Hi, I am Paige Bright. I am a rising senior at MIT. I am interested in math, specifically analysis and geometric measure theory. This is a simple webpage for hosting different URLs and whatnot of mine from projects to writing. Enjoy!
Blog: The Home Paige
Curriculum Vitae: CV (Last Updated: September 17, 2023)
Math Coursework Only: Listing
MITAdmissions: Working for MITAdmissions blogging! Blogs written are also put on The Home Paige.
Math Coursework I am currently enrolled in:
- 18.225: Graph Theory and Additive Combinatorics, taught by Prof. Yufei Zhao
- 18.675: Theory of Probability, taught by Prof. Konstantinos Kavvadias
- 18.745: Lie Groups and Lie Algebras I, taught by Prof. Ju-Lee Kim
- 18.905: Algebraic Topology I, taught by Prof. Paul Seidel
SMALL REU at Williams College: Studying point configurations over finite fields.
UROP: Undergraduate Research Opportunity. Extended my SPUR Project with Shengwen Gan and Larry Guth, continuing to explore exceptional set estimates and other such questions in metric geometry. Culminated in paper linked below.
Exceptional set estimates in finite fields
Then I participated in a new UROP project with Postdoc Marjorie Drake which will likely continue into Fall 2023.
UA: Undergraduate Assistant for 18.102: Introduction to Functional Analysis, taught by Richard Melrose.
PRIMES Circle: A high school mathematics enrichment program for underrepresented students. Will be meeting weekly with two high school students reading a purposefully chosen text and developoing a presentation and expository paper.
- 18.156: Differential Analysis II, taught by Prof. David Jerison
- Typing lecture noters for some lectures (to be uploaded here)
- Learning about Hardy spaces and BMO on my own using Elias Stein's "Harmonic Analysis".
- 18.158: Fourier Analysis to Analytic Number Theory, taught by Prof. Larry Guth
- 18.821: Project Lab in Mathematics, taught by Prof. Lisa Piccirillo
- Project 1: Exploring the relation between random walks and harmonic functions, solving the Discrete Dirichlet Problem using probability.
- Project 2: Exploring Young Tableau with linear algebraic conditions, with relations to combinatorics.
- 18.966: Geometry of Manifolds II, taught by Prof. Tobias Colding
Teaching 18.S190 (previously 18.S097): Introduction to Metric Spaces. Held TR9-10:30 in-person in 2-131. See IAP 2022 for more information on how the class was held last year and more general information.
This year, the module on applications to differential equations will be replaced with a module on completions of metric spaces (analogous to the completions of the rationals leading to the real numbers). This new module will discuss what the completion of a metric space is, and define L^p spaces, p-adic integers, and more.
DRP: Directed Reading Program in Course 18 over IAP. Reading the lecture notes from Larry Guth's 2017 topics class on Decoupling (notes transcribed by various students in the course), as well as Steven Krantz' "A Panorama of Harmonic Analysis" with Postdoc Marjorie Drake. Will ultimately create a presentation on some topic in this reading.
MIT Monologues: In the process of writing a piece for this year's performance on my experiences as a trans-person.
UROP: Continuing my UROP with Shengwen Gan and Larry Guth.
UA: Undergraduate for 18.101: Analysis and Manifolds, taught by Richard Melrose. Providing feedback on lecture notes, grading problemsets, and typesetting problemset solutions weekly for this class. I have also been holding weekly office hours and occassionally review sessions.
Associate Advising: Traditional Associate Advisor for Bill Minicozzi.
Steering Committee: Providing Monthly feedback on Associate Advising for the Office of the First Year.
18.100*: Mentoring for undergraduate real analysis courses.
USWIM: Mentoring for the Undergraduate Society for Women in Mathematics.
Dead Maths Society: More to come soon!(?)
- 18.112: Complex Analysis, taught by Prof. Roman Bezrukavnikov
Using this time to explore deRham theory on real and complex manifolds so I can better understand the algebraic topology/homology theory behind certain theorems in complex analysis. Reading Bott and Tu's book on this matter.
- 18.965: Geometry of Manifolds I, taught by Prof. Bill Minicozzi
- 18.994: Seminar in Geometry, taught by Prof. Qin Deng
- On minimal surfaces, using the textbook developed by Bill Minicozzi and Tobias Colding.
- Presented on Section 3.3 of do Carmo's text with Victor Luo, discussing the minimizing properties of Geodesics.
- Presented on the first variation formula for minimal surfaces, defining minimal surfaces as being a critical point of the volume functional, and showing that this implies the mean curvature must be zero everywhere on the minimal surface (in fact this is an equivalent relationship).
- Presented on Section 4.3-4.5.1 with Carlos on 1) Solving the Plateau problem and 2) harmonic maps.
- Final project: Studying the relationship and the proofs of Sobolev inequalities and the Isoperimetric inequality on minimal surfaces. Related to my project paper developed in my 2021 Summer UROP (see below). In particular, studying the equivalence of these inequalities on Riemannian manifolds embedded into Euclidean space.
