PhD in Mathematics - Geometry and Topology in Irvine United States | University of California Irvine

The Mathematics Department faculty at UC Irvine are distinguished scholars dedicated to teaching, conducting groundbreaking research in both theoretical and applied mathematics, and serving the community through STEM outreach initiatives. With 34 permanent faculty members and 4 adjunct instructors, the department is further enriched by postdocs, lecturers, and visiting professors who contribute significantly to both instruction and research. Established in 1965, UC Irvine blends top-tier academic research with Southern California's ideal setting, featuring excellent climate and a vibrant, diverse campus. Our programs equip undergraduate and graduate students with professional expertise in teaching, mathematical research, or applied fields, while also delivering essential math courses to the broader UCI student body. The department serves about 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 requirements 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.

UCI's Geometry & Topology Group brings together experts working across various disciplines with diverse methodologies. The group hosts dynamic seminars and emphasizes the exchange of ideas between geometry and topology. Faculty research spans geometric PDEs, differential geometry, integrable systems, mirror symmetry, 4-manifolds, symplectic/contact topology, and knot theory. With a strong tradition of mentoring, the group is committed to outstanding graduate and postdoctoral education: