We study the real Chevalley involution on some connected reductive algebraic group defined over the field of real numbers. Then we study some groups whose every representation is self-dual. The material is mainly based on Prof. Jeffrey Adams' papers.

The seminar presents mathematical ranking theories (PageRank, HodgeRank) and their practical algorithms in various application scenarios. The presenter also provides a literature review on static learning approach for the ranking problem. His study on the area is clearly discussed, e.g.

Community detection is one of the most important tools in understanding network topology. Even though its methods are initially developed for static networks, the extension to the dynamic case has been widely utilized to analyze the dynamic networks as its prevalence in numerous applications.

With rapid development of wireless communication technologies, such as global position system, location-based social networks (LBSNs), like Foursquare, Facebook, etc., have attracted millions of users to share their social friendship and locations via check-in.

Current neural network-based classifiers are susceptible to adversarial examples even in the black-box setting, where the attacker could only query the output of the network. We present a new method for black-box adversarial attack.

We study some properties of singular positive solutions to the conformally invariant equations. We prove an asymptotic blow rate estimate for positive solutions near the singular set with some conditions about the Minkowski dimension of the set.