Doctor of Philosophy in Mathematics - Logic and Foundations

The faculty of the Department of Mathematics at the University of California, Irvine are prominent scholars engaged in teaching, fundamental research in both pure and applied mathematics, and service to the local community with outreach efforts to foster success in STEM disciplines (science, technology, engineering, and mathematics). The Department includes 34 permanent faculty members together with 4 permanent adjunct instructors and is augmented by an equal number of postdoctoral researchers, lecturers, and visiting assistant professors, who play a vital role in teaching and research. Founded in 1965, the University of California, Irvine combines the strengths of a major research university with the perfect Southern California location, wonderful weather, and a diversified campus community and culture. We offer undergraduate and graduate students a program of study leading to professional competence in teaching, mathematical research, or in an area of application. Additionally, we serve the entire student population at UCI by providing required courses in Mathematics. The Department population includes approximately 110 graduate students, over 615 undergraduate majors, and numerous students completing minors, specializations, and concentrations.

When accepted into the doctoral program, the student embarks on a program of formal courses, seminars, and individual study courses to prepare for the Ph.D. written examinations, advancement to candidacy oral examination, and dissertation. By the start of the second year, students must achieve at least two passes at the M.S. level among three exams in Real Analysis, Complex Analysis and Algebra. By the start of the third year, students must achieve at least two passes at the Ph.D. level among three exams in Real Analysis, Complex Analysis and Algebra. To satisfy the exam requirements, students may take the Core Assessment Exams (offered in the Spring of every year) or the Qualifying Exams (offered before the start of the fall quarter) in these areas. Students may not attempt to take an exam in a particular subject area more than 3 times. A student who passes a Qualifying examination prior to taking the corresponding course will be exempted from taking the course.

The UCI research group on Logic and Foundations of Mathematics focuses on set theory and model theory. Within set theory, there is an emphasis on forcing, large cardinals, inner model theory, fine structure theory, regular and singular cardinal combinatorics, and descriptive set theory. Two aspects of descriptive set theory are studied: the interaction with and application of it in mainstream mathematics, most importantly ergodic theory, as well as its connections to large cardinals, inner models, and determinacy. Within model theory, there is an emphasis on applications of model theory to other areas of mathematics, such applications often come via nonstandard analysis. There is also an emphasis on model theory of metric structures, e.g. the model theory of operator algebras.

Hold a bachelor's degree (or equivalent) from a recognized academic institution with degree standards equivalent to those of the University of California
Have a minimum cumulative undergraduate GPA of 3.0
Transcripts Applicants must upload unofficial transcripts for all institutions attended since high school. If an applicant is admitted, official transcripts will be requested only from the institutions were a degree was earned. Foreign applicants must provide transcripts converted to English, and a calculated US GPA
Personal History Statement This will be required by all students, please see the Graduate Division website for more information.
Letters of Recommendation We require three letters of recommendation. Letters must be uploaded digitally, paper LORs will not be accepted.
GRE Official scores are required for the General and Subject GRE exam taken within the last five years for MS
TOEFL iBT minimum score of 80
IELTS - An overall minimum score of 7.0 for admission, with a score of no less than 6.0 on any individual module.