We are thankful to be welcome on these lands in friendship. The lands we are situated on are covered by the Williams Treaties and are the traditional territory of the Mississaugas, a branch of the greater Anishinaabeg Nation, including Algonquin, Ojibway, Odawa and Pottawatomi. These lands remain home to many Indigenous nations and peoples.

We acknowledge this land out of respect for the Indigenous nations who have cared for Turtle Island, also called North America, from before the arrival of settler peoples until this day. Most importantly, we acknowledge that the history of these lands has been tainted by poor treatment and a lack of friendship with the First Nations who call them home.

This history is something we are all affected by because we are all treaty people in Canada. We all have a shared history to reflect on, and each of us is affected by this history in different ways. Our past defines our present, but if we move forward as friends and allies, then it does not have to define our future.

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September 23, 2015

Speaker: Dr. Lennaert van Veen, Ontario Tech University
Title: Towards numerical evidence for - or against - Yakhot's conjecture
Abstract: The Kardar-Parisi-Zhang model describes the growth of interfaces with a semilinear stochastic differential equation. In particular, it predicts the value of universal exponents for roughness and growth. These exponents have been found in a number of numerical and laboratory experiments, and several discrete statistical models for particle deposition have been shown to fall in the KPZ universality class. In 1981, Yakhot showed that the Kuramoto-Sivashinsky equation can be linked to the KPZ model by (somewhat murky) renormalization arguments. The high wave number fluctuations in the deterministic KS equation then play the role of stochastic forcing. The statement that the KS dynamics fall into the KPZ universality class is now referred to as "Yakhot's conjecture". In this joint work with Kazumasa Takeuchi, we try to produce accurate numerical data to either support or refute the conjecture. The first step is to consider the stochastically forced KS initial-boundary value problem in the limit of vanishing amplitude of the forcing.