The afternoon lecture is intended to introduce Math majors (any anyone else who is curious) to the field of Arithmetic Dynamics.
Arithmetic Dynamics: A Modern Meld of Number Theory and Dynamical Systems
3:30 in RNS 410 at St. Olaf College
Abstract: Dynamics is the study of what happens when we take a function f(x) and repeatedly apply it to a real or complex number b. Number theory is the study of integers and rational numbers. The new field of “Arithmetic Dynamics” merges these venerable areas and asks what can happen when we repeatedly apply f(x) to an integer or rational number b. In this talk I will survey some known results and some outstanding conjectures in arithmetic dynamics, including a discussion of the following two motivating problems:
(1) How many starting rational numbers b come back to themselves when we repeatedly apply f(x)?
(2) If we repeatedly apply f(x) to a rational number b, when can we get infinitely many different integers?
In the evening lecture Prof. Silverman will introduce a broader audience to ideas from number theory and their connections to, well, all sorts of things.
Taxicabs and Sums of Two Cubes – An Excursion in Number Theory
7:30 in the Weitz Cinema at Carleton College
Abstract: Some numbers, such as 9 = 13 + 23 and 370 =33 + 73, can be written as a sum of two cubes. Are there numbers that can be written as a sum of two cubes in two (or more) essentially different ways? This elementary question will lead us into beautiful areas of mathematics where number theory, geometry, and algebra interact in surprising ways. And there will be taxis and internet security, too! (This talk uses only high school math and will be accessible to the general public.)