Analysis of Self-Organization

The dissertation is devoted to the study of problems in calculus of variation, free boundary problems and gradient flows with respect to the Wasserstein metric. More concretely, we consider the problem of characterizing the regularity of minimizers to a certain interaction energy. Minimizers of the interaction energy have a somewhat surprising relationship with solutions to obstacle problems. Here we prove and exploit this relationship to obtain novel regularity results. Another problem we tackle is describing the asymptotic behavior of the Cahn-Hilliard equation with degenerate mobility. By framing the Cahn-Hilliard equation with degenerate mobility as a gradient flow in Wasserstein metric, in one space dimension, we prove its convergence to a degenerate parabolic equation under the framework recently developed by Sandier-Serfaty.

Self-Presentation Styles, Status, and Influence

This research examined effects of individual self-presentation styles on influence in groups. Perceived competence and social acceptance both play a role in determining how much influence group members enjoy. Aggrandizing and deprecating self-presentation styles may affect perceived competence, social acceptance, and ultimately influence. I predicted that aggrandizing self-presentation would lead to perceptions of competence and that self-deprecation would lead to social acceptance. The anticipated strength of those trends, however, was unclear, and I proposed that they would vary depending on status. I conducted two studies designed to assess whether aggrandizing or deprecating self-presentation styles lead to differences in influence outcomes for high and low-status individuals. In Study 1, participants gave feedback and a promotion recommendation for a fictitious (male or female) job candidate based on employee evaluation information presenting the candidate as either deprecating or aggrandizing. The main findings from Study 1 were that aggrandizers were rated as less likable than deprecators. No other predictions were supported. Study 2 was an online experiment in which participants made hiring recommendations in reference to résumés from fictitious applicants that varied by race, gender, and presentation style (aggrandizing, deprecating, or neutral). Results provided some evidence that low-status candidates were punished for using aggrandizing self-presentation strategies. The results of the studies suggest no one- best technique for self-presentation and that there may be costs for aggrandizing or deprecating depending on race and gender.