probability theory is the mathematical study of randomness.  while the subject’s origins come from gambling and simple games of chance, probability theory has developed into a fundamental area of mathematical research, with deep connections to other branches of mathematics such as analysis, combinatorics, geometric group theory, operator theory, and partial differential equations, as well as to statistics.  probability theory impacts a broad range of applications in areas such as biological science, computer science, data science, electrical engineering, information science, mathematical physics, mathematical finance, network science, and operations research.  the probability group at uc san diego includes faculty with expertise in a variety of areas, including markov processes, mathematical population genetics, random geometry, random graphs, random matrices, random walks on groups, schramm-loewner evolution, stochastic differential equations, and stochastic networks.