# Nic Fellini (Queen's University)

Date

Monday March 11, 20242:30 pm - 3:30 pm

Location

Jeffery Hall, Room 202## Number Theory Seminar

**Monday, March 11th, 2024**

**Time:** 2:30 p.m. **Place:** Jeffery Hall, Room 202

**Speaker:** Nic Fellini (Queen's University)

**Title:** Diophantine equations, linear recurrences, and p-adic analysis

**Abstract:** In some instances, problems from Diophantine equations can be translated into problems concerning linear recurrences. A question that arises through this connection is the following: If (u_n) is a sequence solving an r-th order linear recurrence relation with integer coefficients, what does the zero set {u_n = 0} "look" like? In a surprising twist, the only known solutions to this question are p-adic in nature. The goal for this talk is to give an example driven explanation of how we can translate problems from Diophantine equations to studying the sets {u_n = a} using p-adic analysis.