TITLE: On Diophantine equations
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