Contributed Talks

The bulk of the OMSC is dedicated to contributed talks, generally given by graduate students from universities across Canada. Talks can be about the speaker's original research or a mathematical topic of their choosing. We recommend that speakers only assume attendees have a standard undergraduate-level mathematics background. Talks are scheduled in a 20 minute intervals, with 15 minutes for the talk and five minutes for questions.

We encourage you to check out previous years' contributed talks in the former proceedings booklets.

Speaker: Joy Liu (Dalhousie University)

Title: From approximate to accurate: Improving Sea Scallop Meat Weight Estimates in the Bay of Fundy through Spatiotemporal Models

Language: English

Abstract: Sea scallops (Placopecten magellanicus) comprise the fifth largest fishery in Canada, the vast majority of which occurs in the Maritimes. The target of the fishery is the adductor muscle (i.e., the meat) with size varying both in time and space. We use spatiotemporal models that incorporate environmental data (depth, salinity, etc.) to explore the variability in scallop meat weight (and scallop shell height) in the Bay of Fundy. These models elicit some interesting patterns regarding the condition of scallops as well as improve current estimates of scallop meat weight for this area. These results can improve science advice and lead to more sustainable management of the stock.

Speaker: Albi Kazazi (York University)

Title: Reconfiguration of Hamiltonian cycles and paths in grid graphs

Language: English

Abstract: Let H and K be any two Hamiltonian cycles in a grid graph G. We are interested in reconfiguring H into K using certain "moves". We will call a unit square face of G a box of G. We say that a box of G with vertices a, b, c, d is switchable in H if it has exactly two edges in H, and these edges are parallel. Let abcd be a switchable box with edges ab and cd in H. We define a switch move on the box abcd in H as follows: remove edges ab and cd and add edges bc and ad. A double-switch move is one in which we simultaneously perform two switch moves on two boxes of G. We show that there exists a sequence of double-switch moves that reconfigures cycle H into cycle K, such that the resulting graph after every move is another Hamiltonian cycle. The result can be extended to the case where H and K are Hamiltonian paths. In addition to double-switch moves, we make use of a single-switch move move called the backbite move, which is needed to relocate the end-vertices of the path.

Speaker: Arman Jahangiri (University of Calgary)

Title: High Dimensional Data Classification with Rare and Weak Signals, Binary Response Variable and Gaussian Predictors

Language: English

Abstract: An ever-growing trend in modern research is the desire to collect a huge amount of data and use it for classification. An important application of classifying high-dimensional data is categorizing the patients into healthy/unhealthy based on their microarray gene expression data. There are various classification algorithms, such as logistic regression or k-nearest neighbors. However, they may perform ineffectively with high-dimensional data, necessitating a change. In this talk, we start by defining successful classification, and introducing adjusted classifiers for high-throughput data, and then focus on Discriminant Analysis as an alternative classification method for two-class classification with rare and weak signals. We will provide the currently found successful and unsuccessful regions and illustrate our advancements on the topic with adopting Quadratic Discriminant Analysis classifier as an alternative to Linear Discriminant Analysis.

Speaker: Dac Nhan Tam Nguyen (University of British Columbia)

Title: Congruent modular forms and logarithms of Heegner points

Language: English

Abstract: Goldfeld’s conjecture predicts that for a fixed elliptic curve, the average rank of its quadratic twists is 1/2. In a recent paper by Daniel Kriz and Chao Li, the authors made significant progress toward this conjecture by studying the logarithms of Heenger points attached to congruent modular forms. In this talk, we will see how one can obtain this congruence-type result over some larger field extensions.

Speaker: Yiyao Jiao (University of Western Ontario)

Title: Integrating Environmental, Social, and Governance (ESG) Preferences into Investment Decisions: A Multi-Attribute Approach

Language: English

Abstract: This presentation showcases the latest research findings from two papers authored by Marcos Escobar-Anel and Yiyao Jiao. The focus of both papers is on ESG modeling, utilizing a shared analytical framework. The first paper primarily delves into multi-attribute utility and optimal portfolio allocation within the context of ESG. The second paper extends this framework by incorporating ambiguity aversion into ESG modeling and explores robust portfolio optimization techniques within this domain. These papers introduce an analytical framework designed to assist investors in integrating ESG preferences into their investment strategies. Through a combination of theoretical analyses and empirical investigations, the studies highlight the benefits and practicality of adopting such approaches.

