data are also used to inform the learning process.

Three geoscience applications inherently challenged with limited training data are well log classification, seismic classification, and bedrock lithology mapping. I apply various semisupervised algorithms to these three geoscience problems and determine if semisupervised algorithms can perform better than supervised methods and under what conditions, if applicable. The semisupervised methods I consider are self-training, label propagation, and semisupervised Gaussian mixture models. I consider several supervised methods in my work, but the most prevalent are gradient boosting decision tree methods (e.g., XGBoost, LightGBM). The results show that semisupervised methods can outperform their supervised counterparts for each of the geoscience applications, but there are situations where this is not always the case. Nonetheless, semisupervised methods are rarely considered for many geoscience disciplines, which is supported by the lack of published examples in the literature. The outcomes of this work help fill this gap, but they also help raise the awareness of semisupervised methods.

Webex link:

https://mun.webex.com/mun/j.php?MTID=mf0e24b554219c531763a22ffce2e82c9

Atlantic Graph Theory Seminar: John Engbers (Marquette University)
2022-04-06 15:30 - 16:30 UTC | Zoom seminar
Extremal questions for vertex colorings of graphs

For graphs $G$ and $H$, an $H$-coloring of $G$ is a map from the vertices of $G$ to the vertices of $H$ so that an edge in $G$ is mapped to an edge in $H$. The graph $H$ can be thought of as the allowable coloring scheme: its vertices are the colors used and its edges indicating colors that can appear on the endpoints of an edge in $G$. When the graph $H$ is the complete graph $K_q$, an $H$-coloring corresponds to a proper vertex coloring of $G$ with $q$ colors; when $H$ is an edge with one looped endvertex, an $H$-coloring corresponds to an independent set in $G$.After familiarizing ourselves with the notion of an $H$-coloring, we will consider the following extremal graph theory question: given a family of graphs and an $H$, which graph in the family has the most number of $H$-colorings, and which has the least number of $H$-colorings? We will discuss some things that are known (and not known!) in a variety of families, including trees and graphs with a fixed minimum degree.

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AARMS Scientific Machine Learning Seminar: Geoffrey McGregor (University of Northern British Columbia)
2022-04-05 11:30 - 12:30 UTC | WebEx seminar
Conservative Hamiltonian Monte Carlo

Markov Chain Monte Carlo (MCMC) methods enable us to extract meaningful statistics from complex distributions which frequently appear in parameter estimation, Bayesian statistics, statistical mechanics and machine learning. Similar to how flipping a coin, or rolling a dice, allows us to sample from the corresponding distributions underlying these processes, MCMC methods enable us to sample from more complex distributions. The sample statistics of the sequence generated by MCMC will converge to those of the target distribution, or “stationary distribution” provided certain acceptance and rejection criteria are satisfied. However, as the dimensionality of the stationary distribution increases, the acceptance rate of traditional MCMC methods inevitably diminishes and their convergence slows down substantially. This has led to recent developments in computational techniques, such as Hamiltonian Monte Carlo (HMC) to improve the performance in convergence and acceptance rate. Specifically, HMC proposes samples for acceptance or rejection by solving a Hamiltonian system of differential equations using volume preserving numerical methods.

In this talk, we introduce the Conservative Hamiltonian Monte Carlo (CHMC) method, which instead utilizes an energy preserving numerical method, known as the Discrete Multiplier Method. We show that CHMC converges to the correct stationary distribution under appropriate conditions and provide numerical examples showcasing improvements on acceptance rates.

This is joint work with Andy Wan from the University of Northern British Columbia.

Webex link:
https://mun.webex.com/mun/j.php?MTID=mdff68bb6ee4a7d34ae94a2b77b2c4888

AARMS Scientific Machine Learning Seminar: Scott MacLachlan (Memorial)
2022-03-29 11:00 - 12:00 UTC | WebEx seminar
Optimization and Learning in the Design of Preconditioners

Computer simulation algorithms are a major tool in many areas of science and industry, particularly in areas where the behaviour of fluids or complex materials governs the physical processes of interest. A typical core of these tools is the numerical approximation of the solution to coupled nonlinear systems of partial differential equations, relying on nonlinear and linear solvers, such as Newton’s method and preconditioned Krylov iterations. Among the most effective preconditioners for these systems are multigrid and domain decomposition methods, which use multiscale representations of the systems to be solved to achieve linear-scaling complexity for the solution of these linear systems. These preconditioners typically rely on heuristics in their construction, to approximate solutions to underlying combinatorial (and other) optimization problems that specify parameters and other components of the preconditioners, based on the discrete problem to which they are being applied. In this talk, I will discuss the use of advanced optimization and machine learning techniques to approximately solve these optimization problems and the impact these techniques can have on advanced preconditioner design.

