# Events

## Honours Thesis Presentation

#### Making Sense of Holes in Spaces Using Algebra

**Alexander Walker **

Date: Monday 29 April 2024

Time: 2:30 p.m.

Location: AT 214

Supervisor: Dr. Robert Dawson

Algebraic topology provides a method for detecting holes in topological spaces by the use of algebra. It turns out that we can make sense of holes by the consideration of two groups: the fundamental group and homology group. On the matter of the fundamental group, there is a generalization to higher dimensions, called higher homotopy groups. In practice these are more difficult to compute, leading the discussion in the direction of homology groups which are easier to compute. In doing this, we address the two varieties of homology groups which are simplicial and singular homology. Even though homology groups are easier to compute, we have to work hard to construct them. In this case, we turn to the Eilenberg-Steenrod approach which takes the properties of homology as axioms.

## Honours Thesis Presentation

#### Point-JEPA: A Joint Embedding Predictive Architecture for Self-Supervised Learning on Point Clouds

**Ayumu Saito **

Date: Thursday 25 April 2024

Time: 11:30 a.m.

Location: AT 214

Supervisor: Dr. Jiju Poovvancheri

Recent advancements in self-supervised learning for point cloud objects have demonstrated significant potential similar to other domains. However, these methods often suffer from drawbacks, including lengthy pre-training time, the necessity of reconstruction in the input space, or the necessity of additional modalities. In order to address these issues, we introduce PointJEPA, a joint embedding predictive architecture designed specifically for the point cloud domain. We introduce a sequencer that orders point cloud tokens to efficiently compute and utilize tokens' proximity based on their indices. This allows shared computation of proximity for point cloud tokens, allowing the efficient selection of spatially contiguous context and target blocks. Experimentally, our method achieves competitive results with state-of-the-art methods while avoiding the reconstruction in the input space or additional modality. Specifically, it outperforms other self-supervised learning methods on linear evaluation and few-shot classification on ModelNet40, showing the robustness of the learned representation. The results show that PointJEPA is an alternative efficient pre-training method to pre-existing methods in the point cloud domain.

## Honours Thesis Presentation

#### Learning Disentangled Representations of Point Clouds via Alpha Complexes for 3D Shape Classification

**Altaf M. Agowun **

Date: Monday 22 April 2024

Time: 2:30 p.m.

Location: Online via MS Teams

Supervisor: Dr. Jiju Poovvancheri

Three-dimensional computer vision tasks have gained much attention in recent times both in academic and industrial research. One of the key tasks of 3D computer vision is object classification. Various approaches based on the representations (e.g., point clouds, voxels, multi-view images and graphs) of the objects have been put forward for object classification. Recently, few works have used graph neural network for point cloud classification and have achieved promising results. Inspired by this, we explore the use of a dual-stream graph neural network combining the alpha complexes constructed on the feature and non-feature regions of the point cloud object. The disentangling of the point cloud geometry into feature and non-feature regions is realized through a gradient structure analysis procedure and a corner and edge detection techniques. The experiments conducted on ModelNet40 benchmark dataset indicate that the proposed graph-based method achieves higher or comparable accuracy to other state of-the-art methods.

Contact mathcs@smu.ca for connection details.

## Honours Thesis Presentation

#### A Critical Exploration, Analysis, and Contextualization of Discrete and Continuous Models of Criminal Behaviour for the Prediction of Future Real-World Crime Occurrence

**Jakob Conrad **

Date: Monday 22 April 2024

Time: 10:00 a.m.

Location: AT 214

Supervisor: Dr. Paul Muir

This interdisciplinary project explores “predictive policing”, a blanket term given to a number of crime prediction algorithms and tools used by police departments across the globe in an effort to predict and pre-empt crime occurrence. This project attempts to cut through the profound amount of both positive and negative rhetoric surrounding predictive policing software to understand what theory they are based on, how they are actually implemented in software, and how they interface with police officers working on-the-beat. Through a literature review of empirical environmental criminology research, a theory of how crime self-concentrates in space and time is discussed, as well as the potential explanations for this behaviour. Using this literature, two predictive models of criminal behaviour are introduced, explained, tested, and analysed, to understand how empirical crime observations can be translated into software. Using numerical results obtained from these models in conjunction with existing meta-critiques of predictive policing tools, the argument is made that while current predictive policing tools may hold theoretical value in the field of crime prediction, they have enough significant drawbacks as to cast doubt on their use to predict real world crime.

