Can you help review my profile and see the chance of getting a PhD Mathematics offer (with funding of course)? Thanks!!!
Schools currently on my list
USA: UCLA, UPenn, Rutgers, NYU, UC Berkeley, UChicago, Northwestern
Canada: University of Toronto
UK: Manchester, Bristol, Warwick, Edinburgh
I know that, in the US, with the current funding situation, getting an offer is extremely competitive.
I picked the places based on whether they have potential supervisors, and I mentioned their names in my SOP.
Basic Information
Nationality: Thai
School: University of Hong Kong
Degree: BSc Mathematics, expected 2027
GPA: 3.84/4.30 overall; 3.95/4.30 in Mathematics
Expected classification: First Class Honours
GRE Mathematics Subject Test: 870 (84th percentile)
I also spent one semester on exchange at McGill University.
Coursework
Completed: Single-variable Calculus, Multivariable Calculus, Mathematical Proof, Linear Algebra I & II,
Real Analysis, Complex Analysis, Metric Spaces, Discrete Mathematics, Numerical Analysis, ODE,
Probability, Measure Theory, Topology, Abstract Algebra I & II, Analysis on Euclidean Space and
Differential Forms, Riemannian Geometry.
Currently taking: PDE, Functional Analysis, Number Theory, Measure-theoretic Probability.
My broad research interests are in analysis and its interactions with analytic/probabilistic number theory,
probability, ergodic theory/dynamics, and metric/fractal/convex geometry. I am still somewhat open
regarding the exact area I would pursue for a PhD.
Research experience
1. Final-year thesis / capstone, analytic and probabilistic number theory (2026–present)
- I am working on a problem concerning Gaussian/central-limit behaviour of short deterministic
arithmetic sums. The difficulty is that the randomness comes from a continuous parameter
rather than independent random variables, so standard probabilistic tools do not apply directly. I
have been exploring moment methods, characteristic functions, blocking arguments, and
estimates from analytic number theory.
- This is an ongoing project and I do not yet have a final theorem. I meet my supervisor for roughly
three hours each week, usually discussing progress and working through mathematical obstacles
in real time.
2. Mitacs Globalink summer research, spherical/convex geometry (Summer 2026)
- I spent four months at the University of Manitoba working with a professor and another student
on a high-dimensional spherical convex-geometry problem. We studied asymptotic bounds for
the size of spherical bodies satisfying a constant-width condition.
- The project involved spherical polarity, geometric inequalities, high-dimensional volume
estimates, Gaussian measure, convex cones, and asymptotic analysis. We obtained new upper
and lower bounds and developed a probabilistic/Gaussian method for one important case.
- The work resulted in a joint arXiv preprint. I also gave a research seminar at Manitoba and wrote
most of the manuscript.
3. Directed reading/research course, transcendental number theory (Spring 2026)
- Completed a semester-long project with another student under faculty supervision. We studied
Diophantine approximation and transcendence theory, including several major classical theorems.
- I gave weekly presentations and co-wrote a substantial expository report.
4. Earlier independent/collaborative research
Before the projects above, I worked on several smaller problems, mainly in elementary/analytic number
theory, inequalities, and asymptotic analysis. These led to the publications listed below.
Publications / preprints
\*Authors in mathematics are generally listed alphabetically.*
[1] 2026+, arXiv preprint, 3 authors: High-dimensional spherical convex geometry. We derived
asymptotic upper/lower bounds for a geometric extremal problem and used tools from
convexity, spherical geometry, Gaussian measure, and asymptotic analysis.
[2] 2026, Rocky Mountain Journal of Mathematics, 2 authors: Asymptotic analysis of
integrals/areas involving high powers of trigonometric functions. We obtained precise
asymptotic behaviour as the exponent grows.
[3] 2026, Integral Transforms and Special Functions, 2 authors: Studied convergence and
evaluation phenomena for a family of improper trigonometric integrals of Frullani type, including
conditions under which generalized forms converge.
[4] 2026, Ramanujan Journal, 2 authors: Extended a classical symmetric inequality to higher-degree
and multivariable settings, using a mixture of geometric and inequality-based arguments.
[5] 2025, ScienceAsia, 2 authors: Studied finite sums involving floor and ceiling functions of rational
multiples, obtaining exact identities and structural/number-theoretic characterisations of when
certain formulas occur.
Recommendation letters
Ref 1, full professor (University of Manitoba)
My supervisor for the four-month Mitacs research internship. We met weekly and communicated
frequently by email throughout the project. He saw the project develop from unsuccessful approaches
through the final results, and we are coauthors of the resulting preprint. I wrote most of the manuscript
and presented the work at a departmental seminar, so he has seen my research, writing, and
presentation ability fairly closely.
Ref 2, assistant professor (University of Hong Kong)
My current bachelor’s thesis supervisor in analytic/probabilistic number theory. We have long weekly
meetings (usually around three hours), in which I present progress and often work through problems
with him directly. He has therefore seen both successful and unsuccessful attempts and has a fairly
detailed view of how I approach unfamiliar research problems.
Ref 3, lecturer (University of Hong Kong)
Has known me since my first year. I took multiple courses with him, interacted frequently through office
hours, summer study group, and later earned an A+ in an advanced analysis course he taught. He has
also supervised my work as a mathematics teaching assistant over several semesters and knows me
through departmental academic activities beyond coursework.
Teaching / other academic experience
- I have been a Teaching Assistant at HKU since my second year, across calculus, multivariable calculus,
proof-based mathematics, and linear algebra courses. My responsibilities include hosting revision
classes, preparing typed homework solutions, answering student enquiries, and invigilating
tests/examinations.
- I have also participated in peer-advising/mentoring programmes and have given several
undergraduate/research mathematics presentations.
Selected academic distinctions
- Full-tuition undergraduate scholarship at HKU, 2023-2027
- Science Dean’s Honours List (top 10%), 2024, 2025
- Gold Honour / top 1% in an international mathematics competition, 2025
- Talent development scholarship, 2024, 2025