## Welcome to the website of the fourth annual OMC!

The Ottawa Mathematics Conference will be held May 13-14, 2011 at the University of Ottawa. This event is a 2-day student-organized conference whose purpose is to provide a venue for area graduate students, postdoctoral researchers, and undergraduate students to showcase their original research in a 20-25 minute presentation. There will also be two invited speakers from Ottawa universities.

This year marks the fourth Ottawa Mathematics Conference.

## Registration Information

There is no registration fee. Interested graduate students, postdoctoral researchers, and undergraduate students in any area of mathematics should register by emailing Camelia Karimianpour at ckari099@uOttawa.ca by April 29, 2011. Please include the following information in your email:

• Name

• Institution

• Contact information

• Major area of research

• Whether you are interested in giving a talk.

Unfortunately, we are unable to provide financial support for travel and accommodation. Nevertheless, participants from out of town are very welcome!

Refreshments will be provided, and a complimentary lunch will be served on May 13.

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## Contributed Talks

The conference will feature talks by graduate students, postdoctoral researchers and undergraduate students on their original research. All talks should be 20-25 minutes in length.

Participants who would like to give a talk must submit a preliminary title and abstract to Camelia Karimianpour at ckari099@uOttawa.ca by Friday, April 29. The deadline for final abstracts is May 6, 2011. Abstracts may be submitted either as plain text in your email or as a TeX file.

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## Schedule

 Friday, May 13 Saturday, May 14 9:00 - 9:30 Coffee/registration Coffee 9:30 - 10:30 Paul Mezo Yves Bourgault 10:30 - 10:45 Break Break 10:45 - 11:10 Sean Kramer Pinar Colak 11:15 - 11:40 Emily Redelmeier Andrew Skelton 11:45 - 12:10 Veronica L. Gheorghiade Steven MacNaughton 12:15 - 2:00 Lunch (provided) Lunch (not provided) 2:00 - 2:25 Kristopher Lee Adolfo Rodriguez 2:30 - 2:55 Md Abdus Samad Bhuiyan Jamal Al Smail 3:00 - 3:25 Emre Coskun Babak Moazzez 3:30 - 4:00 Break Break 4:00 - 4:25 Deping Ye Bernard S. Chan 4:30 - 4:55 Mustazee Rahman Vyacheslav Morozov

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## Abstracts

• Yves Bourgault, University of Ottawa

Title: Understanding the heart - problems, models and methods

Abstract: The talk will cover the challenges and approaches associated with building mathematical models of the heart. Topics covered include how to get heart geometries from medical imaging and ways to understand the electrical and mechanical activity of the heart.

• Paul Mezo, Carleton University

Title: Number theory meets harmonic analysis

Abstract: Both number theory and harmonic analysis are colossal areas in mathematics, so they overlap in more ways than one. Our modest aim is to sketch a path in each area and arrive at a particular point of overlap. In the world of number theory, our path is in the direction of modular forms. In harmonic analysis we follow representations of locally compact groups. The technical core of this talk is to explain how (cuspidal) modular forms may be converted into (automorphic) representations. In making this conversion, an immense potential for generalization becomes apparent.

• Md Abdus Samad Bhuiyan, Brock University

Title: Joule heating effect on magnetohydrodynamic (MHD)-conjugate natural convection flow from an isothermal horizontal circular cylinder

Abstract: Magnetohydrodynamic (MHD)-conjugate natural convection flow along the outer surface from the lower stagnation point to the upper stagnation point and from an isothermal horizontal circular cylinder considering joule heating effect is investigated. The developed governing equations with the associated boundary conditions for this analysis are transferred to dimensionless forms using a suitable transformation. The transformed non-dimensional governing equations are then solved using the implicit finite difference method with Keller box-scheme. Numerical results are found for different values of the joule heating parameter, magnetic parameter and Prandtl number. Detail results of the velocity profiles, temperature distributions, skin friction and rate of heat transfer are shown graphically.

• Jamal Al Smail, University of Ottawa

Title: Optimal shape design of the cathode air channel of hydrogen fuel cells

Abstract: Hydrogen fuel cells (HFCs) are batteries that convert chemical energy (through the reaction of oxygen and hydrogen gases) to electrical energy. One great advantage of HFCs is that they have safe emissions to the environment: water. We will consider the cathode part of HFCs: the air channel, the graphite diffusive layer and the catalyst layer, modeled as an interface, and the membrane. The objective is find the optimal shape design of the air channel to improve the efficiency of HFCs by

• Maximizing the oxygen transport at the membrane

• Minimizing the variance of the oxygen flux on the membrane

To reach this objective, our talk will involve a careful mathematical modeling of the cathode part of HFCs. Then, we consider a shape optimization problem to minimize a cost functional measuring the efficiency of HFCs.