Webex link:
https://mun.webex.com/mun/j.php?MTID=m8e73e9072ce63a9072b87874c1ee7cae

Dalhousie-AARMS AAMP Seminar: Manuela Girotti (Saint Mary's Uni.)
2022-03-25 16:00 - 17:00 (America/Halifax) | Zoom seminar
Title: Asymptotic Analysis of the Interaction Between a Soliton and a Regular Gas of Solitons (a.k.a. Gulliver and the Lilliputians)
Abstract: N. Zabusky coined the word “soliton” in 1965 to describe a curious feature he and M. Kruskal observed in their numerical simulations of the initial-value problem for a simple nonlinear PDE. The first part of the talk will be a broad introduction to the theory of solitons/solitary waves and integrable PDEs (the KdV and modified KdV equation in particular), describing classical results in the field.

The second part will focus on some new developments and growing interest into a special case of solitons defined as “solitonic gas” or “integrable turbulence”. In particular, we will discuss a recent work on long-time asymptotic behaviour of such type of solitons. We will achieve our results by first framing the problem in the setting of a Riemann–Hilbert problem and then by rigorously analyzing it using the powerful technique of nonlinear steepest descent.

This is a joint work with Tamara Grava (U. Bristol/SISSA), Bob Jenkins (UCF), Ken McLaughlin (CSU) and Alexander Minakov (U. Karlova).
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 Canada Actuarial Student Conference
2022-03-25 - 2022-03-26 | University of Prince Edward Island, Charlottetown, Prince Edward Island, Canada
We invite all Actuarial Science students from across the Atlantic region to join us for the 2022 Atlantic Canada Actuarial Student Conference!
Hosted in beautiful downtown Charlottetown, this year’s event will provide students with an opportunity to meet others from the region, gain insightful knowledge about the actuarial field from industry professionals, and provide networking opportunities through a career fair. It is a fantastic opportunity to find potential internships or full-time positions in French and English with several sponsors.

Atlantic Graph Theory Seminar: Theodore Kolokolnikov (Dalhousie)
2022-03-16 15:30 - 16:30 UTC | Online via Zoom
We study the algebraic connectivity for several classes of random semi-regular graphs. For large random semi-regular bipartite graphs, we explicitly compute both their algebraic connectivity and as well as the full spectrum distribution. For an integer d in [3,8], we find families of random semi-regular graphs that have higher algebraic connectivity than a random d-regular graphs with the same number of vertices and edges. On the other hand, we show that regular graphs beat semi-regular graphs when d >8. More generally, we study random semi-regular graphs whose average degree is d, not necessary an integer. This provides a natural generalization of a d-regular graph in the case of a non-integer d. We characterise their algebraic connectivity in terms of a root of a certain 6th-degree polynomial. Finally, we construct a small-world-type network of average degree 2.5 with a relatively high algebraic connectivity. We also propose some related open problems and conjectures.

Dalhousie-AARMS AAMP Seminar: Justin Tzou (Macquarie U.)
2022-03-11 16:00 - 17:00 (America/Halifax) | Zoom seminar
Title: Modeling and analysis of localized vegetation patterns on curved topography

Abstract: We propose a two-component reaction-advection-diffusion model for vegetation density and soil water concentration on a curved terrain which accounts for downhill flow of soil water, spatially dependent effective evaporation of soil water, and vertical rainfall on a curved surface. In the limit of slow diffusion of vegetation, we construct a one-spot localized solution corresponding to one patch of a periodic spotted vegetation pattern. We derive an ODE for the motion of the spot and determine how it is impacted by different aspects of the terrain. One such aspect is captured by the regular part of a certain Green’s function on the curved surface; I will briefly discuss how we numerically compute this quantity. Joint work with Leo Tzou.
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: Pjotr Buys (University of Amdsterdam)
2022-03-09 15:30 - 16:30 UTC | Online via Zoom
About a year ago Jason Brown spoke in our seminar (of the university of Amsterdam) about the two-terminal reliability polynomial and left us with some questions about the closure of the complex zeros of all such polynomials (the zero-locus). In this talk I will define a way to capture, for a certain parameter, whether the set of all two-terminal reliability polynomials behaves chaotically around this parameter or not, i.e. whether this parameter is active or passive. I call the set of all active parameters the activity-locus and I will show that it is equal to the zero-locus. I will use this framework to prove some fun things about the zero-locus. Although I have not yet figured out how to use this to answer any of the open questions posed by Jason, I am hopeful it might be a step in the right direction.

