Graduate Studies

Area of Interest: I use mathematical and statistical tools to address questions at the intersection of evolution, ecology, and epidemiology. Infectious pathogens have important consequences for human and wildlife populations alike. I develop what are known as phylodynamic (phylogenies+ epidemiological dynamics) methods to understand and control ongoing epidemics. In particular, my research focuses on quantifying how both host and pathogen genetics shape disease spread and severity. In addition to this focus on emergent pathogens, by studying the genetics and evolutionary dynamics long-term associations between hosts and their infectious pathogens I strive to understand how these complex coevolutionary interactions shape the biological diversity of the natural world.

Assistant Professor Ben Adcock was awarded the 2015 Sloan Research Fellowship for his outstanding accomplishments in the field of mathematics. “I work in computational math, at the intersection of numerical analysis, computational harmonic analysis, approximation theory and data science. I'm interested broadly in how we recover objects from data,” he explains. “A typical example is Magnetic Resonance Imaging, when you have an MRI scan, the machine acquires certain measurements, and then at the end of the process the MRI practitioner gets an image. I’m trying to make this recovery faster, by allowing you to take fewer measurements while at the same time producing better quality images.”

Adcock heads up a research group in the Department of Mathematics, working closely with postdocs and PhD, MSc and undergraduate students. “I think being open-minded and intellectually curious is very important—if you don't have that, then you will struggle to get far in research and academia,” he explains. “We do a range of things related to the group’s research. We all meet every two weeks, and I also meet with everyone individually. I like students to have different projects to work on. I like them to have variety,” he says.

In addition to his research, Adcock spends his time in the department lecturing. “I enjoy teaching a lot. I like seeing students work hard and learn new concepts. I especially enjoy seeing students develop and progress—I get a lot of satisfaction from that,” he explains. “I would like to dispel the myth that there's a huge dose of God-given talent in doing mathematics. A lot of what I do is about hard work.”

Outside of his work in the department, Adcock is an avid cyclist and hiker, taking advantage of the coastal mountains surrounding the campus.

Dr. Bojan Mohar is recognized as one of the leading discrete mathematicians in the world. He is a Canada Research Chair and his main area of research is Graph Theory, which has applications in theoretical computing. “I've worked on many different problems, resolved open problems and conjectures, and opened new areas of research with possible applications outside of mathematics,” he says. “One of my main subjects is Topological and Structural Graph Theory and that has a lot of applications in the design of algorithms.”

For Mohar, his work is full of variety and possibility. “I love it because there is always something new. You're learning all the time. You're uncovering new things and developing your own ideas. You can make a new theory or a new proof. It's very vibrant and it's very alive so you're never bored,” he explains.

Mohar has published widely, including a co-authored book that’s widely used in discrete mathematics and computer science. “I've done some pioneering work with the application of graphs and eigenvalues in the structure of Graph Theory and in optimization in computer science. Probably my most famous result is a very efficient algorithm for embedding graphs on surfaces,” he says.

As a leading research faculty in the department, Mohar works closely with graduate students and postdoctoral fellows. “We have a weekly meeting where we discuss any progress someone made or new and important results coming in that we need to get acquainted with,” he says. “Mathematics is collaborative. Even if you work by yourself on an open problem, it's always good to have someone you can explain your progress to. My students sometimes get joint work, or joint publication because they talk to each other.”

Area of Interest: My work is at the interface of mathematics and the epidemiology and evolution of pathogens. I hold an Canada 150 Research Chair in Mathematics for Evolution, Infection and Public Health. In my group we develop mathematical tools connecting sequence data to the ecology and evolution of infections. I also have a long-standing interest on the dynamics of diverse interacting pathogens. For example, how does the interplay between co-infection, competition and selection drive the development of antimicrobial resistance? To answer these questions, my group is building new approaches to analyzing and comparing phylogenetic trees derived from sequence data, studying tree space and branching processes, and developing ecological and epidemiological models with diversity in mind.

Area of Interest: Broadly, my research interests include quantum information & computation; nonlocality & contextuality; and operator algebras & noncommutative geometry. I am keenly interested in helping to elucidate the structural origins of computational and communicational advantages in both concrete quantum models and abstract postclassical models. These questions sit at the foundations of logic, computer science, and physics, and involve disparate areas of maths: e.g. algorithms & complexity theory, functional analysis, number theory, and category theory.

I previously worked at the Centre for Quantum Information and Foundations in the Department of Applied Mathematics and Theoretical Physics (a part of the Centre for Mathematical Sciences) at the University of Cambridge, in the group of Richard Jozsa FRS. I was a member of King's College.

Prior to this, I worked in the Department of Computer Science, UCL as the Researcher Co-Investigator of the EPSRC-funded project Contextuality as a resource in quantum computation: a collaboration between UCL and the University of Oxford headed by Simone Severini and Samson Abramsky FRS.

I spent a semester as a Visiting Scientist at the Simons Institute for the Theory of Computing at the University of California, Berkeley. Previously, I completed my DPhil in Computer Science in the Quantum Group (Logic, Foundations, and Structures), supervised by Samson Abramsky FRS and Bob Coecke, as a Clarendon Scholar at Merton College, University of Oxford. I completed my MSc in Mathematics and my BSc in Mathematics and Physics at the University of Toronto where my supervisor was George Elliott FRSC. In Toronto, I was a Visiting Member of the Fields Institute for Research in Mathematical Sciences, supported by NSERC Undergraduate Student Research Awards.

Canada Research Chair Dr. Paul Tupper develops mathematical tools for psychologists and linguists. “Mathematical modelling is looking at the world and looking at phenomena and trying to find a mathematical model that helps you to understand it,” he says. “It's very well developed for certain fields, like physics. Nowadays, linguists are getting more and more interested in quantitative things and so I've been able to establish connections with people in that field.”

One of Tupper’s interests is how people modify their speech in situations where they want to be more clearly understood. “There's this whole field of linguistics that studies what makes speech comprehensible. And there's applications for teaching English as a second language,” he explains.

In addition to his own research, Tupper spends his time teaching and meeting with students. “I really like math and I enjoy doing it—doing calculations and trying to figure things out. And I like people, so it's a good combination.”