PhD in Mathematics - Ergodic Theory and Dynamical Systems in Irvine United States | University of California Irvine

The Mathematics Department at UC Irvine boasts distinguished faculty who excel in teaching, conducting groundbreaking research across pure and applied mathematics, and supporting local STEM initiatives through community outreach. With 34 tenured professors and 4 adjunct instructors, the department is further strengthened by postdoctoral fellows, lecturers, and visiting professors who contribute significantly to both education and research. Established in 1965, UC Irvine merges top-tier academic research with Southern California's ideal climate and vibrant campus life. Our programs equip undergraduate and graduate students with professional expertise in teaching, mathematical research, or applied fields, while also delivering essential math courses to all UCI students. The department serves roughly 110 graduate students, more than 615 undergraduate majors, and many others pursuing minors or specialized studies.

Doctoral candidates follow a structured path of coursework, seminars, and independent study to prepare for Ph.D. qualifying exams, candidacy reviews, and dissertation work. First-year students must pass two M.S.-level exams in Real Analysis, Complex Analysis, or Algebra by their second year, followed by two Ph.D.-level passes in these subjects by year three. Students can fulfill these through annual Core Assessment Exams or fall Qualifying Exams, with a maximum of three attempts per subject. Passing a Qualifying Exam before taking the related course grants exemption from that course.

Faculty research focuses on Ergodic Theory and Dynamical Systems across topological, smooth, and Hamiltonian frameworks, with special attention to intersections with other mathematical and scientific disciplines like Logic, Celestial Mechanics, and Economics. The group maintains active collaborations with leading global institutions in dynamical systems, including Cornell, Hebrew University, and Northwestern, enhancing UCI's mathematical community.