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AARMS Scientific Machine Learning Seminar: Simone Brugiapaglia (Concordia University)
2022-03-08 11:00 - 12:00 UTC | WebEx seminar
The curse of dimensionality and the blessings of sparsity and Monte Carlo sampling: From polynomial approximation to deep learning in high dimensions
In data science and scientific computing, the approximation of high-dimensional functions from pointwise samples is a ubiquitous task, which is made intrinsically difficult by the so-called curse of dimensionality. In this talk, we will illustrate how to alleviate the curse thanks to the “blessings” of sparsity and Monte Carlo sampling.

First, we will consider the case of sparse polynomial approximation via compressed sensing. Focusing on the case where the target function is smooth, but possibly highly anisotropic, we will show how to obtain sample complexity bounds only mildly affected by the curse of dimensionality, near-optimal accuracy guarantees, stability to unknown errors corrupting the data, and rigorous convergence rates of algebraic and exponential type.

Then, we will illustrate how the mathematical toolkit of sparse polynomial approximation can be employed to obtain a “practical existence theorem” for deep learning in the context of high-dimensional Hilbert-valued function approximation. This result shows not only the existence of neural networks with desirable approximation properties, but also how to compute them via a suitable training procedure in order to achieve best-in-class performance guarantees.

We will conclude by discussing ongoing and future research directions.

Webex link:

https://mun.webex.com/mun/j.php?MTID=m3908ed63dfe6896d1e2421f4a3356bc9

AARMS Scientific Machine Learning Seminar: Stijn De Baerdemacker (UNB)
2022-03-01 11:00 - 12:00 UTC | Newfoundland and Labrador
Deep Learning Chemistry: extracting chemical features from Graph Convolutional Neural Networks

The task of quantum chemistry is to compute chemical properties of molecular compounds from the fundamental laws of quantum mechanics. This poses a tremendous challenge as the most accurate methods also come with a perniciously scaling computational cost, limiting systematic and meaningful calculations mostly to medium-small molecules. This is an undesirable situation as there is a high potential for computationally driven discovery of chemical compounds. For this reason, there have been significant advances in the design of Machine Learning (ML) algorithms to interpolate chemical observables from precomputed data, rather than engaging into costly computations. At present, the ML methods of choice in (quantum) chemistry are based upon Graph Convolutional Neural Networks (GCNN), as molecular compounds are easily reinterpreted into graph-based structures.

In this presentation, I will discuss recent results from the QuNB group on the analysis of the feature space of SchNet, a popular GCNN for quantum chemistry with high predictive power. I will show that chemical information from chemical functional groups is learned and encoded in the feature space of the GCNN, giving a strong quality hallmark of interpretability to the GCNN ML algorithm.

Joint work from the QuNB group (UNB) with Guillaume Acke (Ghent University)

Webex link: https://mun.webex.com/mun/j.php?MTID=m8b04b29275dfeb0c3617be2958e577ff

AARMS Scientific Machine Learning Seminar: Alison Malcom (Memorial University)
2022-02-22 11:00 - 12:00 UTC | WebEx seminar
Using Normalizing Flows for Seismic Data Interpolation
Normalizing Flows are a type of neural network that allow us to map one probability distribution into another. The advantage of such a technique is that they allow us to relate a simple distribution, like a Gaussian, to a more complicated distribution that may be more difficult to estimate and sample from. In uncertainty quantification for inverse problems, we are trying to estimate one of these more complicated distributions, thus normalizing flows can help to speed up this process and improve our ability to use and analyze our results. This will be an applied talk, giving an introduction to normalizing flows, discussing how we chose the particular machine learning method and explaining how it improves our understanding of seismic data processing and the associated uncertainties.

