Relevant Thesis-Based 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.
ADVICE AND INSIGHTS FROM UBC FACULTY ON REACHING OUT TO SUPERVISORS
These videos contain some general advice from faculty across UBC on finding and reaching out to a potential thesis supervisor.
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.
Bar-Natan observed that the knots 5₁ and 10₁₃₂ have identical Jones polynomial, while recent work of Baldwin, Hu and Sivek shows that the cinquefoil 5₁ is detected by Khovanov homology. These two knots are related by a Jones-cosmetic tangle replacement, under which the (3,-2) pretzel tangle found within 10₁₃₂ is replaced by a rational tangle. The theory of immersed curves developed by Kotelskiy, Watson and Zibrowius provides us with a combinatorial means of computing reduced Bar-Natan homology, via which we investigate the existence and uniqueness of Jones-cosmetic pairs formed of a two-bridge knot and a rational tangle closure of the (3,-2) pretzel tangle with determinant less than or equal to 5. Using the observation that Jones polynomials with different spans are different, we prove that there does not exist a Jones-cosmetic pair associated with the (3,-2) pretzel tangle involving the unknot or the trefoil. Moreover, we prove that 5₁ and 10₁₃₂form the unique Jones-cosmetic pair associated with the (3,-2) pretzel tangle with determinant equal to 5.
The purpose of this thesis is to explore the properties of closed curves which are length-minimizing in a nontrivial homotopy class of a compact Riemannian manifold with boundary. This project was inspired by a question asked by Professor Liam Watson about the existence of length-minimizing curves on a torus with finitely many disks removed, and whether these curves leave the boundary components tangentially. In our research, we extend the question to compact smooth Riemannian manifolds with smooth boundary. We first discuss some preliminary results to determine an appropriate class of curves to minimize over. We then explore the properties of the length and energy functionals, showing that a minimizer of the energy is also a minimizer of the length. We directly minimize the energy functional to show the existence of a length-minimizing curve in any nontrivial homotopy class of a compact Riemannian manifold with boundary. Finally, we address the regularity of length-minimizing curves, showing that they are piecewise geodesics (possibly with infinitely many pieces).
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.