Undergrad research

I enjoy explaining mathematical ideas to general audiences and developing ideas for undergraduate research.

In Spring 2019, I was the faculty mentor of an undergraduate research project “Finite Reflection Groups and Related Topics”. I mentored three motivated undergraduates at UIUC. They spent six weeks reading and discussing about Lie groups and algebraic groups in a learning seminar. Then they worked on the following problem (and its variants): given a complex Lie group G of exceptional type with maximal torus T, determine when the natural surjection N_G(T) \to W(G,T)=N_G(T)/T (the latter being the Weyl group of G) has a group-theoretic section. This problem stemmed from my thesis research. My students were able to make progress by using computational softwares GAP and MAGMA.

In Spring 2021, I mentored another undergraduate research project “P-adic Numbers and Ultrametric Calculus” (virtual). In this project, four motivated undergraduates read Schikhof’s book “Ultrametric Calculus” under my guidance. Then they investigated properties of the Artin-Hasse exponential AH(x). In particular, they proved a combinatorial formula for a generalized form of the Artin-Hasse exponential. And they studied properties of AH(x) as an analytic function of on the open unit disk of C_p (the field of p-adic complex numbers) and gave a proof of the fact that AH(x) runs over the pth power roots of unity in C_p. The following is a draft version of their work.

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