Dalhousie-AARMS AAMP Seminar: Micah Milinovich (U. Mississippi)
2022-02-18 16:00 - 17:00 (America/Halifax) | Zoom seminar
Title: Fourier optimization, prime gaps, and zeta zeros

Abstract: There are many situations where one imposes certain conditions on a function and its Fourier transform and then wants to optimize a certain quantity. I will describe two ways these types of Fourier optimization problems can arise in the context of the explicit formula, which relates the primes to the zeros of the Riemann zeta-function. Using information from the zeros to study the primes, I will show how one can prove the strongest known estimates in the classical problem of bounding the maximum gap between consecutive primes assuming the Riemann hypothesis. Using the explicit formula in the other direction, one can also use Fourier optimization to prove the strongest known conditional estimates for the number of zeta zeros in an interval on the critical line. This is based on joint works with E. Carneiro, V. Chandee, and K. Soundararajan.
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: Ferenc Bencs (University of Amsterdam)
2022-02-16 15:30 - 16:30 UTC | Zoom seminar
In this talk, I will show regions that contain no complex zeros the edge-cover polynomials of hypergraphs. The edge cover polynomial of a graph $G$ is the generating function of edges that covers $V(G)$. It is known that the zeros of this polynomial have length at most $frac{(2+sqrt{3})^2}{1+sqrt{3}}$, that we strengthen by showing that it is at most $4$. We use the general subgraph counting polynomial of Wagner to establish this result along with its generalization for the edge cover polynomial of hypergraphs. As another example, we will establish a new bound on the length of the zeros of the domination and total domination polynomials of graphs in terms of the maximum degree.

Joint work with P’eter Csikv’ari and Guus Regts.

Dalhousie-AARMS AAMP Seminar: Cyril Letrouit (École Normale Supérieure)
2022-02-11 16:00 - 17:00 (America/Halifax) | Zoom seminar
Title – Propagation of singularities in subelliptic PDEs
Abstract – In this talk, we consider the wave equation where the Laplacian is replaced by a sub-Laplacian (also called “Hörmander sum of square”), which is an hypoelliptic operator. We handle the problem of describing the propagation of singularities in such equations : the main new phenomenon that we describe is that singularities can propagate along abnormal curves at any speed between 0 and 1. This general result extends an idea due to R. Melrose, and we then illustrate it on anexample, the Martinet case, following a joint work with Y. Colin de Verdière. Our statements are part of a classical/quantum correspondance between sub-Riemannian geometry (on the classical side) and the hypoelliptic operator (on the quantum side), which is also helpful to interpret results in control theory and spectral theory of hypoelliptic operators.
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: Margaret-Ellen Messinger (Mount Allison University)
2022-02-09 15:30 - 16:30 UTC | Zoom seminar
Reconfiguration for Dominating Sets

Given a problem and a set of feasible solutions to that problem, the associated reconfiguration problem involves determining whether one feasible solution to the original problem can be transformed to a different feasible solution through a sequence of allowable moves, with the condition that the intermediate stages are also feasible solutions. Any reconfiguration problem can be modelled with a reconfiguration graph, where the vertices represent feasible solutions and two vertices are adjacent if and only if the corresponding feasible solutions can be transformed to each other via em one allowable move.The domination reconfiguration graph of a graph $G$, denoted ${mathcal D}(G)$, has a vertex corresponding to each dominating set of $G$ and two vertices of ${mathcal D}(G)$ are adjacent if and only if the corresponding dominating sets differ by the deletion or addition of a single vertex. We are interested in properties of domination reconfiguration graphs. For example, it is easy to see that they are always connected and bipartite. We can also characterize exactly which graphs yield domination reconfiguration graphs with Eulerian circuits. While none has a Hamilton cycle, we explore families of graphs whose reconfiguration graphs have Hamilton paths.

