Lethbridge Number Theory and Combinatorics Seminar: Yu-Ru Liu

Let ℤ be the ring of integers, and let 𝔽p[t] be the ring of polynomials in one variable defined over the finite field 𝔽p of p elements. Since the characteristic of ℤ is 0, while that of 𝔽p[t] is the positive prime number p, it is a striking theme in arithmetic that these two rings faithfully resemble each other. The study of the similarity and difference between ℤ and 𝔽p[t] lies in the field that relates number fields to function fields. In this talk, we will investigate some Diophantine problems in the settings of ℤ and 𝔽p[t], including Fermat's Last Theorem and Waring's problem.