At the 2017 meeting of the International Linear Algebra Society, Prof. Mahya Ghandehari was designated as a Linear Algebra and Applications (LAA) early career speaker. This honor is given to "linear algebra's emerging leaders" and carries with it the opportunity to address the conference. ILAS2017 was held at Iowa State University and featured an impressive 25 mini-symposia, 10 plenary speakers, and 6 LAA early career speakers.
Prof. Ghandehari spoke on "Geometric graphs and uniform embeddings" and her abstract reveals something of the exciting world of modern linear algebra:
Abstract. Many real-life networks can be modelled by stochastic processes with a spatial embedding. The spatial reality can be used to represent attributes of the vertices which are inaccessible or unknown, but which are assumed to inform link formation. For example, in a social network, vertices may be considered as members of a social space, where the coordinates represent the interests and background of the users. The graph formation is modelled as a stochastic process, where the probability of a link occurring between two vertices decreases as their metric distance increases. A fundamental question is to determine whether a given network is compatible with a spatial model. That is, given a graph how can we judge whether the graph is likely generated by a spatial model, and if so whether the model is uniform in nature? Using the theory of graph limits, we show how to recognize graph sequences produced by random graph processes with a linear embedding (a natural embedding into real line). We then discuss whether a linear embedding is uniform in nature, that is whether it is possible to "transform" the linear embedding into one in which the probability of a link between two vertices depends only on the distance between them. We give necessary and sufficient conditions for the existence of a uniform linear embedding for random graphs with finite number of probability values. Our findings show that for a general linear embedding the answer is negative in most cases. This talk is based on joint articles with H. Chuangpishit, M. Hurshman, J. Janssen, and N. Kalyaniwalia.
The department congratulates Prof. Ghandehari on this honor.