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Curriculum Vitae: CV (Last Updated: August 25, 2025)
Master's Thesis: Progress in Projection Theory
Email: paigeb@mit.edu

About Me

My name is Paige Bright and I use she/her pronouns. I completed my undergraduate studies at MIT majoring in Course 18: Mathematics in Spring 2024, and recently completed my masters student at UBC studying mathematics under Izabella Łaba, Pablo Shmerkin, and Josh Zahl. I am now a graduate student at MIT pursing my Ph.D in Mathematics under Larry Guth. I'm interested in analysis, and more specifically, harmonic analysis, projection theory, and geometric measure theory.

In my masters thesis, entitled "Progress in Projection Theory and other dimensional developments," I give an introduction into the field of projection theory through the lens of incidence and fractal geometry. In this thesis, I give surveys on three major topics in this area, including orthogonal projections, Furstenberg sets, and radial projections, motivating said topics from discrete/incidence theoretic analogues. Using these tools, I discuss two problems that can utilize tools from, and motivate conjectures in, projection theory, namely Beck-type theorems for lines and a Falconer-type distance problem for dot products, based on joint work with Marshall and Marshall-Senger respectively (see below). It is my hope that this thesis may be a helpful resource both for those familiar with the area, and for those who are interested in learning more about the topic.

As an undergraduate, I conducted research under graduate students of Larry Guth, including Yuqiu Fu, Shengwen Gan, Alex Ortiz, and Dima Zakharov. Within mathematics, I am interested in how problems from discrete geometry generalize to the continuum setting using tools such as Hausdorff dimension and Fourier analysis (and vice versa). I am also deeply passionate about education, writing, communication, and collaboration.

My Erdős Number is 3.

For more information regarding the mathematics coursework I have taken or the projects I have been working on, please see the links at the top of the page.

click on the titles to see short explanations

Publications and Preprints

Geometric Measure Theory and Harmonic Analysis
  1. A Continuum Beck-type Theorem for Hyperplanes
  2. Progress in Projection Theory and other dimensional developments
  3. Spread Furstenberg Sets, with Manik Dhar
  4. Pinned Dot Product Set Estimates, with Caleb Marshall and Steven Senger
  5. A continuum Erdős-Beck theorem, with Caleb Marshall
  6. Radial projections in \(\mathbb{R}^n\) revisited, with Yuqiu Fu and Kevin Ren [arXiv:2406.09707]
  7. A study guide to "Kaufman and Falconer estimates for radial projections", with Ryan Bushling, Caleb Marshall, and Alex Ortiz [arXiv:2402.11847]
  8. Exceptional set estimates in finite fields, with Shengwen Gan. Annales Fennici Mathematici, 50(2), 467-481, 2025.
  9. Exceptional set estimates for radial projections in \(\mathbb{R}^n\), with Shengwen Gan. Annales Fennici Mathematici, 49(2), 631-661, 2024.
Combinatorics
  1. On a radial projection conjecture in \(\mathbb{F}_q^d\), with Ben Lund and Thang Pham [arXiv:2311.05127]
  2. Generalized point confiruations in \(\mathbb{F}_q^d\), with X. Fang, B. Heritage, A. Iosevich, T. Jiang, H. Parshall, M. Sun. Finite Fields and Their Applications, 99, 102472, 2024.
  3. Improved bounds for embedding certain configurations in subsets of vector spaces over finite fields, with X. Fang, B. Heritage, A. Iosevich, M. Sun. Bulletin of the Hellenic Mathematical Society, 68:10-30, 2024.
Mathematics Education and Pedagogy
  1. "18.S063: Matrix Calculus" Lecture Notes, taught by Profs. Alan Edelman and Steven G. Johnson
  2. "18.S190: Introduction to Metric Spaces", taught IAP 2022 and 2023
  3. "Communication is the Whole Game", Chalk Radio interview with Prof. Haynes Miller [Podcast]
  4. "18.100A: Real Analysis" Lecture Notes, taught by Prof. Casey Rodriguez [OCW Course]
  5. "When Students Create OER...", with Ashay Athalye, Sarah Hansen, and Curt Newton [YouTube Video]

Conferences, Presentations, and Activities

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Last updated: October 16, 2025