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. I'm 27. I spend a lot of my free time at the dog park or watching Youtube when I am not doing math or playing the trumpet. I'm working on my PhD at the university of Illinois in mathematics. As an undergraduate, I had very scattered interests, and I did a lot of degrees before finally deciding that what I really liked was mathematical reasoning. I love math because it feels like building something. Each new definition and theorem adds a little piece to the puzzle and at the end you have something beautiful.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 very deep, and it is because 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.