Cohomology is a basic and powerful tool that arises in many fields of geometry and topology. I will motivate this technique and demonstrate its use in some simple examples.
The inverse scattering transform (IST) is used to solve the Cauchy problem for integrable nonlinear partial differential equations on the line. Matrix Riemann-Hilbert problems (RHPs) are a key component in the IST. Historically, RHPs have made the IST amenable to rigorous asymptotic analysis with the Deift-Zhou method of nonlinear steepest descent. More recently, techniques for oscillatory singular integral equations have been employed to solve RHPs numerically and compute the IST. Importantly, nonlinear dispersive evolution equations can be solved numerically without any need for time-stepping. Errors are seen to be uniformly small for arbitrarily large times. Combining this approach with the so-called dressing method allows for the computation of a wide class of non-decaying solutions.
The choices that scientists make early in their careers will impact them for a lifetime. I will use the experiences of scientists who have had great careers to identify universal distinguishing traits of good career choices that can guild decisions in education, choice of profession, and job opportunities to increase your chances of having a great career with long-term sustained accomplishments.
I ran a student internship program at Los Alamos National Laboratory for over 20 years. Recently, I have been tracking the careers past students and realized that the scientists with great careers weren't necessarily the top students, and that some of the most brilliant students now had some of the most oh-hum careers.
I will describe how the choices made by the scientists with great careers were based on following their passion, building their talents into a strength supporting their profession, and how they identified a supportive engaging work environment. I will describe some simple guidelines that can
help guide your choices, in school and in picking the right job that can lead to a rewarding career and more meaningful life.
The topic is important because, so far as I can tell, life is not a trial run - we have one shot to get it right. The choices you are making right now to planning your career will impact your for a lifetime.
Please join us for an engaging discussion on how to make the choices that
will lead to a great career.
