Nic Fellini (Queen's University)
Date
Monday March 11, 20242:30 pm - 3:30 pm
Location
Jeffery Hall, Room 202Number 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.