Mahnav Petersen
I am a first-year PhD student at MIT studying pure math. Previously, I was an undergraduate at UChicago.
Email: mp51 {at} mit.edu
Here is my CV (updated July 2025).
In Summer 2024, I participated in Georgia Tech's math REU, in the dispersive PDE group under the mentorship of Prof. Gong Chen. Our work resulted in a poster, which is intended to be nontechnical and accessible to undergraduate math majors.
Expository Papers:
Applications of Topological Dynamics to Combinatorics. 2025. Description: This is a short paper that proves the Furstenberg-Weiss theorem in topological dynamics and then uses this theorem to prove a few major results in combinatorics, including van der Waerden's theorem. It is intended for a reader familiar with point-set topology and a little group theory. It can be found here.
Embedding and Immersing Smooth Manifolds in Euclidean Space. 2024. Description: This is a short paper that proves (certain versions of) the Whitney embedding theorem and Whitney immersion theorem. It is intended for a reader who knows the basics of smooth manifold theory and a little measure theory. It can be found here.
An Introduction to Measure-theoretic Probability. 2023. Description: This paper is a rigorous development of several standard topics in measure-theoretic probability and is intended for a reader familiar with measure theory. It can be found here.
Classical Topics in Measure-theoretic Probability. 2023. Description: This is a shorter version of the preceding paper ("An Introduction to Measure-theoretic Probability"). It can be found here.
An Introduction to Fourier Series and their Applications. 2022. Description: This is an elementary introduction to Fourier series and some of their applications in math. It is intended for a reader who has just learned introductory real analysis. It can be found here.