## Events

### Math Across the Cannon

Our speaker this year is Joseph Silverman from Brown University.

Math Across the Cannon

Carleton College and St. Olaf College

Speaker:

Joseph H. Silverman

Professor of Mathematics

Brown University

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Public Lecture:

Title: Taxicabs and Sums of Two Cubes - An Excursion in Number Theory

Location: Carleton College, Weitz Cinema from 7:30-8:30 p.m.

Abstract: Some numbers, such as

9 = 1^3 + 2^3 and 370 =3^3 + 7^3,

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.)

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Undergraduate Lecture for Mathematics Students:

Title: Arithmetic Dynamics: A Modern Meld of Number Theory and Dynamical Systems

Location: St. Olaf College, Regents Hall of Natural Science 410 from 3:30-4:30 p.m.

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?

Sponsored by Mathematics. Contact: Sue Jandro, x4360