## Speakers and Abstracts

### Keynote Speakers

Mohamedou Ould Haye, Carleton University **Title:**Frequency-domain test for dependence in time series analysis**Abstract:**A new frequency-domain test statistic is introduced to test for short memory versus long memory or nonstationarity. We provide its asymptotic distribution under the null hypothesis and show that it is consistent under any long memory alternative. Some simulation studies show that this test has better empirical sizes and power compared to various time-domain tests. This is a joint work with Gennadi Gromykov (currently at Skyworks, Ottawa).

Damien Roy, University of Ottawa **Title:**Diophantine equations, Diophantine approximation, and geometry of numbers**Abstract:**A Diophantine equation is an equation to be solved in integers. The fascination for such equations goes back to antiquity. In this talk, we explain, by way of examples, how the resolution of such equations is often linked to approximation to algebraic numbers by rational numbers. One important tool in studying such questions of approximation is Minkowski's geometry of numbers. We conclude this talk by presenting the main result of Minkowski on the successive minima of a convex body, and a related recent result of Schmidt and Summerer describing the behavior of those minima for an important parametric family of convex bodies.

### Other Speakers

**Kivilcim Alkan**, Brock University**Title:**Inelastic Curve Flows in 2- and 3- Dimensional Minkowskian Space**Abstract:**In this project, I derive integrable systems from inelastic curve flows in 2 and 3 dimensional Minkowskian space by using Hasimoto variables.I introduce a Lorentzian version of a moving parallel frame and show that its structure equations encode the Hasimoto variables in natural way. For timelike/spacelike curves in the Minkowskianplane, I obtain the defocusing mKdV equation and its bi-Hamiltonian structure. For null curves, I find Burgers equation. For timelike curves in 3 dimensional Minkowskian space, I derive the complex defocusing mKdV equation and the NLS equation, whereas for spacelike curves, I find similar equations with complex numbers replaced by hyperbolic numbers.

**Alena Antipova**, University of Western Ontario**Title:**Motion of a Ni disk in a nematic liquid crystal due to the action of a magnetic field**Abstract:**here

**Cyril Batkam**, Université de Sherbrooke**Title:**Multiple solutions of a noncooperative elliptic system with concave and convex nonlinearities**Abstract:**We consider a class of elliptic systems leading to strongly indefinite functionals, with nonlinearities which involve a combination of concave and convex terms. Using variational methods, we prove the existence of infinitely many large and small energy solutions. Our approach relies on new critical point theorems which generalize the fountain theorems of T. Bartsch and M. Willem. This is a joint work with Fabrice Colin.

**Ryan Bradshaw**, University of Ottawa**Title:**Arithmetic Properties of Values of Lacunary Series at Algebraic Points**Abstract:**A lacunary series is a Taylor series with large gaps between its non-zero coefficients. In this talk we will give a quick survey on different methods of Diophantine approximation which we use to study arithmetic properties of values of lacunary series at algebraic points. Among these methods we will be focusing on Liouville's Theorem, Mahler's method, and a new approach due to Jean-Paul Bézivin.

**Emily Campling**, University of Ottawa**Title:**The pearl complex for Lagrangian submanifolds**Abstract:**The concept of a Lagrangian submanifold of a symplectic manifold first emerged from the study of Hamiltonian mechanics in physics, but these submanifolds also play a key role in understanding the topology of symplectic manifolds. Therefore it is of interest to develop a system of invariants that can help to distinguish these submanifolds. One approach to this problem which applies to a large subclass of Lagrangian submanifolds is to consider the homology of the pearl complex, first introduced by Yong-Geun Oh in 1996. We will review the required concepts from Morse theory and then explain the construction of the pearl complex for a Lagrangian submanifold in analogy with the construction of the Morse complex for an arbitrary compact smooth manifold. Finally we will discuss some work in progress involving the development of a Künneth theorem for the homology of the pearl complex.

**Hubert Duan**, University of Ottawa**Title:**Novel and customized learning algorithms developed for the 2012 Cybersecurity Data Mining Competition**Abstract:**The 2012 Cybersecurity Data Mining Competition was an international machine learning competition where research teams were invited to construct supervised learning algorithms to make predictions in three areas relevant to cybersecurity: electronic news classification, intrusion detection, and hand-writing recognition. As part of the University of Ottawa Data Science Group, the team consisting of the speaker, Varun Singla, and Dr. Vladimir Pestov, finished 3rd overall in this competition. In this talk, I will first introduce the problem of supervised classification from a machine learning perspective and detail the process of training a classifier to make new predictions. I will then explain the learning algorithms that we developed for the data mining competition; in particular, I will present a novel classifier for text classification, based on similarities between discrete probability measures, and a modified version of the nearest neighbour classifier.

**Chi-Kwong Fok**, Cornell University**Title:**Real K-theory of compact simply-connected Lie groups**Abstract:**here

**Jan Foniok**, Queen's University**Title:**Adjoint functors in graph theory**Abstract:**Adjoint functors are a standard notion in category theory. Only recently have we realised that some proofs of theorems on undirected or directed graphs are actually applications of adjoint functors in the category of graphs or digraphs and their homomorphisms. I will try to convey this unifying view of some of the old applications as well as some of the more recent ones, in particular to graph colouring and to constraint satisfaction problems. (Constraint satisfaction problems are important computational problems stemming from artificial intelligence; we are interested in their computational complexity, i.e., "P vs NP".)

