# Physics

There have been 4 completed talks and 4 topic suggestions tagged with physics.

## Completed Talks

### Cantor Set and Dynamical Systems

Delivered by James Bai on Friday March 31, 2017

The talk will be begin on the cosnstruction of the most commonly used tenary Cantor set. The talk will then talk about the common properties of Cantor set and methods of evaluating the size of the set. Then, depending on time, a brief introduction will be given on the dynamical system and chaos.

A summary of this talk is available here.

### Lie Groups and Special Relativity

Delivered by Mohamed El Mandouh on Friday March 24, 2017

### Brachistochrone

Delivered by Manas Joshi on Friday March 24, 2017

In the late 1600’s, Johann Bernoulli came out with a problem to challenge the world’s greatest mathematicians. The problem, known as the Brachistochrone, had garnered some interest and eventually was solved by Johann, Jacob Bernoulli and Newton amongst others. In this talk, we will analyze the solution given by Leonard Euler (and Lagrange), which started a new field of Calculus, called the Calculus of Variations. We will prove the most fundamental equation, Euler-Lagrange, and see how this can be applied to solve the Brachistochrone problem.

### How to Complicate Fourier Analysis

Delivered by Mohamed El Mandouh on Friday December 2, 2016

Fourier analysis was initially introduced as a way to study the thermodynamic heat equation. At its simplest, it is the study of how to represent functions as an infinite sum of sines and cosines. However, the evil mathematicians felt that Fourier analysis was too simple and decided to steal it from the hardworking physicists and expand on it. In addition, they decided to complicate it by introducing Harmonic analysis. So, what is the difference between Harmonic and Fourier analysis? We say that Harmonic analysis is the process of representing functions on a locally compact group G as a sum of the characters of the group, and Fourier analysis restricts this process to abelian groups.

In this talk I will introduce the Fourier series, the Fourier transform and how it applies to abelian groups. What about non-abelian groups, you might ask? The answer is Harmonic analysis! Finally, I will explain the role of Fourier transform in quantum mechanics, specifically how the Fourier transform interchanges position and momentum space.

## Talk Suggestions

### Fermi Estimation

Physicist Enrico Fermi was known for his impressive order-of-magnitude estimation. He was famously able to estimate the yield of the Trinity test atomic bomb to about a factor of two. Why is Fermi estimation so useful and accurate? What are the techniques to make better approximations? How can and do scientists, mathematicians, engineers, and others use Fermi estimation in their work?

Possible reference materials for this topic include

### Geometry and Billiards

The second topic studies which billiard table shapes are optimal.

Possible reference materials for this topic include