Department of Mathematics

Title: Fast Diffusion Equations on Bounded Domains. Sharp Extinction Rates and singular asymptotic behaviourAbstract: We begin with an overview of the ``classical'' homogeneous Dirichlet problem for the Fast Diffusion Equation $u_t=Delta u^m$, posed in a smooth bounded domain $Omegasubset mathbb{R}^N$, with $min (0,1)$.We then focus to the ``supercritical'' exponent range $m_s=(N-2)_+/(N+2)<m<1$ and focus on the […]

Title: What Deep Networks Can Represent — and What Training Can FindAbstract: Deep learning raises two basic questions: what functions deep networks can represent efficiently, and when training algorithms can actually find those representations. This talk brings these questions together through recent results on approximation and optimization. On the approximation side, depth and activation design […]

Title: Plateau borders and wet soap films Abstract: We discuss a model where soap films are understood as three-dimensional objects with small volume ("wet" soap films) rather than as two-dimensional surfaces satisfying the classical Plateau's laws ("dry" soap films). These wet films serve as physical approximations of their dry counterparts in the limit as the enclosed […]

Title: Towards a derived geometry for 2-rings with applications to the representation theory of finite groups