• Bernard S. Chan, University of Western Ontario

Title: Synchrony-breaking Hopf bifurcation in a model of antigenic variation

Abstract: In this presentation, we analyze the bifurcation dynamics of a model of antigenic variation of plasmodium falciparum. We apply techniques of coupled cell systems to analyze the model. It is found that synchrony-breaking Hopf bifurcation occurs from a nontrivial fully synchronous equilibrium. In proving that Hopf bifurcation occurs, we also find a condition to describe the possible synchrony patterns resulting from the bifurcation. These patterns are qualitatively similar to many conditions associated with within-host behaviour of antigenic variation. Our results are illustrated with specific examples and numerical simulations.

• Pinar Colak, Simon Fraser University

Title: Two-sided chain conditions in Leavitt path algebras

Abstract: Leavitt path algebras are a natural generalization of the Leavitt algebras, which are a class of algebras introduced by Leavitt in 1962. For a directed graph, the Leavitt path algebra $L_K(E)$ of $E$ with coefficients in $K$ has received much attention both from algebraists and analysts over the last decade. So far, some of the algebraic properties of Leavitt path algebras have been investigated, including primitivity, simplicity and being Noetherian. First, we explicitly describe the generators of two-sided ideals in Leavitt path algebras associated to arbitrary graphs. We show that any two-sided ideal $I$ of a Leavitt path algebra associated to an arbitrary graph is generated by elements of the form $(v+\sum_{i=1}^n\lambda_i g^i)(v-\sum_{e\in S}ee^*)$, where $g$ is a cycle based at a vertex $v$ and $S$ is a finite subset of $s^{-1}(v)$. Then, we use this result to describe necessary and sufficient conditions on an arbitrarily sized graph $E$ under whic h the Leavitt path algebra associated to $E$ satisfies two-sided chain conditions. This is joint work with Dr. Gene Abrams, Dr. Jason P. Bell and Dr. Kulumani M. Rangaswamy.

• Emre Coskun, University of Western Ontario

Title: Pfaffian quartic surfaces and representations of Clifford algebras

Abstract: Given a nondegenerate ternary form $f(u,v,w)$ of degree 4 over an algebraically closed field of characteristic 0, we use the geometry of K3 surfaces to construct a positive-dimensional family of irreducible representations of the generalized Clifford algebra associated to $f$.

• Veronica L. Gheorghiade, University of Guelph

Title: An agent-based model of stock market investors with social network effects

Abstract: This work extends an existing cellular automata model of market investors' interaction when they are considered socially connected and the effect their behaviour has on the prices of market instruments. We take here an agent-based approach to their interactions, which helps us investigate further properties of the effects of social connectivity on their decision making (buying, selling or holding). In particular, we consider them related over three types of social networks; we further assume that each agent is influenced in a different manner by various others, and that an agent's social links can evolve (appear or disappear), making the underlying network structure time-dependent.

• Sean Kramer, Clarkson University

Title: Finite-time Lyapunov exponents on the Gulf oil spill and modeling ecology by remote sensing

Abstract: Mixing mechanisms and modeling transport are two general problems in fluid dynamics that were highlighted during the tragic Gulf oil spill in April of 2010. We study the flow dynamics of the Gulf during this time using vector fields produced by a nonautonomous model describing oceanic flows. We simulate the oil spill as tracers advected throughout the Gulf by the model, and analyze mass transport via Lagrangian coherent structures based on finite-time Lyapunov exponents. These tools are being used to model plankton blooms initialized by remote sensing data over coastal regions.

