Student engagement in various classroom exercises is critical and one of many evidence-based effective pedagogical methods. During this session, I will discuss the various engagement methods I have recently incorporated in the Statistics classes I have instructed and reflect ‘how much is too much’ .
This talk requires no prior knowledge and will be a gentle introduction to colouring graphs, suitable for a broad audience including students. We will start with some historical tales, including the four colour map problem and the chromatic polynomial. We will then meet the chromatic symmetric function, dating from 1995, which is a generalization of the chromatic polynomial. A famed problem on it, called the Stanley-Stembridge (3+1)-free problem, has been the focus of much research lately including resolving another problem of Stanley of whether the (3+1)-free problem can be widened. The resulting paper on the latter problem was recently awarded the 2023 David P. Robbins Prize, and we will hear this story too.
Cryptography in class groups of quadratic fields dates back to 1988 with the advent of the first protocol for exchanging cryptographic keys, whose security resides in the intractability of extracting discrete logarithms in the class group of an imaginary quadratic field. Since then, the area has undergone a turbulent history. A host of other class group based cryptosystems were put forward, founded on the hardness of both the discrete log problem and the integer factorization problem. Following devastating breaks of the factoring-based schemes in 2009, the area made a come-back in 2015 when class groups of imaginary quadratic fields turned out to facilitate linearly homomorphic encryption, which can be used for electronic voting for example. The suitability of class groups as a setting for zero knowledge proofs and in block chain technology further rejuvenated the subject. Research has intensified with the recent innovation of supersingular elliptic curve isogeny based cryptographic schemes – again with successes as well as spectacular failures. This talk tells the tumultuous tale of class group based cryptography, from its beginnings 37 years ago to current state-of-the-art research into protocols that are resistant to attacks by quantum computers. No mathematical knowledge beyond familiarity with very basic abstract algebra (groups, rings) is required to follow the story.
This talk presents some problems and results in the theory of differential equations, and describes their relation to fundamental questions in acoustic imaging. From a practical perspective, the goal is to understand how information about a particular layered structure - for example in the built environment, or biological tissue such as the retina or abdominal wall, or geological structure such as sedimentary rock - is encoded in acoustic echoes reflected back from the structure. Certain animals such as porpoises, bats and shrews use this type of information to perceive their environment, much as we perceive our surroundings using reflected light. But we do not fully understand how this works. Layered structures provide a simplified setting in which to explore the issue, and comprise and important special case of interest in its own right. Analysis of the simplest mathematical model governing sound propagation in layered media leads to a surprising diversity of mathematical connections, including in combinatorics, differential geometry and quantum mechanics. In turn, mathematical results in each of these areas provide insight into the original acoustic setting. Ultimately, these lead to a much more detailed understanding of how acoustic echoes encode the physical structure from which they emanate. The talk is intended to be accessible to a wide audience.
Jim Stallard is a Professor (Teaching) in the Department of Mathematics & Statistics at the University of Calgary and the recipient of the 2024 Distinguished Educator Award from the Statistical Society of Canada. Over his 25-year teaching career, he has taught 10 different courses, many of them large service classes, inspiring thousands of students through his innovative, student-centred teaching. Jim’s active learning approach emphasizes engagement, small-group exercises, and immediate feedback, earning him 14 nominations for the Calgary Student Union Teaching Award and the Faculty of Science Teaching Excellence Award.
Jim has also made significant contributions to statistics education nationally, helping build the Canadian Statistics Education community. He gave an impactful presentation at the 2006 SSC Annual Meeting special session on creative education initiatives. He chaired the Statistics Education Section, co-led the design of Calgary’s Data Science programs, and continues to advance evidence-based teaching practices. His dedication to teaching and service has made him a leader in promoting active learning and mentorship across Canada.
Stephanie van Willigenburg is a Professor of Mathematics at the University of British Columbia (UBC). Her research has earned her numerous accolades, including the Krieger-Nelson Prize from the Canadian Mathematical Society in 2017 and the Robbins Prize from the Mathematical Association of America in 2023, both recognizing her outstanding contributions to mathematics. She was also inducted as a Fellow of the American Mathematical Society in 2023.
In addition to her research achievements, Stephanie has been recognized for her exceptional teaching with a Killam Award in 2008. She has delivered numerous plenary lectures, including an Invited Address at the Joint Mathematics Meetings, the largest mathematics conference in the world.
Currently, Stephanie serves as the Associate Dean for Equity, Diversity, and Inclusion in Science at UBC. She is also a co-founder of the Algebraic Combinatorics Research Community, which promotes mentoring, research collaborations, and networking opportunities for underrepresented groups in algebraic combinatorics and related fields.
Renate Scheidler is a German-Canadian mathematician and computer scientist. Her research focuses on algorithms and computations in global fields—algebraic number fields and algebraic function fields over finite fields—within the contexts of algebraic number theory, arithmetic geometry, and cryptography.
She is a professor in the Departments of Mathematics & Statistics and Computer Science at the University of Calgary. Renate serves as the co-editor-in-chief of Contributions to Discrete Mathematics and is one of the founders of the Women in Number Theory research community and the Women in Numbers conference series.
In recognition of her contributions to mathematics, she was awarded the 2024 Krieger-Nelson Prize. Renate has also held leadership roles, including serving as Graduate Director in the Department of Mathematics & Statistics at the University of Calgary and as an adjudicator for NSERC Discovery Grants.
Peter Gibson is a Professor in the Department of Mathematics & Statistics at York University in Toronto. His research spans various areas of pure and applied mathematics, including combinatorial and differential geometry, complex and harmonic analysis, numerical methods, inverse problems, and mathematical physics.
After earning his Ph.D. in Pure Mathematics from the University of Calgary in 2000, Professor Gibson held an NSERC Postdoctoral Fellowship at TU Darmstadt, the Mathematical Sciences Research Institute (MSRI) in Berkeley, and the University of Washington in Seattle. He continued his postdoctoral work at the Universities of Karlsruhe and La Réunion before joining York University in 2004.
Since then, he has held visiting positions at PUC-Rio de Janeiro (2011) and the University of Calgary (2017–2018). In 2023, he was awarded a Simons Fellowship to conduct research at the Isaac Newton Institute in Cambridge, UK.