## Keynote Speakers

• Vida Dujmović, Carleton University
• Title: Geometry and Graphs
• Abstract: A graph is a ubiquitous mathematical structure that model information arising from many fields including economics, engineering and social sciences. In the first part of the presentation, I will talk about reconfigurations of geometric graphs (that is, straight-line drawings of graphs with possibly lots of edge crossings). To untangle a geometric planar graph means to move some of its vertices so that the resulting geometric graph has no crossings. A popular on-line game, called Planarity, asks a player to untangle a given geometric planar graph by moving as few vertices as possible. I will discuss some mathematical aspect of that problem. In the second half of the talk, I will try to further highlight the rich connections between geometry and graphs by presenting Székely's simple proof of the Szemerédi–Trotter theorem on incidence between lines and points.
• Philip Scott, University of Ottawa
• Title: Category Theory and the Foundations of Mathematics
• Abstract: A new branch and language of mathematics developed in the 1940's in the work of Eilenberg and Mac Lane: category theory. This has led to a radical reappraisal of logic and the foundations of mathematics. In the 1950's and 60's, the tools and language of category theory revolutionized algebraic topology and algebraic geometry (the latter, from the work of Grothendieck). Category theory has since influenced a vast array of mathematics. The works of F.W. Lawvere, espe cially, have led to a radical categorical reformulation of the very foundations of logic and set theory, not to mention mathematics itself. This in turn led to new (but sometimes controversial) ways of examining old mathematics. In addition, category theory has played an important role in certain areas of theoretical computer science (and, recently, quantum computation). I shall give a self-contained introduction to parts of category theory and the foundations of mathematics and categorical logic, built in part on Lawvere's program.

## Other Speakers

• Kivilcim Alkan, Brock University
• Title: Inelastic Curve Flows in Minkowskian Plane
• Abstract: The purpose of this talk to derive integrable systems from inelastic curve flows in the Minkowskian plane by using a moving parallel frame. For timelike/spacelike curves, we obtain the defocusing mKdV equation and its bi-Hamiltonian structure in terms of Hasimoto variables. For null curves, we obtain Burger’s equation.
• Golshid Chatrchi, Carleton University
• Title: Robust small area estimation with emphasis on variance components estimation
• Abstract: Small area estimation (SAE) provides efficient estimators for small domains by borrowing strength from other related areas. Modern techniques for small area estimation rely on explicit modeling assumptions. These methods can be highly affected by the occurrence of outliers. Robust SAE methods have been developed to remedy this problem. This study considers estimators based on Robustified Maximum Likelihood (RML) equations (S. Sinha and J.N.K Rao, 2009) and mainly concentrates on the estimation of variance components in a one fold nested error linear regression model. A fixed point iterative method is proposed for solving the RML equations. Results of a simulation study are reported.
• Alexander Caviedes, University of Toronto
• Title: Upper bounds for the Gromov width of grassmannian manifolds
• Abstract: I would show how capacity problems in symplectic geometry can be solved by means of pseudoholomorphic theory. In particular, I would show how a Gromov width of grassmannians can be found by computing a Gromov-Witten invariant
• Greg Doyle, Carleton University
• Title: A Recursive Formula for the Convolution Sum of Divisor Functions
• Abstract
• Hubert Duan, University of Ottawa
• Title: Bounding the Fat Shattering Dimension of a Composition Function Class Built Using a Continuous Logic Connective
• Abstract: We first introduce the Vapnik-Chervonenkis (VC) dimension, an important combinatorial parameter in statistical machine learning, and its generalization, the Fat Shattering dimension of scale e. We also give a few examples of their calculations and state some main known results in learning theory involving these dimensions. As the main goal of this talk, we explore the construction of a new function class, obtained by forming compositions with a continuous logic connective, a uniformly continuous function from the unit hypercube to the unit interval, from a collection of function classes. Using results by Mendelson-Vershynin and Talagrand, we bound the Fat Shattering dimension of scale e of this new function class in terms of the Fat Shattering dimensions of the collection's classes.
• Nathan Grieve, Queen's University
• Title: Cup-product problems on an abelian variety
• Abstract: This is a report on work in progress concerning certain cup-product problems of line bundles on an abelian variety. At present the state of affairs is as follows. (i) Such problems are not, in general, independent of the numerical classes of the given line bundles; (ii) After scaling every non-trivial problem results in a surjective map; (iii) Variants of the above hold for (higher rank) vector bundles and translations thereof. As an application we deduce that, after scaling, certain (higher) skew-Pontrjagin products are globally generated.
• Richard Kohar, Royal Military College of Canada
• Title: Hemodynamics: A Source of Intrigue for Pure and Applied Mathematicians
• Abstract: Fluid dynamics has appeal for both applied and pure mathematicians. The study of blood flow, or hemodynamics, began with Poiseuille in the early 19th century when he was looking to mathematically describe blood flow through narrow tubes. This encouraged other mathematicians to investigate fluids leading to the famous Navier-Stokes (NS) equations, and the beginning of fluid dynamics. For pure mathematicians, there is still a continued search for 3-dimensional solutions to the NS-equations, and if they do exist, are the solutions smooth. For applied mathematicians, solving the NS-equations is a difficult task. In 3-dimensions, we turn to using numerical techniques such as the Finite Element Method (FEM). An example of blood flow in the human aorta using the FEM will be presented graphically.
• Andrew McEachern, University of Guelph
• Title: Side Effect Machines and Ring Optimization
• Abstract: The explosion of available sequence data necessitates the development of sophisticated machine learning tools with which to analyze them. This study introduces a sequence-learning technology called side effect machines, and an optimization technique using ring structure. A comparison is done between side effect machines evolved in the ring structure and side effect machines evolved using a standard evolutionary algorithm based on tournament selection. At the core of the training of side effect machines is a nearest neighbor classifier. A parameter study was performed to investigate the impact of the division of training data into examples for nearest neighbor assessment and training cases. The parameter study demonstrates that parameter setting is important in the baseline runs but had little impact in the ring-optimization runs. The ring optimization technique was also found to exhibit improved performance and also more reliable training performance. Side effect machines are tested on two types of synthetic data, one based on GC-content and the other checking for the ability of side effect machines to recognize an embedded motif. Three types of biological data are used, a data set with different types of immune-system genes, a data set set with normal and retro-virally derived human genomic sequence, and standard and nonstandard initiation regions from the cytochrome-oxidase subunit one in the mitochondrial genome.
• Ali Moatadelro, University of Western Ontario
• Title: A Riemann-Roch theorem for NC-two torus
• Abstract: We prove the analogue of the Riemann-Roch formula for the noncommutative two torus $A_{\theta} = C(\mathbb{T}_{\theta}^2)$ equipped with an arbitrary translation invariant complex structure and a Weyl factor represented by a positive element $k\in C^{\infty}(\mathbb{T}_{\theta}^2)$. We consider a topologically trivial line bundle equipped with a general holomorphic structure and the corresponding twisted Dolbeault Laplacians. We define an spectral triple ($A_{\theta}, \mathcal{H}, D)$ that encodes the twisted Dolbeault complex of $A_{\theta}$ and whose index gives the left hand side of the Riemann-Roch formula. Using Connes' pseudodifferential calculus and heat equation techniques, we explicitly compute the $b_2$ terms of the asymptotic expansion of $\text{Tr} (e^{-tD^2})$. We find that the curvature term on the right hand side of the Riemann-Roch formula coincides with the scalar curvature of the noncommutative torus recently defined and computed in Connes-Moscovici and Fathizadeh-Khalkhali. We also show that the Chern form vanishes as expected. For a trivial holomorphic bundle we recover the Gauss-Bonnet theorem of Connes-Tretkov and Fathizadeh-Khalkhali.
• Babak Moazzez, Carleton University
• Title: Sensitivity analysis for mixed integer programming
• Abstract: TBA
• Jeff Musgrave, University of Ottawa
• Title: How Dispersal in Patchy Landscapes Affects Persistence and Spread
• Abstract
• Micheal Pawliuk, University of Toronto
• Title: A problem about uniform continuity in topological groups
• Abstract: The so-called Itzkowitz' problem asks whether two ways of describing "closeness from the left and right" are equivalent in topological groups. One way to describe such closeness is when a topological group has a basis of neighbourhoods of the identity that are invariant under conjugation, which is the SIN property. The property that every left uniformly continuous function on a space is right uniformly continuous also measures how similar left closeness and right closeness are. It is known that these two properties are equivalent for a large class of topological groups, but it is not known in the general case. I will explain the progress that has been made on this problem and how set theoretic methods seem helpful for resolving the general case.
• Ricardo Restrepo Lopez, University of Toronto
• Title: The hard-core model in graphs: The problem of counting weighted independents sets
• Abstract: We will outline several recent results and methods from the author and others that allow us to get a better understanding of this exemplary model of phase transitions in combinatorics, statistical physics and computational complexity.
• Trevor Wares, University of Ottawa
• Title: Stone duality
• Abstract: Stone's representation theorem for boolean algebras states that every boolean algebra is isomorphic to a eld of sets. However Stone proved much more; the category of boolean algebras is dual to a category of topological spaces, appropriately called stone spaces. Today we have an abundance of dualities between varied categories of orders (such as booleans algebras, distributive lattices, domains,) and categories of spaces (stone spaces, coherent spaces, scott topologies) which are all known as forms of 'stone duality'. We will review the formal concept of a duality as provided by category theory, and present a very general form of stone duality which provides the foundation of "pointless topology".