## Mathematics & Computing Science Department Seminar Series

#### Extremal Problems in Fractal Geometry

**Dr. Benjamin Bruce, (Department of Mathematics, University of British Columbia)**

Date: Tuesday 6 February 2024

Time: 11:30 a.m.

Location: AT 214

Suppose a group of mathematicians attends a colloquium talk. How many math-philes must be present so that the probability two of them share a birthday is at least 50 percent? Consider a standard 8 x 8 chessboard. How many knights can be placed on it so that no two of them are attacking each other? These two questions are examples of *extremal* *problems* — they ask for a size threshold beyond which an object must always exhibit a particular property.

Extremal problems are ubiquitous in mathematics, appearing in combinatorics, number theory, and analysis, among other areas. In this talk, I will discuss my work on extremal problems in the field of fractal geometry, where “size” is measured by “fractal dimension”. Specifically, I will present results stating that fractals of high enough dimension must contain certain point configurations governed by smooth curves. No prior knowledge of fractals is assumed!

## Mathematics & Computing Science Department Seminar Series

#### Mirror Symmetry Viewed Through Combinatorics and Noncommutative Algebra

**Dr. Jesse Huang, (Department of Mathematical & Statistical Sciences, University of Alberta)**

Date: Wednesday 31 January 2024

Time: 11:30 a.m.

Location: AT 214

Homological Mirror Symmetry (HMS) is a field of mathematics which predicts a deep connection between algebraic and symplectic geometry. A case where we can really understand this relationship comes from combinatorics. Starting from combinatorial data, we can produce spaces in algebraic geometry called toric varieties and their mirror geometry as well. This creates an extensive dictionary which allows us to translate abstract questions in algebraic and symplectic geometry into concrete and tractable combinatorics.

In this talk, I will discuss how to exploit this dictionary to obtain structural results about derived categories of toric varieties using polyhedral geometry and noncommutative algebra. This includes my work on an enhanced version of HMS in families and a recent proof of a conjecture of Orlov.

## Mathematics & Computing Science Department Seminar Series

#### Apollonian Circle Packings and Thin Groups

**Dr. James Rickards, (Department of Mathematics, University Colorado Boulder)**

Date: Monday 29 January 2024

Time: 11:30 a.m.

Location: AT 214

I will introduce Apollonian circle packings, and describe the local-global conjecture, which predicts the set of curvatures of circles occurring in a packing. I will then describe reciprocity obstructions, a phenomenon rooted in reciprocity laws (for instance, quadratic reciprocity), that disproves the conjecture in most cases. This is joint work with Summer Haag, Clyde Kertzer, and Katherine E. Stange, and originated from an REU (research for undergraduates) project in 2023. This talk will be accessible to advanced undergraduates who have seen modular arithmetic.

## Mathematics & Computing Science Department Seminar Series

#### Eigenvalue Problems for Two and More Parameters

**Dr. Tomaž Košir, (Faculty of Mathematics and Physics, University of Ljubljana; Ljubljana, Slovenia)**

Date: Wednesday 22 November 2023

Time: 2:30 p.m.

Location: AT 214

We will review the classical theory of two-parameter eigenvalue problems developed by F. V. Atkinson in the 1960s. We will show how it can be used to study two-parameter rectangular eigenvalue problems. The results can be generalized to more parameters. The motivation for the study comes from applications to optimal least squares ARMA and LTI models. We will not consider the applications in this talk.

## Mathematics & Computing Science Department Seminar Series

#### Equilibria of Polyhedra

**Gergő Almádi (Budapest University of Technology and Economics)**

Date: Friday 3 November 2023

Time: 2:30 p.m.

Location: AT 214

## MSc in Applied Science Thesis Defense

#### Error Estimation of Collocation Solutions

**Andrew Fraser (Department of Mathematics & Computing Science, SMU)**

Date: Tuesday 24 October 2023

Time: 2:30 pm

Location: Online - MS Teams

Contact mathcs@smu.ca for connection details.

## Mathematics & Computing Science Department Seminar Series

#### Jumping Around a Circle Irrationally

**Dr. Mitja Mastnak (Department of Mathematics & Computing Science, SMU)**

Date: Wednesday 18 October 2023

Time: 2:30 p.m.

Location: AT 214

I will give a brief overview of several classical results regarding properties of the sequence of multiples of a fixed irrational angle (in degrees) on a circle. Among other results, I will also briefly mention connections with the Goldbach conjecture (that conjectures that every even number greater then 2 can be written as a sum of two primes) and with Sturmian words (infinite non-periodic binary words of minimal complexity).