Speaker: David Worley (University of Ottawa)

Title: Grid Minors and Products

Language: English

Abstract: Motivated by recent developments regarding the product structure of planar graphs, we study relationships between treewidth, grid minors, and graph products. We show that the Cartesian product of any two connected n-vertex graphs contains an Ω(√n)×Ω(√n) grid minor. This result is tight: The lexicographic product (which includes the Cartesian product as a subgraph) of a star and any n-vertex tree has no ω(√n)×ω(√n) grid minor.

Speaker: Chris Karpinski (McGill University)

Title: A Tits alternative for groups acting on buildings

Language: English

Abstract: Buildings are a class of combinatorial objects (simplicial complexes) with a highly symmetric structure introduced by Jacques Tits in the 1950's. They appear in many areas of mathematics from number theory to topology to group theory and are intricately related to Coxeter groups. We study groups acting on buildings and show that we can deduce an interesting algebraic dichotomy for a group acting nicely on a building, known as the weak Tits alternative: the group is either very large (contains the free group F_2) or very small (has an abelian subgroup of finite index). This is joint work with Damian Osajda and Piotr Przytycki.

Speaker: John Tsang (University of Ottawa)

Title: Correcting Selection Bias in Non-probability Two-Phase Payment Survey

Language: English

Abstract: This presentation extends the Pseudo Maximum Likelihood (PML) estimator to the non-probability two-phase sampling by leveraging the probability sample at the individual level. Using the Bank of Canada 2020 Cash Alternative Survey Wave 2, we compare the performance of our proposed method to alternative methods, which either do not account for a two-phase sampling design or do not explicitly model the selection probability. The results show that the PML-based approach performs better than raking in reducing the selection bias for both phases' payment-related variables, especially for the low-response youth group. Furthermore, the two-phase PML weighting scheme both accounting for phases' selection mechanisms has a smaller bias than Phase-2-Only alternatives of ignoring Phase 1's design and simply treating Phase 2 as a standalone single-phase design. The presentation will end with a discussion about variance estimation for both phases.

Speaker: Archishman Saha (University of Ottawa)

Title: Moser Transformation of a Stochastically Perturbed Kepler Problem

Language: English

Abstract: We consider a stochastic Kepler problem perturbed by a Hamiltonian noise affecting the angular momentum vector. We show that while the angular momentum and the Laplace-Runge-Lenz vectors are not conserved, their norms satisfy the usual deterministic dynamics. This allows us to determine the set of initial conditions leading to collisions. Further, in a procedure similar to Moser regularization, we transform the stochastic Kepler problem to obtain its dynamics as a stochastic geodesic flow on a 3-sphere.

Speaker: Ali Selseleh (York University)

Title: Application of Mathematical Modelling & Data Analytics for Predicting & Controlling Drug Resistant Hospital Acquired Infections (Superbugs)

Language: English

Abstract: Mathematical modelling is widely used in healthcare to predict disease spread and analyze data. By converting mathematical data into medical predictions, healthcare professionals can make informed decisions and prioritize treatments in superbugs infections. During the COVID-19 pandemic, models were crucial in guiding healthcare systems on medication allocation and health outcomes. Artificial intelligence and software are sometimes utilized to analyze data for optimal solutions. Data from patients, medical journals, and biology are collected to predict disease trends. While mathematical models offer accuracy, they are software-driven and may require human input for reliable predictions. It is important to recognize the limitations of software and emphasize the role of human expertise in healthcare decision-making. Future research should consider a balanced approach that values both technology and human insight in disease treatment.

Speaker: Joseph Gondek (Carleton University)

Title: A notion of amenability for inverse semigroup actions

Language: English

Abstract: Cayley's theorem tells us that group theory can be called the study of "global symmetry", where the symmetry in question is realized by bijections on a set. Inverse semigroups are a generalization of groups which represent the passage from "global symmetry" to "partial symmetry". This presentation examines inverse semigroup actions which possess a powerful analytic property called amenability. We are motivated by the group case, where amenability is known to have many interesting structural and representation-theoretic consequences.

Speaker: Amélie Comtois (University of Ottawa)

Title: Frobenius Algebras and Topological Quantum Field Theories

Language: English

Abstract: Frobenius algebras are vector spaces equipped with some additional algebraic structure. Despite the simplicity of the definition, they have many applications in topology and physics. The best framework for studying Frobenius algebras is category theory, specifically monoidal category theory. All of the equational structure can be written down using diagrammatic language, and can be considered in broader settings than just vector spaces. This leads to the consideration of the category of 2-cobordisms where Frobenius algebras have an explicitly topological interpretation, and in fact this category has a remarkable characterization as a free structure. Understanding these structures requires only a minimal amount of category theory, which the speaker will provide.

