Ben Williams

Associate Professor

Research Classification

Research Interests

Algebraic topology
Motivic homotopy theory
A1 homotopy theory

Relevant Thesis-Based Degree Programs

Research Options

I am available and interested in collaborations (e.g. clusters, grants).
I am interested in working with undergraduate students on research projects.
 
 

Recruitment

Master's students
Doctoral students
Postdoctoral Fellows

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.

I am open to hosting Visiting International Research Students (non-degree, up to 12 months).

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Attend an information session

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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.

Great Supervisor Week Mentions

Each year graduate students are encouraged to give kudos to their supervisors through social media and our website as part of #GreatSupervisorWeek. Below are students who mentioned this supervisor since the initiative was started in 2017.

 

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!

Nina Arcila Maya (2019)

 

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!

Niny Arcila Maya (2019)

 

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.

Decomposition of topological Azumaya algebras in the stable range (2021)

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.

Classifying spaces for topological azumaya algebras (2020)

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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Membership Status

Member of G+PS
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Program Affiliations

Academic Unit(s)

 

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