## Mathematics & Computing Science Department Seminar Series

#### Colour By Numbers

**Dr. John Irving (Department of Mathematics & Computing Science, SMU)**

Date: Wednesday 27 September 2023

Time: 2:30 p.m.

Location: AT 214

Suppose you are given a graph G and are tasked with assigning one of k possible colours to each of its vertices so that no two adjacent vertices share the same colour. In how many ways can this be done? We will discuss this classic combinatorial problem and a few surprising connections to other enumerative questions concerning graphs.

## MSc in Applied Science Thesis Defense

#### Modelling Shade-Intolerant Tree Responses to Forest Edges

**Kara-Lyne Shaw (Department of Mathematics & Computing Science, SMU)**

Date: Thursday 14 September 2023

Time: 2:00 pm

Location: Online - MS Teams

Contact mathcs@smu.ca for connection details.

Amidst growing global forest fragmentation, understanding the impacts of edges on forest ecosystems has become increasingly important for researchers and conservationists. However, the expanding scope of edge creation highlights the limitations of field studies. Models offer an accessible means to simulate edge effects in a time and cost-effective manner. This thesis explores the potential of ordinary differential equation (ODE) models to describe simulated vegetation responses of shade-intolerant trees following the establishment of a clear-cut edge in a boreal ecosystem. Through time-dependent parameters, I developed a suite of nested models capturing observable population trends in seedlings, saplings, and adult shade-intolerant trees. Sensitivity analyses were conducted to assess model robustness and predictive capability. This research will contribute to future implementations of edge vegetation response models, aiming to enhance our understanding of the long-term effects of edge creation.

## MSc in Applied Science Thesis Defense

#### Enhancing Satellite Trail Detection in Night Sky Imagery with Automatic Salience Thresholding

**Nikolaus Kollo (Department of Mathematics & Computing Science, SMU)**

Date: Friday 25 August 2023

Time: 10:00 am

Location: Online - MS Teams

Contact mathcs@smu.ca for connection details.

This study proposes a novel automatic thresholding method called Automatic Salience Thresholding (AST) for creating binary masks for detecting satellite streaks in night sky imagery. The approach utilizes a combination of Gaussian filtering, a salience-based thresholding technique, shape-based morphological filtering and line detection using Probabilistic Hough Transform to identify the satellite trail in the image. We evaluated our method on diverse datasets of night sky images containing satellite trails in varying lighting conditions. The results show that AST outperforms other methods in terms of a number of performance metrics. The proposed AST method was also used to generate annotated binary masks for Hubble Space Telescope (HST) image data with promising results.

## Honours Thesis Presentation

#### Comparing the performances of Sequence Alignment Software: Bandage, SPAligner and GraphAligner

**Yusreen Shah**

Date: Monday 14 August 2023

Time: 4:00 p.m.

Location: Online via Zoom

Supervisor: Dr. Somayeh Kafaie

Contact mathcs@smu.ca for connection details.

## Honours Thesis Presentation

#### Application of Error Control Differential Equation Software to Information Flow Models

**Evan Lucas-Currie**

Date: Wednesday 24 May 2023

Time: 10:30 a.m.

Location: Online

Supervisor: Dr. Paul Muir

Contact mathcs@smu.ca for connection details.

## Honours Thesis Presentation

#### Simultaneous Triangularization

**Alexander Saunders **

Date: Monday 24 April 2023

Time: 11:00 a.m.

Location: AT 214

Supervisor: Dr. Mitja Mastnak

A matrix A acting on a finite dimensional vector space V is said to be upper triangular if it has all zeroes below the diagonal. It is triangularizable, if there exists an invertible transformation U such that the matrix U^(−1)AU is triangular. For a vector space over an algebraically closed field it is known that every matrix is triangularizable. The question of simultaneous triangularization is whether for a given collection of linear transformations there exists a single invertible matrix such that all transformations are simultaneously upper triangular. Equivalently, whether there exists a basis of the vector space such that every transformation is upper triangular with respect to said basis. We discuss a sampling of classical results on sufficient conditions for simultaneous triangularizability before introducing more modern results which find approximate versions of classical conditions and describe the structure of matrix groups satisfying certain triangularizing conditions.

