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CNA Seminar/Colloquium/Joint PittCNA Colloquium
Ihsan Topaloglu McGill University Title: Minimization of an Energy Defined via an AttractiveRepulsive Interaction Potential Abstract: Recently, aggregation models given by the active transport equation of the form $\rho_t  \nabla \cdot (\rho(\nabla K \ast \rho)) = 0$, where $\rho$ denotes the density of aggregation and $K$ is an interaction potential, have received much attention. This PDE is, indeed, the gradient flow of the energy $E[\rho]=\iint_{\mathbb{R}^n\times\mathbb{R}^n} K(xy)\rho(x)\rho(y)dxdy$ with respect to the Wasserstein metric. These models have a wide range of applications including biological swarms, granular media and selfassembly of nanoparticles.In this talk I will concentrate on the energy $E$ defined via interaction potentials of the form $K(x)=x^q/q  x^p/p$ in the parameter regime $n
