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January 2022
Atlantic Graph Theory Seminar: Andrea Burgess (UNB)
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…
Find out more »February 2022
Atlantic Graph Theory Seminar: Melissa Huggan (Mount Allison)
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…
Find out more »Atlantic Graph Theory Seminar: Margaret-Ellen Messinger (Mount Allison University)
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…
Find out more »Dalhousie-AARMS AAMP Seminar: Cyril Letrouit (École Normale Supérieure)
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…
Find out more »Atlantic Graph Theory Seminar: Ferenc Bencs (University of Amsterdam)
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…
Find out more »Dalhousie-AARMS AAMP Seminar: Micah Milinovich (U. Mississippi)
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…
Find out more »AARMS Scientific Machine Learning Seminar: Alison Malcom (Memorial University)
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…
Find out more »March 2022
AARMS Scientific Machine Learning Seminar: Stijn De Baerdemacker (UNB)
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…
Find out more »AARMS Scientific Machine Learning Seminar: Simone Brugiapaglia (Concordia University)
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…
Find out more »Atlantic Graph Theory Seminar: Pjotr Buys (University of Amdsterdam)
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…
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