## MSc in Applied Science Thesis Defense

#### HyperInvoFusion: Depth Aware and Parameter Efficient Object Detection from RGB-D Data

**Mehfuz A. Rahman (Department of Mathematics & Computing Science, SMU)**

Date: Thursday 6 April 2023

Time: 1:00 p.m.

Location: Online

Contact mathcs@smu.ca for connection details.

Over the last decade, there has been an upsurge in the availability of low-cost commodity depth sensors. Nowadays, a vast majority of modern devices, ranging from smartphones to conventional augmented reality devices are equipped with depth sensors. Depth images produced by such sensors contain complementary information for computer vision tasks such as object detection when used with color images. Despite the benefits, it remains a complex task to simultaneously extract photometric and depth features in real-time because of the immanent difference between depth and color images. We investigate into the use of depth weighted involution kernel for an improved object detection from RGB-D images. The defense talk will emphasize the concept of involution, depth weighted involution, and RGB-depth fusion for object detection.

## Research Presentation

#### Computing with string

**Dr. Robert Dawson (Department of Mathematics & Computing Science, SMU)**

Date: Wednesday 8 February 2023

Time: 2:30 p.m.

Location: AT 214

Pieces or loops of string have been used for centuries to construct circles, straight lines, ellipses, and other ovals. What other curves can be computed in this way? In this talk, I offer two rigorous answers, one valid for systems that must maintain their own tension and another for systems that are externally tensioned.

## Research Presentation

#### Can we give an approximate answer to whether a given regular expression matches all possible strings?

**Dr. Stavros Konstantinidis (Department of Mathematics & Computing Science, SMU)**

Date: Wednesday 25 January 2023

Time: 2:30 p.m.

Location: AT 214

The question of whether a given regular expression matches all strings is a hard problem (PSPACE-complete). This is equivalent to whether a given NFA (nondeterministic finite automaton) accepts all strings, which is known as the NFA universality problem. For example the regular expression (0|1)* matches all binary strings but 1* | (0|10|111*)* does not match the strings that end with 01. We investigate the approximate problem of whether a given NFA accepts at least 99% of all strings. Is this problem any easier? In this talk we will deal with the subproblem of whether a given NFA accepts all strings of some given length n, which is still hard (coNP-complete), and its approximate version.

## Research Proposal Presentation

#### Collocation and Runge-Kutta Software for Boundary Value Ordinary Differential Equations

**Mark Adams (Department of Mathematics & Computing Science, SMU)**

Date: Wednesday 14 December 2022

Time: 2:30 p.m.

Location: AT 214

Boundary value ordinary differential equations (BVODEs) are systems of ODEs with conditions imposed at both ends of the problem domain. COLNEW and BVP_SOLVER2 are state-of-the-art numerical software which can compute an approximate solution to a BVODE. These Fortran solvers are widely used directly and are also available within problem solving environments (PSEs) such as, Scilab and R, and within well known scripting languages such as Python. COLNEW and BVP_SOLVER2 are capable of efficiently computing solutions to a wide range of complex real-world problems which mathematically model many aspects of science and engineering that are based on BVODEs. In this proposal, we discuss the development of the next generation of these BVODE solvers, COLNEWSC and BVP_SOLVER3, which will have improved design, more reliability, increased efficiency, and new capabilities. We have already made substantial progress in several key areas, one of which involves the development of a more efficient approach for solving difficult and computationally intensive problems in the area of aerospace engineering.

2022-2023 Colloquium Series

#### Universality limits for orthogonal polynomials

**Dr. Milivoje Lukic (Rice University, Houston, Texas)**

Date: Wednesday 23 November 2022

Time: 2:30 p.m.

Location: AT 214

It is often expected that the local statistical behavior of eigenvalues of some system depends only on its local properties; for instance, the local distribution of zeros of orthogonal polynomials should depend only on the local properties of the measure of orthogonality. This phenomenon is studied using an object called the Christoffel-Darboux kernel. The most commonly studied case is known as bulk universality, where the rescaled limit of Christoffel-Darboux kernels converges to the sine kernel.

In this talk, we will survey this subject, prior results, and a recent result which gives for the first time a completely local sufficient condition for bulk universality. The new approach is based on a matrix version of the Christoffel-Darboux kernel and the de Branges theory of canonical systems, and it applies to other self-adjoint systems with 2x2 transfer matrices such as continuum Schrodinger and Dirac operators.

The talk is based on joint work with Benjamin Eichinger (TU Wien) and Brian Simanek (Baylor University).

#### Contact us

**Mathematics & Computing Science Department**