Relevant Degree Programs
Mathematics, almost any field
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
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.
The goal of this thesis is to understand the topology of representation varieties. To be more precise, let G be a complex reductive linear algebraic group and let K ⊂ G be a maximal compact subgroup. Given a finitely generated nilpotent group Γ, we consider the representation spaces Hom(Γ,G) and Hom(Γ,K) endowed with the compact-open topology. Our main result shows that there is a strong deformation retraction of Hom(Γ,G) onto Hom(Γ,K). We also obtain a strong deformation retraction of the geometric invariant theory quotient Hom(Γ,G)//G onto the ordinary quotient Hom(Γ,K)/K. Using these deformations, we then describe the topology of these spaces.
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 construct a convenient presentation of weak n-categories for 0
We prove a power saving over the local bound for the L∞ norm of uniformly non-tempered Hecke-Maass forms on arithmetic hyperbolic manifolds of dimension 4and 5. We use accidental isomorphism and use the Hecke theory of the correspond-ing groups to show that if the automorphic form is non-tempered at positive densityof finite places then the Hecke eigenvalues are large; amplifying the saving comingfrom the non temperedness we get a power saving.
The purpose of this thesis is to construct a codimension 1 cocompact Sp₂gℤ-equivariant strong deformation retract Wg of Siegel's upper half space hg . This yields a partial contribution towards the problem of constructing a strong spine for the real linear symplectic group Sp₂gℝ.
Let F be a number field, G = PGL(2,F_∞), and K be a maximal compact subgroup of G. We eliminate the possibility of escape of mass for measures associated to Hecke-Maaß cusp forms on Hilbert modular varieties, and more generally on congruence locally symmetric spaces covered by G/K, hence enabling its application to the non-compact case of the Arithmetic Quantum Unique Ergodicity Conjecture. This thesis generalizes work by Soundararajan in 2010 eliminating escape of mass for congruence surfaces, including the classical modular surface SL(2,Z)\H², and follows his approach closely.First, we define M, a congruence locally symmetric space covered by G/K, and articulate the details of its structure. Then we define Hecke-Maass cusp forms and provide their Whittaker expansion along with identities regarding the Whittaker coefficients. Utilizing these identities, we introduce mock P-Hecke multiplicative functions and bound a key related growth measure following Soundararajan’s paper. Finally, amassing our results, we eliminate the possibility of escape of mass for Hecke-Maass cusp forms on M.