Ben Williams
Research Interests
Relevant Thesis-Based Degree Programs
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Recruitment
The A1- and classical homotopy theory of algebraic groups, and their applications to algebra.
A strong background in algebra and (algebraic) topology, and a fondness for matrices.
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.
Supervision Enquiry
Great Supervisor Week Mentions
I am very grateful for all the support that you have extended to me during my time here at UBC. I deeply appreciate how you have been continuously encouraging and guiding me in the last two years, and also how you have always been so friendly and supportive of all of my efforts and struggles. Working under your supervision has been very enjoyable and I have learned and grown a lot.
Thanks Ben!
I am very grateful for all the support that you have extended to me during my time here at UBC. I deeply appreciate how you have been continuously encouraging and guiding me in the last two years, and also how you have always been so friendly and supportive of all of my efforts and struggles. Working under your supervision has been very enjoyable and I have learned and grown a lot. Thanks, Ben!
Graduate Student Supervision
Doctoral Student Supervision
Dissertations completed in 2010 or later are listed below. Please note that there is a 6-12 month delay to add the latest dissertations.
In this thesis, we establish decomposition theorems for topological Azumaya algebras, and topological Azumaya algebras with involutions of the first kind. Decomposition of topological Azumaya algebrasLet A be a topological Azumaya algebra of degree mn over a CW complex X. We prove that if m and n are relatively prime, m
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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.
In this thesis, we study a family of smooth varieties, whose members are denoted B_n^r(C), that bears a similar relationship to topological Azumaya algebras as the Grassmannians G_{n,r}(C) do to complex vector bundles. Specifically, we will show that the varieties B_n^r(C) form homotopical approximations to the classifying space BPGL_n(C). The varieties B_n^r(C) are obtained by first considering the variety of r-tuples of nxn complex matrices that generate the matrix algebra Mat_n(C), and then taking the quotient by an evidently free PGL_n(C)-action. The focus of this thesis is a computation of the singular cohomology groups of B_n^r(C) when n=2. We will show how these cohomological computations have applications in bounding the minimal number of generating sections of a topological Azumaya algebra over a paracompact space.
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