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QUIGS Seminar: Triply generated matrix algebras

John Holbrook, University of Guelph, Ontario, Canada An old result, often called Gerstenhaber's Theorem, states that the algebra of polynomials in two commuting nxn matrices has dimension at most n. Here we discuss the possibility of extending this result to algebras generated by THREE commuting matrices. This talk is largely based on joint work with Kevin O'Meara. See, for example: Some thoughts on Gerstenhaber's theorem, J. Holbrook and K.C. O'Meara, Linear Alg. Appl. 466, 267--295 (2015).

PhD Math Defence: Dynamic Transmission Models: The Impact of Behavioural Feedbacks and Parametrization Methods on Intervention Effectiveness

Michael Andrews, Ph.D. Defence Infectious diseases impose significant health and economic burdens across the world, continuously threatening human quality of life.  Mathematical models of infectious disease epidemiology can help to gain insight on potential health outcomes of a population that is vulnerable to disease spread.  Models that incorporate decision-making mechanisms can furthermore capture how behaviour-driven aspects of transmission such as vaccination choices and the use of non-pharmaceutical interventions (NPIs) interact with disease dynamics. 

QUIGS Seminar: Quantum Channels with Dilations on Matrix Spaces

Jeremy Levick (AIMS - University of Guelph) We present a generalized Stinespring dilation for unital quantum channels: the Stinespring dilation can be thought of as a unitary 1-dilation for a channel. We discuss when a unital channel has such dilations, and specifically, when a channel can be dilated to a matrix space and have a dilation. This is joint work with Rob Martin at UCT.

PhD Math Defence: Models of Cytokine Dynamics During Cytokine Storms and Synergy During Virus and Drug Combination Therapy

Marianne Waito, Ph.D. Thesis Defence This thesis presents two mathematical models that aim to support biological researchers in the fight against cancer. They are based on biological phenomena observed by researchers at the Ontario Veterinary College (OVC). The first models interactions of cytokines during a fatal cytokine storm, while the second models effects of combining an oncolytic virus and an epigenetic modifier.

MSc Math Defence: A Novel Representation for Graph Evolution

Meghan Timmins, M.Sc. Thesis Defence Networks and combinatorial graphs are commonly used in a wide variety of types of mathematical modelling to represent structures such as contact networks in epidemiology, road networks in urban planning, and scheduling conflicts.

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