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Martin Lorenz, Temple University
After providing some more group-theoretical background, I will focus on“representable” algebras in this talk. By definition, these are algebras that can be embedded into matrix algebras over some commutative algebra. Despite the seemingly elementary nature of this class of algebras, there are quite a few mysteries remaining to be resolved.
Elie Abdo, Temple University
We consider an electroconvection model describing the evolution of a surface charge density interacting with a 2D fluid. We investigate the model on the two-dimensional torus: we study the existence, uniqueness and regularity of solutions, and we show the existence of a global attractor.
Rose Kaplan-Kelly, Temple University
Abstract: Traditionally, alternating links, links with a projection diagram that can be given an orientation such that the link's crossings alternate between over- and under-crossings, are studied with alternating diagrams on \(S^2\) in \(S^3\). In this talk, we will consider links which are alternating on higher genus surfaces \(S_g\) in \(S_g x I\). We will define what it means for such a link to be right-angled generalized completely realizable (RGCR) and show that this property is equivalent to the link having two totally geodesic checkerboard surfaces, and equivalent to a set of restrictions on the link's alternating projection diagram. We will then use these diagram restrictions to classify RGCR links according to the polygons in their checkerboard surfaces and provide a bound on the number of RGCR links for a given surface of genus g. Along the way, we will answer a question posed by Champanerkar, Kofman, and Purcell about links with alternating projections on the torus.
There are no conferences next week.