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Atlantic Graph Theory Seminar: Melissa Huggan (Mount Allison)
2022-02-02 15:30 - 16:30 UTC | Zoom seminar
The Orthogonal Colouring Game
The Orthogonal Colouring Game is a combinatorial game in which two players alternately colour vertices of a pair of isomorphic graphs while respecting the properness and the orthogonality of the colouring. Each player aims to maximize her score, which is the number of coloured vertices in the copy of the graph she owns. An involution $sigma$ of a graph $G$ is strictly matched if its fixed point set induces a clique and any non-fixed point $v in V(G)$ is connected with its image $sigma(v)$ by an edge.
In this talk, we introduce the game and our main result that the second player has a strategy to force a draw in this game for graphs that admit a strictly matched involution. We will also give a structural characterization of graphs admitting a strictly matched involution.
This is joint work with Stephan Dominique Andres, Francois Dross, Fionn Mc Inerney, and Richard J. Nowakowski.
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Atlantic Graph Theory Seminar: Andrea Burgess (UNB)
2022-01-26 15:30 - 16:30 UTC | Zoom seminar
Mutually Orthogonal Cycle Systems
A $k$-cycle system of order $n$ is a set of $k$-cycles whose edges partition the edge set of $K_n$. We say that two cycle systems $mathcal{C}$ and $mathcal{C}’$ are {em orthogonal} if every cycle in $mathcal{C}$ shares at most one edge with each cycle in $mathcal{C}’$. Orthogonal cycle systems arise naturally from simple Heffter arrays and biembeddings of cycle decompositions.
A collection of cycle systems is {em mutually orthogonal} if any two of the systems are orthogonal. In this talk, we give bounds on the number of mutually orthogonal $k$-cycle systems of order $n$ and provide constructions for sets of mutually orthogonal cyclic cycle systems.
This is joint work with Nicholas Cavenagh and David Pike.
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Atlantic Graph Theory Seminar: Robert Kooij (Delft University of Technology)
2022-01-19 15:30 - 16:30 UTC | Zoom seminar
Robustness of Complex Networks
Network Science aims to understand the graph structure of networks and the dynamic processes that take place on networks. Examples of processes on networks are transport of items (IP packets with digitalized information, cars, containers) and diffusion (epidemics, electric current, water flows, human emotions). The Network Architectures and Services Section at the Delft University of Technology contributes to the fundaments of Network Science: we investigate amongst others geometric representations of networks, epidemic spread on networks, spectra of graphs and network algorithms. In addition, we apply our mathematical knowledge to the design, management and control of critical infrastructures, such as telecom networks and power grids, in order to make these networks robust, resilient, efficient and reliable. In this talk we will give three examples of our results in the field of robustness of complex networks, namely robustness with respect to malware spread, robustness of network controllability and the robustness of a real-world critical infrastructure.
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Atlantic Graph Theory Seminar: Iain Moffat (Royal Holloway, University of London)
2022-01-12 15:30 - 16:30 UTC | Zoom seminar
Spanning Trees and Graphs Embedded in Surfaces

To what extent is a graph determined by the trees contained in it? That is, if we know the edge sets of each of the spanning trees (i.e., maximal acyclic subgraphs) in a connected graph, then do we know the graph itself? It only takes a little bit of thought to see that the answer is “no” (e.g., suppose the graph is a tree). But this “no” is really a “more or less, yes”. A classical result of Whitney states that we know the graph up to some simple moves.

In this talk we consider what changes if we ask this question not for graphs in the abstract, but graphs that are embedded on surfaces. We shall see how this question brings together a seemingly disjoint collection of topics in mathematics and brings new approaches to topological graph theory.

Atlantic Graph Theory Seminar: Sandra Kingan (Brooklyn College and Graduate Center, CUNY)
2021-12-08 15:30 - 16:30 UTC | Zoom seminar
I will begin by giving a general overview of what it means to find monarchs for excluded minor classes of graphs and matroids. In a paper that appeared in 2018, I used the Strong Splitter Theorem to give a short proof of Oxley’s result that the class of binary matroids with no 4-wheel minor consists of a few small matroids and an infinite family of maximal 3-connected rank r matroids known as the binary spikes. Such a family is called a monarch for the excluded minor class. This proof essentially comes down to finding the monarchs for non-regular matroids with no minors isomorphic to a 9-element rank 4 matroid known as P9 or its dual P*9. In a paper that appeared this year (Australasian Journal of Combinatorics, 79(3), 302–326), I was able to strengthen the result by characterizing the class of binary non-regular matroids with no minor isomorphic to just P*9. The only members of this class are the rank 3 and 4 binary projective geometries, a 16-element rank 5 matroid, and two monarchs: the rank r binary spikes with 2r+1 elements mentioned earlier and another infinite family with 4r−5 elements. As a consequence, a simple binary matroid of rank at least 6 with no P*9-minor has size at most r(r+1)/2 and this bound is attained by the rank r complete graph. This is one of few excluded minor classes for which the members are so precisely determined.

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