Title: Taxicabs and Sums of Two Cubes: An Excursion in Mathematics

Speaker: Joseph H. Silverman (Brown University)

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 any numbers that can be written like this in two (or more) different ways? This elementary question will lead us into a beautiful area of mathematics where number theory, geometry, algebra, and calculus interact in surprising ways. The talk will be accessible to undergraduates at all levels.

Speaker: Gideon Zamba (U. Iowa)

Title: Data-Driven Sciences: Another Way to Bring Math to the World and the World to Math

Abstract: Applied mathematics is a field of constant adaptability to the world’s contingencies. Such adaptability requires a solid training and understanding of theoretical and pure mathematical thinking—as the activity of applied thinking is vitally connected with research in pure mathematics. One such applied mathematical field is the field of statistics. As the world continues to rely more on data for decision making, statistics and associated data-driven fields have gained increased recognition. The purpose of this talk is to educate the audience about the field of statistics, about statistical involvements, and further provide examples of settings where statistical theory finds an application and where real world application calls for a new statistical development. The presentation further elaborates on Biostatistics and provides some general advice about mathematical and computational skills needed for a successful graduate degree in Biostatistics or Statistics.

The presentation is semi-technical.

TITLE: On Diophantine equations

ABSTRACT:

A Diophantine equation is an equation of the form F(X_1, X_2, … , X_m) = c (with a fixed c in Z) for which we look for the solutions (x_1, x_2, … , x_m) in Z^m verifying F(x_1, x_2, … , x_m) = c. The most famous result is probably the solution of Fermat’s last theorem X^n + Y^n = Z^n found by Andrew Wiles using so-called elliptic curves. A small survey of a few results will be given and the notion of elliptic curve will be introduced. The lecture is accessible to anyone, most particularly to undergraduates.

Speaker: Asaf Hadari (UH Mānoa)

Title: Hilbert’s third problem – how to cut and paste using linear algebra

Abstract: In the year 1900 the mathematician David Hilbert famously gave a list of 21 problems that he felt were the most important challenges facing the mathematical community of the day.

The third problem, though stated differently, essentially asked whether it was necessary to use calculus to do basic geometry in three dimensions. For instance, is there a geometric way to calculate the volume of a pyramid?

This was the first of his problems that was answered, using a neat idea from linear algebra. I’ll show you how, and discuss some of the neat mathematics surrounding this problem.

Speaker: Chris Nowlin (NSA)

Title: Mathematics at NSA

Abstract: We will discuss career opportunities for mathematicians at the National Security Agency. The speaker will share reflections on his 5-year career, including the application process, the types of problems NSA mathematicians work on, and some of the good and the bad associated with working for NSA. Questions from the audience are encouraged.

Title: Wave driven inundation for reef fringed atolls

Speaker: Prof. Janet M. Becker, Department of Geology and Geophysics

Abstract: As sea level rises, the threat of wave driven inundation for low lying atolls is anticipated to increase. Wave driven inundation results from three dynamically distinct components: sea and swell energy, breaking wave setup, and low frequency (infragravity) energy. Here, results from field experiments in Ipan, Guam and Majuro and Roi-Namur, RMI are presented that demonstrate the importance of low frequency energy on fringing reefs. The observations are described in terms of linear and nonlinear dynamics. Projections of wave driven inundation that include all components for Roi-Namur under future sea level scenarios are presented.

Title: A brief overview of topological data analysis