Wyatt K
- Research Program Mentor
PhD candidate at University of Illinois at Urbana Champaign (UIUC)
Expertise
Mathematics, Physics, Mathematical Physics, Coding, Data Analysis. My area of expertise in mathematics is symmetry, and generalized symmetries that arise in mathematical physics.
Bio
Hi! I'm Wyatt. When I'm not at work, you'll find me at the dog park, playing the trumpet, or doing amateur home repairs. I'm working on a PhD at the University of Illinois on higher symmetries in mathematical physics. I'm also adjunct faculty at Parkland college. I enjoy introducing students to the more creative side of mathematics that gets left out of the classroom.Project ideas
Why is there no quintic formula?
You've probably heard of the quadratic formula. Did you know there is a formula for the roots of degree 3 and degree 4 polynomials too? But not degree 5! The reason is that polynomial roots have certain symmetries that allow you to find the formulas for their roots. It turns out that the symmetry group of degree 5 polynomials has properties to ensure that a formula is impossible, and you can actually prove it! This is a good place to start some research into how symmetry groups can help you find solutions to really complicated problems!
Algebra of groupoids
Groupoids are a slight generalization of groups and they capture symmetries of most geometric objects. The algebraic theory of groups is known by just about every mathematician, and you can read all about it on Wikipedia. The algebraic theory of groupoids is known by very few. You could read about the theory of groups and see if you can find and prove analogous algebraic facts for groupoids.
Facial Recognition
Linear algebra is a very powerful branch of mathematics which computers are very good at. To a computer, a face is just a very big matrix of pixels, and you can compare faces by essentially turning that face into a vector and comparing the vectors in a huge-dimensional space. If you are good at coding, you can tweak this basic idea to write a pretty good facial recognition algorithm.
Topological Data Analysis
Did you know data has a "shape" that can be formally analyzed? Instead of just throwing more and more AI at our data issues, we can analyze deeper structures in data using topology. You could help me develop some formal tools and procedures for this type of analysis, and aplly it to your favorite datasets.