#### Date of Submission

Spring 2020

#### Academic Program

Mathematics

#### Project Advisor 1

Steven Simon

#### Abstract/Artist's Statement

The Centerpoint Theorem states that for any set $S$ of points in $\mathbb{R}^d$, there exists a point $c$ such that any hyperplane goes through that point divides the set. For any half-space containing the point $c$, the amount of points in that half-space is no bigger than $\frac{1}{d+1}$ of the whole set. This can be related to how close can any hyperplane containing the point $c$ comes to equipartitioning for a given shape $S$. For a function from unit circle to real number, it has a Fourier interpretation. Using Fourier analysis on the Torus, I will try to find a multi centerpoint theorem for many points in the plane such that any hyperplanes go through those points are close to equipartitioning a given shape.

#### Open Access Agreement

Open Access

#### Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

#### Recommended Citation

Chen, Yan, "A Multi Centerpoint Theorem via Fourier analysis on the Torus" (2020). *Senior Projects Spring 2020*. 327.

https://digitalcommons.bard.edu/senproj_s2020/327

This work is protected by a Creative Commons license. Any use not permitted under that license is prohibited.