**Adela Gherga**, McMaster University**Title:**Brauer-Kuroda Relations for Higher Class Numbers**Abstract:**here

**Lisa Handl**, University of Ulm**Title:**Stochastic 3D modeling of gas diffusion layers in PEM fuel cells**Abstract:**The morphological microstructure of complex porous materials is closely related to their physical properties, in particular to the transport of gas and fluids within the material. Thus, the systematic development of 'designed' morphologies with improved physical properties is an important task. Mathematical models from stochastic geometry can help to solve this problem since they can be used to provide a detailed quantitative description of complex microstructures in existing materials. In this talk, I will present a parameterized stochastic 3D model which describes the micro-structure of (strongly) curved fiber-based materials. First, the stochastic model itself is introduced, together with a fitting procedure for its parameters. Subsequently, the model is fitted to 3D X-ray synchrotron data from a non-woven gas-diffusion layer (GDL) of polymer exchange membrane fuel cells. The main idea is to model single fibers, which are represented by 3D polygonal tracks, by using multivariate time series. A 3D germ-grain model then forms the complete model, where the single fibers dilated in 3D are the grains and a 3D Poisson point process represents the germs. Due to the manufacturing process (water entanglement), the course of the fibers in z-direction is not homogeneous in the experimental GDL. To include this behavior in our model, we fit the single fiber model only to selected background fibers and later add a perturbation in z-direction to the fiber system. An iterative avoidance algorithm ensures that a system of non-overlapping fibers is obtained.

**Richard Kohar**, Royal Military College**Title:**Optimization Of A Wireless Channel**Abstract:**Given that there are n nodes each competing for access to a single wireless channel, if there are two or more nodes that try to broadcast simultaneously, then this results in a collision, garbled data, and wasted airtime. In every round, the nodes try to access the wireless link on a time slot basis with a predetermined probability, resulting in a distribution of user transmission over slots that is used for contention resolution. Using function component analysis, we will go through a proof to find the global optimum for the case of three slots.

**Eric Naslund**, University of British Columbia**Title:**Roth's Theorem in the Primes**Abstract:**Let $A\subset{1,...,N\}$ be a set of prime numbers containing no non-trivial arithmetic progressions. Suppose that $A$ has relative density $\alpha=|A|/\pi(N)$, where $\pi(N)$ denotes the number of primes in the set ${1,...,N}$. By modifying Helfgott and De Roton's work, we improve their bound and show that for every $\epsilon>0$ $$\alpha\ll_{\epsilon}\frac{N}{(\log\log N)^{1-\epsilon}}.$$

**Ndouné Ndouné**, Université de Sherbrooke**Title:**The Fomin-Shapiro-Thurston Theorem for the infinity-gon**Abstract:**Cluster algebras were invented in 2002 by Fomin and Zelevinsky in order to understand the crystal bases of quantized enveloping algebras associated to semi-simple Lie algebras. A cluster algebra is a commutative ring with a distinguished set of generators, called cluster variables. The set of all cluster variables is constructed recursively from an initial set by using a procedure called mutation. Today the cluster algebras are related with numerous fields of mathematics, for example Lie theory, Poisson geometry, representation theory of algebras, mathematical physics, integrable systems. In the study of Cluster algebras arising from maked surfaces, Fommin, shapiro and thurston have shown that the cluster algebras associated to a triangulation of a marked surface (S,M) does not depend to the choice of triangulation, but uniquely to the surface (S,M). We show that this result does not hold for the cluster algebras arising from the infinity-gon. Finally we give the classification of the cluster algebras arising from the infinity-gon.

**Melkior Ornik**, Queen's University**Title:**Evolutionary rescue: Modeling the influence of mutations and density independent dispersal on population survival**Abstract:**Faced with a strong and sudden deterioration of environment, a population encounters two options - adapt or perish. Indeed, experimental research has shown that it is possible for evolution to act quickly enough to allow for continued survival under new conditions. Results obtained by Bell and Gonzalez (2011) show, in fact, that populations undergoing significant stress may adapt more successfully than those where changes in the environment are less significant. Such a phenomenon presents an interesting modeling challenge. I will introduce a model based on the influence of population dispersal, as well as (potentially beneficial) mutations. Results obtained by this model will be shown and discussed with regards to experimentally obtained data.

**Haifeng Song**, Memorial University of Newfoundland**Title:**Overlapping Resonances in Open Quantum Systems**Abstract:**We consider an open quantum system consisting of a $N-$level quantum system interacting with a reservoir at positive temperature. We analyze the reduced dynamics of the system, in the regime where the coupling strength $\lambda$ is much larger than the spacing $\sigma$ of the system energy levels. For vanishing $\sigma$, there is a manifold of states invariant under the coupled system-reservoir dynamics. The manifold dissolves as the energy level is split, for small $\sigma>0$. This talk is based on joint work with Dr. Marco Merkli.

**Graeme Turner**, Carleton University**Title:**The Discriminant and Conductor of Bicyclic Quartic Fields**Abstract:**here