My name is Abraham and I am studying a Bachelor of Science (Advanced Mathematics) at the University of Sydney. I will have completed my third year after this semester finishes, and I am going into honours next year for my final year of undergraduate studies. For primary and secondary education, I only attended kindergarten and was home-schooled from Grade One until university, attending Macquarie University for my first year with the intention of doing a chemistry major before transferring to the University of Sydney to study a mathematics and physics double major, finally dropping the physics major and just pursuing mathematics alone. For a long time, I disliked mathematics. The introduction to calculus was probably the first thing in mathematics that excited me, but my view on mathematics was still limited to thinking it a dull secondary tool used in the sciences, which I enjoyed. First year changed my opinion when I saw theorems being proved rigorously and being used to prove other things, and I have been in love with mathematics ever since. Mathematics aside, I enjoy reading books and viewing documentaries on military history, eating food, watching anime, and playing table tennis, which I have done so competitively since the age of eight. I also have an extreme passion for following and watching cricket. My family consists of my parents, sister and brother-in-law, and has supported my pursuit in mathematics. I am excited to participate in the AMSI Vacation Research program.
The Dirichlet-to-Neumann operator
The aim of this project is to establish a mathematical definition of the Dirichlet-to-Neumann operator and to investigate its fundamental properties. Using variational methods, we study the relationship with other differential operators.