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 where I teach both struggling students and advanced honors students. In research, I enjoy introducing students to the more creative and abstract ideas of mathematics that get left out of the classroom.Project ideas
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 every mathematician, and you can read all about it on Wikipedia or many books. 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 is the basis of most statistics and modern AI. 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.
Banach Tarski Paradox
Banach and Tarski devised an algorithm in 1924 to essentially copy a sphere without adding any new points. This leads to a whole host of other paradoxical ideas in math and logic. It would be a very interesting project to read the proof of the original theorem, explore some of its consequences, and the modern perspective that "fixes" the issue using measure theory, then use modern tools to address the paradox and all its variations.