Relevant Degree Programs
Complete these steps before you reach out to a faculty member!
- Familiarize yourself with program requirements. You want to learn as much as possible from the information available to you before you reach out to a faculty member. Be sure to visit the graduate degree program listing and program-specific websites.
- Check whether the program requires you to seek commitment from a supervisor prior to submitting an application. For some programs this is an essential step while others match successful applicants with faculty members within the first year of study. This is either indicated in the program profile under "Admission Information & Requirements" - "Prepare Application" - "Supervision" or on the program website.
- Identify specific faculty members who are conducting research in your specific area of interest.
- Establish that your research interests align with the faculty member’s research interests.
- Read up on the faculty members in the program and the research being conducted in the department.
- Familiarize yourself with their work, read their recent publications and past theses/dissertations that they supervised. Be certain that their research is indeed what you are hoping to study.
- Compose an error-free and grammatically correct email addressed to your specifically targeted faculty member, and remember to use their correct titles.
- Do not send non-specific, mass emails to everyone in the department hoping for a match.
- Address the faculty members by name. Your contact should be genuine rather than generic.
- Include a brief outline of your academic background, why you are interested in working with the faculty member, and what experience you could bring to the department. The supervision enquiry form guides you with targeted questions. Ensure to craft compelling answers to these questions.
- Highlight your achievements and why you are a top student. Faculty members receive dozens of requests from prospective students and you may have less than 30 seconds to pique someone’s interest.
- Demonstrate that you are familiar with their research:
- Convey the specific ways you are a good fit for the program.
- Convey the specific ways the program/lab/faculty member is a good fit for the research you are interested in/already conducting.
- Be enthusiastic, but don’t overdo it.
G+PS regularly provides virtual sessions that focus on admission requirements and procedures and tips how to improve your application.
Graduate Student Supervision
Master's Student Supervision
Theses completed in 2010 or later are listed below. Please note that there is a 6-12 month delay to add the latest theses.
Khovanov homology is a combinatorially-defined invariant of knots and links, with various generalizations to tangles. Recently, Lawson, Lipshitz, and Sarkar generalized Khovanov homology to a spectrum-valued Khovanov homotopy type, from which the Khovanov homology can be recovered. This thesis is primarily a ground-up survey of the Khovanov homotopy type; beginning with the Jones polynomial, we weave our way through Khovanov homology and the Khovanov homotopy type for links, before finishing with the construction of the Khovanov homotopy type for tangles. Throughout, we place a special emphasis on Conway mutation, an operation on links which involves replacing a tangle within a link by a related tangle. Despite its non-triviality, Conway mutation is impossible to detect with the Jones polynomial, and difficult to detect with Khovanov homology. The extent to which the Khovanov homotopy type is able to detect mutation is an open question, and the Khovanov homotopy type for tangles seems to be particularly well-suited for investigating this question.
Despite the analytic underpinnings of Heegaard Floer theory and its refine- ment to knots, there is an interesting class of knots, the (1, 1) knots, which have the special property that their knot Floer homology can be computed na ̈ıvely, straight from the definition, using only combinatorial techniques. In this thesis, we survey (1,1)-knots, describe their knot Floer homology, and focus in particular on the landscape of the manifolds obtained by Dehn surgery on these knots. More precisely, J. Greene, S. Lewallen and F. Vafaee recently described a simple criterion for determining if a (1, 1) knot admits a nontrivial surgery to an L-space, using the orientation of the curves in a doubly pointed genus-1 Heegaard diagram for the knot. This character- ization is formally very similar to a characterization due to J. Hanselman, J. Rasmussen and L. Watson, using a graphical calculus they developed for working with the bordered Floer theory. We relate these two perspectives, by providing in the final chapter a novel proof of Greene et al.’s criterion using the graphical calculus, recently expanded by A. Kotelskiy, Watson and C. Zibrowius.