Speaker: Hin Lon Lao (York University)

Title: Directly decomposing certain relatively complemented lattices

Language: English

Abstract: Birkhoff showed that congruence relations are in one to one correspondence with the standard ideals of a sectionally complemented lattice, and Dilworth showed that a relatively complemented lattice is either without proper congruence relation, or directly decomposable. We try to explore the conditions under which a relatively complemented lattice has non-trivial standard ideals and we will go through some examples.

Speaker: Cyrus Rezaei Feyzabady (Université de Montréal)

Title: Measuring and regularizing networks in function space

Language: English

Abstract: In neural network optimization, emphasis often falls on parameter fine-tuning. However, our study delves deeper, targeting the optimization of the fundamental function that translates inputs to outputs. We address concerns regarding the alignment between parameters and function, demonstrating the simplicity of calculating distances in an L^2 Hilbert space. We observe intriguing behaviors in typical networks and unveil a relationship between ℓ^2 parameter distances and L^2 function distances during optimization. We propose practical applications, including constraining function changes in multitask learning and introducing a learning rule to limit network travel distance per update in L^2-space. These applications highlight the direct measurement and regularization of function distances, surpassing reliance on parameters or local approximations.

Speaker: Zander Karaganis (University of Ottawa)

Title: Euclidean Buildings and Representation Theory

Language: English

Abstract: Euclidean buildings carry valuable information about the structure theory of connected reductive groups over local fields. Specifically, they can be used in order to construct certain classes of representations. In this talk, we will explore how we may relate representations of tori of a given connected reductive p-adic group to special representations of the group, by using the Bruhat-Tits building. These special representations give information about how to generate the category of smooth representations of the group.

Speaker: Yuliya Nesterova (Carleton University)

Title: Negative Queues Explain Quantum Phenomena

Language: English

Abstract: From line-ups at Starbucks to packets awaiting service at an internet server, from call centre traffic to files infected by virus: queueing theory gives us rigorous models to study the science of orderly waiting. In quantum computing, entanglement is exploited to give information transmission an advantage over classical computing, using the mind-stretching reality that one half of an entangled pair holds information about the other half. Could queueing theory help us understand quantum transmissions? We use the simplest possible queue with negative customers to elucidate the bare-bones behaviour of the qubit world... somewhat successfully! The expected queue length and waiting time for an M/M/1 queue with stacked negative customers is examined.

Speaker: Finlay David Rankin (Carleton University)

Title: Commuting squares and quantum groups

Language: English

Abstract: Wang constructed a compact quantum group associated to finite-dimensional von Neumann algebra. Banica generalized the work of Wang and did it for a unital inclusion of finite-dimensional von Neumann algebras and in certain cases gave the representation theory of the associated compact quantum group. We generalize Banica's work and assign a compact quantum group to nondegenerate commuting square of finite dimensional von Neumann algebras and talk a bit about the representation theory of this compact quantum group.

Speaker: Khalil Besrour (University of Ottawa)

Title: Modular Solutions to a level 2 Schwarz differential equation

Language: English

Abstract: This presentation concerns the study of the Schwarz differential equation {h, τ} = sF where F is a weight 4 modular form of level 2 and s is a complex parameter. In particular, we determine all the values of s for which the solutions h are modular functions for a finite index subgroup of the modular group. We do study these subgroups, compute their genus and explicitly give their hauptmodul in the genus 0 case. We do this using the theory of modular forms on the complex upper-half plane as well as an analysis of the representation theory of subgroups of the modular group. This also leads to the solutions to an order 2 Fuchsian differential equation.

Speaker: Leila Gholizadeh Zivlaei (Carleton University)

Title: Existence and Uniqueness of Some Fractional Sturm-Liouville Equations

Language: English

Abstract: In this presentation, we provide existence and uniqueness results for the initial value problems associated with mixed Riemann-Liouville/Caputo differential equations in the real domain. We show that, under appropriate conditions in a fractional order, solutions are always square-integrable on the finite interval under consideration. The results are valid for equations that have sign-indefinite leading terms and measurable coefficients. Existence and uniqueness theorem results are also provided for two-point boundary value problems in a closed interval. (Fractal Fract. 2024, 8, 148. Open access)