University of Alberta

Existence of nonnegative weak solutions is shown for thin film approximations of the Muskat problem which include either gravity forces or capillary forces or both. The model describes the space-time evolution of the heights of the two fluid layers...

In this talk I am going to describe a measure valued stochastic process called Super Brownian Motion(SBM) and how one can obtain certain conditional distributions of this process via X-harmonic functions. I will show an explicit construction of a...

Spatially localized structures arise frequently in nature. Examples include localized buckling, spot-like structures in optics and in reaction-diffusion models, vortices in fluid dynamics, as well as localized oscillations known as oscillons. In all...

We discuss how the derived category of a smooth algebraic stack of finite type changes as one removes certain types of closed substacks. As an application, we show how wall-crossing in moduli of stable sheaves and Bridgeland stable objects yields...

One version of homological mirror symmetry relates the algebraic geometry of certain varieties to the symplectic topology of a Lefschetz pencil. Extracting symplectic (i.e. Floer theoretic) invariants from these fibrations is quite difficult, even in...

We consider the problem whether small perturbations of integable mechanical systems can have very large effects. It is known that in many cases, the effects of the perturbations average out, but there are exceptional cases (resonances) where the...

It is well-known that there exist many problems in numerical computation for three-dimensional nonlinear partial differential equations. For example, in solving 3D Navier-Stokes equations numerically, we need to consider the following difficulties:1...

Given a Calabi-Yau complete intersection in a toric Fano variety, there are various ways to construct the mirror. Sometimes these mirrors are isomorphic and sometimes they are not. These distinct 'double' mirrors should be equivalent in some way if...

I will discuss the relationship between degenerations of Fano varieties to toric varieties and expressions for their mirror Landau-Ginzburg models as Laurent polynomials. I will present some recent results that make this relationship precise in the...