SPUR: Summer Program for Undergraduate Research in Course 18, with Larry Guth and Shengwen Gan. Researching Marstrand's projection theorem and the high-low method.
Associate Advising: One of two associate advising captains this summer, developing materials with OFY: The Office of the First Year to prepare associate advisors for the upcoming school year.
18.100A: Real Analysis (on Rn) prior to this spring was not available on MIT OpenCourseWare (OCW), which I advocated for. Working with Dr. Casey Rodriguez and OCW, I typed lecture notes for the Fall 2020 course taught by Casey, recorded asynchronously. The material is now found on OCW, including notes, lecture videos, problemsets, and notes from some of the recitations. Both a link to the OCW site and a folder of my typed notes is included below.
Typed Notes (.zip)
Primes Circle: A high school mathematics enrichment program for underrepresented students. Met weekly with two high school students reading Thomas Sibley's "Thinking Geometrically: A Survey of Geometries". Guided the writing of a 15 page expository paper on triangles in spherical, hyperbolic, and single elliptic geometries.
- 18.157: Microlocal Analysis, taught by Prof. Richard Melrose
- 18.099: Independent Study with Prof. Richard Melrose
- To ask clarifying questions about Microlocal Analysis over the course of the semester.
- 18.118: Introduction to Chaotic Dynamics, taught by Prof. Semyon Dyatlov
- 18.952: Introduction to Differential Forms, taught by Prof. Victor Guillemin
18.S097: Introduction to Metric Space, developed and taught by me. Advocated for and created a bridge class between real analysis on Rn and real analysis on a general metric space to make the mathematics department more accessible.
Blog Post by Peter Chipman
DRP: Directed Reading Program in Course 18 over this IAP. Read the first chapter of John Conway's "A Course in Operator Theory", and created a presentation in Beamer with my partner Esha Bhatia and mentor Elena Kim. Learned quite a bit about the functional calculus as presented in Conway's "A Course in Functional Analysis".
18.100B Mentoring: Mentoring students weekly in 18.100A and 18.100B through the UMA mentoring program.
18.A09: Associate advising for 18.A09: Symmetry with Haynes Miller, advising eight first years.
UROP: Undergraduate Research Opportunities Program, with Larry Guth and Yuqiu Fu. Closely analyzed "A View from the Top" by Alex Iosevich, solved exercises and presented proofs. Wrote a clear and digestible expository paper proving a Sobolev inequality in 2-dimensions.
- 18.155: Differential Analysis, taught by Prof. Semyon Dyatlov
- 18.101: Analysis and Manifolds, taught by Prof. Richard Melrose
- 18.705: Commutative Algebra, taught by Prof. Wei Zhang
Started work with OCW for the first time, helping develop a online modulized version of 18.03: Differential Equations with Jennifer French.
- 18.702: Algebra II, taught by Prof. Michael Artin
- 18.102: Introduction to Functional Analysis, taught by Prof. Casey Rodriguez
- 18.901: Introduction to Topology, taught by Prof. George Lusztig
Tetrahedra UROP: Looked into finding the algebraic relations relating the six side lengths and the cosines of the
dihedral angles of a tetrahedron under Prof. Bjorn Poonen, as a volunteer.
18.S097: Grader for the 18.S097 Proof Writing Workshop developed by the UMA.
- 18.03: Differential Equations (ASE)
- 18.701: Algebra I, taught by Prof. Bjorn Poonen
- 18.100B: Real Analysis, taught by Prof. Tobias Colding
- 18.A06: What is a Number, taught by Prof. Haynes Miller
- A first year seminar on the construction of numbers, with numerous philosophical conversations on what objects should or shouldn't be considered numbers.
- Discussing Peano Axioms, Dedekind cuts, constructions of the real numbers, construction of the complex numbers, quarternions, surreal numbers, p-adic numbers, etc.
Before MIT, I attended Design Science Middle College High School (DSMCHS) in Fresno, California.
Here, I had the opportunity to study math problemsolving skills with Fresno Math Circle, which I heavily recommend to anyone in the area. If you have the ability to do so, I also recommend donating to their program as it gives the opportunity for many underpriviledged kids to learn mathematics skills.
While here, I also got to work with Fresno City College as an embedded tutor and drop-in tutor, tutoring from college algebra (precalculus) to linear algebra. In fact, at Fresno City College I graduated with my Associate's Degree in Mathematics for Transfer. This allowed me the opportunity to transfer over coursework listed below.
- Math 5A: Mathematical Analysis I (Differential Calculus)
- Math 5B: Mathematical Analysis II (Integral Calculus), taught by Travis McDonald
- Math 6: Mathematical Analysis III (Multivariable Calculus), taught by Matt Woods
- Math 7: Differential Equations, taught by Travis McDonald
- Math 26: Linear Algebra, taught by Matt Woods
Last updated: May 29, 2023