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The topology of defects

Analysis, Dynamics, and Applications Seminar

The topology of defects
Series: Analysis, Dynamics, and Applications Seminar
Location: MATH 402
Presenter: Shankar Venkataramani, Department of Mathematics, University of Arizona

Codimension two (or higher) defects arise in many pattern forming systems, often coexisting with codimension one defects (domain walls). These codimension two defects usually carry a topological "charge" which strongly constrains their dynamics.

I will talk about point defects in various 2D systems (convection patterns, liquid crystals, and thin hyperbolic elastic sheets). I then discuss the nontrivial ways in which the underlying topology of these defects governs their birth, dynamics, stability, and their role in applications.