• Kristopher Lee, Clarkson University

Title: On the generality of assuming that a family of continuous functions separates points

Abstract: In the study of algebras of continuous functions on a compact Hausdorff space $X$, it is standard to assume that the algebra separates points, which is to say that given $x,y\in X$ such that $x\neq y$, there exists an $f$ in the algebra such that $f(x)\neq f(y)$. The natural question to ask is whether this assumption is strictly a hypothesis or whether it holds "without loss of generality." We show that if a family $\mathcal{A}$ does not separate points, then there exists a family $\hat{\mathcal{A}}$ on a compact Hausdorff space $Y$ that does separate points and there exists a bijective mapping $\mathcal{A}\mapsto\hat{\mathcal{A}}$ that preserves the uniform norm. Additionally, we investigate whether other norms are preserved and show that for a family of Lipschitz functions $\mathcal{A}$ on a compact metric space $X$, the family $\hat{\mathcal{A}}$ is defined on a compact metric space $Y$ and the mapping $\mathcal{A}\mapsto\hat{\mathcal{A}}$ preserves t he Lipschitz constant.

• Steven MacNaughton, Brock University

Title: Conservation laws and symmetries of quasilinear wave equations in multi-dimensions

Abstract: An explicit classification of energy-momentum type conservation laws is presented for a general class of physically and analytically interesting wave equations with power nonlinearities in $n>1$ spatial dimensions. All special powers or dimensions for which these wave equations admit, in particular, dilational energies or conformal energies are determined.

• Babak Moazzez, Carleton University

Title: Polyhedral structure of mixed integer programs and subadditive duality

Abstract: Linear programming along with its duality theory has been developed very well and now it is one of the most useful tools in scientific and industrial optimization. Meanwhile many efforts have been made to build a strong duality theory for (mixed) integer programming, which is a very useful and challenging branch of optimization. Subadditive duality was introduced a few decades ago. Although it has not been very helpful as a computational approach, subadditive duality gives us a better understanding of the linear integer and mixed integer polyhedra and the structure of minimal valid inequalities. It is a known result by Laurence Wolsey (1981) that the convex hull of a pure integer program is representable by a finite number of subadditive functions. This means that we can find a finite set of subadditive functions such that their corresponding valid inequalities form a defining system of inequalities for the convex hull of a pure integer program. We have generalized this result to the mixed integer case by using a new class of subadditive functions called generator functions introduced by Diego Klabjan (2005).

• Vyacheslav Morozov, University of Ottawa

Title: Statistical model to improve prediction of over-represented motifs in nucleotide sequences

Abstract: In the last decades position sensitive score matrices (PSSMs) became the tool of choice for searching over-represented words (motifs) in biological sequences. Constructively these ($m\times n) matrices are compiled from$nknown aligned motifs (so-called protein binding sites), which are experimentally validated as true binding sites. However, the binding specificity of the protein is generally unknown and bioinformaticians suggest that other unknown possible binding motifs should be similar to what was known. The formalization of biologically relevant definitions of similarity is a matter of additional research. The existing discovery tools perform poorly in terms of sensitivity and specificity. An original recurrent procedure uses PSSMs from known motifs to computationally sample putative binding sites. The goal of our study is to analyze the ability to predict new binding sites using Matte's correlation coefficient as a similarity measure and optimiz ation criterion. The predictive performance of new refined PSSMs compares to that of matrices published in TRANSFAC and JASPAR databases of biological information. • Mustazee Rahman, University of Toronto Title: Nested recursions and trees Abstract: A nested or "meta-Fibonacci" recursion is one where the arguments of the recursive formula can depend on earlier values of the sequence, e.g. Hofstadter'sQ$-sequence, defined as$Q(n)=Q(n-Q(n-1))+Q(n-Q(n-2))$. We explore emerging connections between the solutions of nested recursions and infinite trees. We show how the solution of certain nested recursions can be related to the properties of corresponding labeled infinite trees, thereby allowing us to solve a large family of so-called Conolly-type recursions. Such recursions have the same general form as Hofstatder's recursion and can include a constant non-homogeneous term. • Emily Redelmeier, Queen's University Title: Surface gluings and a central limit type theorem for large real random matrices Abstract: Independent large random matrices drawn from many of the important ensembles exhibit a phenomenon known as freeness, one of the noncommutative analogues of independence. Free probability then provides a method of studying the moments of large random matrices. In order to extend these techniques to the fluctuations of random matrices (a sort of central limit-style theorem), we examine the behaviour of large independent random matrices. However, while both real and complex random matrices satisfy the same freeneess condition, real random matrices satisfy a second-order freeness condition different from complex random matrices. In my talk, I will present combinatorial tools related to surface gluings motivating the two distinct definitions. Specifically, nonorientable surfaces appear in the expansion for real random matrices, while only orientable ones appear in that of complex random matrices. • Adolfo Rodriguez, Universite du Quebec Title: Laurent phenomena and non-intersecting lattice paths Abstract: The Gessel-Viennot method for the enumeration of a non-intersecting collection of paths in a graph is one of the most powerful elementary results in combinatorics. By providing connections between seemingly unrelated topics, it has found many applications that range from simpler proofs of well known results in linear algebra and graph theory to completely new results in algebraic and enumerative combinatorics with applications to statistical mechanics. This talk is intended as an introduction to this method and an overview of some original applications yielding positivity and Laurentness properties of certain compositions of rational functions that appear as the solutions to recursive equations in lattice arrays. • Andrew Skelton, Brock University Title: Response curves in deterministic and probabilistic cellular automata Abstract: Cellular automata (CA) have been used as discrete models in areas as diverse as disease spread, forest fires and traffic flow. One of the most important properties in any binary CA model is the proportion of cells in a specific state (0 or 1) after a given number of time iterations. We approach this problem using patterns in preimage sets - that is, the set of blocks which iterate to our desired output. This allows us to construct a response curve - a relationship between the proportion of cells in state 1 after$n$-iterations as a function of the initial proportion of cells in state 1. We first derive response curves for a class of two-dimensional deterministic CA rules, including an important subset of surjective rules. We conclude by considering a class of one-dimensional probabilistic CA rules. • Deping Ye; Fields Institute, Carleton University, and University of Ottawa Title: Threshold for separability of random induced states Abstract: Quantum information theory is now one of the most active fields in science since the prospect of building quantum computers has become more and more concrete. First discovered by Einstein-Podolsky-Rosen in 1935, quantum entanglement is a fundamental ingredient for many objects in quantum information, such as quantum algorithms, quantum key distributions, and quantum teleportation. Thus, detecting quantum entanglement is a central problem in quantum information theory. In this talk, I will present recent progress on estimating the threshold$K\$ for a random induced quantum state being separable and/or entangled. Our proofs rely on random matrices and geometric functional analysis. This talk is based on recent joint work with G. Aubrun and S. Szarek.

