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Fig.1 A plane wave incident on a hedgehog and the associated scattered wave. The dashed line indicates the artificial boundary we’d put around Hedgie while computing the scattered wave. δ − ǫ: How does your research relate to what is taught in undergraduate courses here? NN: I admire the undergraduate program broadly for instilling a sense of mathematical fearlessness. On the many occasions when I’m stuck on a research problem, I think to myself - ‘if this were a homework problem, and I were a McGill undergrad, when would I quit?’ A lot of my work requires functional analysis and PDE (not just separation of variables!). You see some of the analytical tools involved in courses like Math 564/565. At an advanced level, the study of PDE merges with analysis (Math 575/580/581). In addition, courses in numerical analysis or matrix computation (Math 317/387, 327/397, 578/579) contain many of the key concepts–stability, accuracy and convergence of numerical algorithms- which I use. Increasingly, algorithms for PDE incorporate tools from differential geometry, which is another field you may see during your studies here. I’m not sure if students in Mathematics take courses in the Physics department. In an ideal world, budding mathematicians interested in the mathematics of scattering theory would see classical mechanics, electrodynamics and quantum mechanics. δ − ǫ: Why did you choose to become a mathematician? What kind of a life is it? NN: Becoming a mathematician didn’t really involve a choice. I’m very fortunate to be able to do what I love, and would be miserable doing anything else. I started off as a student of Physics, realized I loved the mathematical aspects of my training most, and ended up pursuing a career in mathematics. Physics has big
The δelta-ǫpsilon
Interview with Professor Nilima Nigam problems, which filter into our collective consciousness - this decade, quantitatively inclined dreamers want to work in String Theory. A millennium ago, High Energy Physics and Cosmology captured my imagination. By the time I got the necessary educational background to begin to understand the science behind these areas, I realized mathematics was my deeper passion. It’s a great life. I’m fortunate enough to enjoy the various aspects of my chosen careerdoing research, teaching, and interacting with other mathematicians and scientists. Some may favour one part of this life, and regard the other bits as distractions. I’m energized by mathematics, and by the belief that fun mathematical questions can be found everywhere. This makes teaching and interacting with people part of the larger search for interesting mathematical questions and their resolution - any given lecture, a student could ask me something thoughtprovoking. δ − ǫ: Are there any particular open problems you’d like to see the solutions to? NN: There are several open and rich questions in mathematics, and several technical questions in my field of interest I’d like to see resolved. However, a particularly challenging mathematical question concerns the existence and regularity properties of solutions of the Navier-Stokes equations in R3 . This system of partial differential equations governs the motion of fluids; the study of their solutions will require huge advances in the analysis of PDE. The question evades standard methods of attack, and a successful approach will likely be both surprising, and intimately connected to many other branches of mathematics. The problem was recently classified as one of the Millennium problems by the Clay Institute; the precise problem statement due to Charles Fefferman is available at http://www.claymath.org/millennium/NavierStokes-Equations/navierstokes.pdf. δ − ǫ: What major mathematical event (beyond your own work) do you remember most vividly? Alternatively, what such event had the biggest impact on your life as a mathematician? NN: This one’s tricky... I cannot think of a single formative experience. Rather, many chance encounters with mathematicians I admire have impacted my career. Reading about the lives of famous mathematicians and their work habits has always inspired me.
McGill Mathematics Magazine