Brett Kolesnik
Why did you decide to pursue a graduate degree?
The world of Mathematics is a limitless source of intrigue and challenge, full of intricate and elegant ideas and tantalising questions. To pursue research in Mathematics is to explore one's creativity, build technical skill, and to search for insight. I chose to pursue a graduate degree in Mathematics so that, in my own way, I can contribute to and take part in this remarkable field of Science.
Why did you decide to study at UBC?
The Mathematics Department at UBC is well known for its outstanding research in Probability Theory. I decided to pursue graduate studies at UBC because of its very active community in this area of Mathematics, and most of all, my interest in the research of my supervisor.
What was the best surprise about UBC or life in Vancouver?
Perhaps the greatest surprise thus far was the opportunity to visit the École Normale Supérieure in Lyon, France March—April 2013, and I thank UBC for partially funding this research experience. For me, some of the best surprises are moments of inspiration or insight, when, for instance, I am beginning to understand an exciting idea.
What advice do you have for new graduate students?
I am confident that most often you will find life as a graduate student to be highly satisfying and purposeful; but sometimes you may become overwhelmed, or lose sight of your goals. Reserve some time now and again when you can shut out all distractions and reflect on your path so far, what you need to do, and where you want to go. If you become tired or burnt out, volunteer your time with young students, and remind yourself of what learning is all about.
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Learn more about Brett's research
I am interested in Probability Theory, and in particular, the scaling limits of random discrete structures. In 1827, the botanist Robert Brown first observed Brownian motion. Since then, Brownian motion has been described and analysed mathematically. Indeed, it is a fundamental object of modern Probability. Brownian motion arises as the scaling limit of many random processes, such as the simple random walk. In this sense, it is universal. Picture Brownian motion as a random continuous trajectory indexed by time. Another universal object has been introduced recently - the Brownian map. This object is a random metric space involving a Brownian motion path, which, instead of being indexed by time, is indexed by another random object, called the continuum random tree. Imagine the Brownian map as a surface, homeomorphic to the surface of a ball, and comprised of many jagged mountains, packed extremely tightly, so that as viewed from a distance all you see is the tops of the mountains. On closer inspection, you find a dense network of valleys connecting the mountaintops to one another. The Brownian map arises as the scaling limit of random planar maps, and exhibits many fascinating mathematical properties. Moreover, since large random planar maps have applications to Theoretical Physics, it is possible that the study of the Brownian map could be relevant to other fields of research.