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## Participants

• Farnoosh Abbas Aghababazadeh (University of Ottawa)

• Md Abdus Samad Bhuiyan (Brock University)

• Jamal Al Smail (University of Ottawa)

• Steven Amelotte (University of Ottawa)

• Balasingham Balamohan (University of Ottawa)

• Renaud Brien (University of Ottawa)

• Amy Cameron (University of Ottawa)

• Jan Cannizzo (University of Ottawa)

• Bernard S. Chan (University of Western Ontario)

• Pinar Colak (Simon Fraser University)

• Matteo Copelli (University of Ottawa)

• Emre Coskun (University of Western Ontario)

• Jason Crann (Carleton University)

• Behrang Forghani (University of Ottawa)

• Veronica L. Gheorghiade (University of Guelph)

• Maryam Haghighi (University of Ottawa)

• Camelia Karimianpour (University of Ottawa)

• Sean Kramer (Clarkson University)

• Kristopher Lee (Clarkson University)

• Joel Lemay (University of Ottawa)

• Aaron Luttman (Clarkson University)

• Steven MacNaughton (Brock University)

• Jiang Mei (University of Ottawa)

• Babak Moazzez (Carleton University)

• Vyacheslav Morozov (University of Ottawa)

• Khoa Pham (Univsersity of Ottawa)

• Mustazee Rahman (University of Toronto)

• Emily Redelmeier (Queen's University)

• Mariolys Rivas (Concordia University)

• Adolfo Rodriguez (Universite du Quebec)

• Fanny Santamaria Ramirez (University of Ottawa)

• Erika Sindelar (Brock University)

• Andrew Skelton (Brock University)

• Brigitte Stepanov (Queen's University)

• Deping Ye (Fields Institute, Carleton University, University of Ottawa)

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## Location

The conference will be held in rooms 135 and 137 of Fauteux Hall (FTX), 57 Louis Pasteur, at the University of Ottawa main campus. (Please note that this is not the mathematics building!)

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## Local Information and Accommodations

Ottawa festivals in May (including the Canadian Tulip Festival).

Catch a play!

Getting to / from Ottawa:

The bus terminal, train station and airport are all conveniently located near public transit. For more information, see the OC Transpo website.

For your convenience, here is a list of some nearby accommodations. Please note that presence on this list does not imply an endorsement of an establishment by the organizers.

For other accommodation options, you can find listings of hotels and bed and breakfasts at the City of Ottawa webpage.

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