Splash Biography

Much of contemporary mathematics is indebted to techniques developed in the 1940s affectionately dubbed "abstract nonsense" by their practitioners, due to their great generality. However, despite the esoteric terminology and notation, these subjects such as category theory and homological algebra are extremely affable and gorgeous when one takes the time to befriend them; and have lead to the development of entirely new fields such as homotopy theory. In this course we will introduce the basic notions of categories, functors, and natural transformations through elementary examples; culminating with a proof of Yoneda's Lemma. The content will be based off of previous experiences teaching this subject at the high school level.

Particle physics is a rich, but sometimes intimidating, branch of physics. You may have heard about a very common pictorial representation of particle interactions: Feynman diagrams. I aim to teach the following: 1. what is a quantum field 2. how a lagrangian describes a given quantum system 3. the Feynman ABCs 4. how to calculate Feynman amplitudes in the ABC theory. By the end, you will know how to evaluate and more importantly have an understanding behind equations like $$\int \int \int (-iq)^3 \frac{i}{q_4^2-m_B^2c^2} \frac{i}{q_5^2-m_A^2c^2} \frac{i}{q_6^2-m_C^2c^2} \cdot (2\pi)^4 \delta^4 (P_1 -q_4-P_3) (2\pi)^4 \delta^4 (q_4 -q_6-q_5) (2\pi)^4 \delta^4 (q_5 + q_6 -P_2) \cdot \frac{d^4 q_4}{(2\pi)^4}\frac{d^4 q_5}{(2\pi)^4}\frac{d^4 q_6}{(2\pi)^4}$$