I am currently working in industry, having recently completed a MSc in probability, but I am looking to apply for US Mathematics/Statistics PhD programs in a few years' time. At the moment I'm trying to
gauge feasibility for certain places in the US based on a rough profile; and
further build the list of research areas or places in the US that I'm considering.
My current progress is below. Any assistance would be greatly appreciated!
Research areas
My interests are mainly theoretical areas in probability or mathematical statistics rather than applications. I'm particularly fascinated by areas that have emerged due to shortcomings in traditional or conventional methods. I'm also interested in areas that offer alternative perspectives on common problems.
Some examples are
extreme value theory and heavy-tailed phenomena
time series
Bayesian nonparametrics
information theory
survival analysis
One other thing: I am not very familiar with the use of probability theory in mathematical physics, even though it seems to be a major research theme in probability in the US. I'm mainly sticking to theoretical areas of probability or stochastic processes that are more aligned with statistics, engineering, and operations research.
Departments I'm considering already
These are mainly inspired by having identified particular members of faculty that I might be interested in doing research with, although there are certainly some that I'm considering simply due to the overall strength/reputation of the department.
Cornell — Operations Research and Information Engineering
Columbia — Statistics
Duke — Statistical Science
Stanford — Management Science and Engineering
UC Davis — Statistics
UC San Diego — Mathematics
Yale — Statistics and Data Science
UNC at Chapel Hill — Statistics and Operations Research
Stanford — Statistics
UC Berkeley — Statistics
Chicago — Statistics
Would love any suggestions here!
Brief profile
Institution: One of the top Australian universities (same place for both undergrad and masters) Major(s): Probability Theory Minor(s): (notionally) Statistics, Actuarial Science GPA: We use a different scale but something like a 3.9/4.0 or above maybe
Type of Student: International Asian male
GRE General Test: Have not sat GRE Subject Test in Mathematics: Have not sat Research Experience: Masters thesis turned into a preprint. Before that I did a 4-week undergrad project on fractional Brownian motion. Awards/Honors/Recognitions: Top masters student among those specialising in probability or statistics. Letters of Recommendation: Should have three from faculty in probability theory. Have taken two or three classes with all of them; one supervised me for my masters thesis, and another was involved in grading my masters thesis.
Maths Grades: Have no idea how the grades or class names translate, but I took all possible probability classes. I'm guessing something like the following:
Probability and Stochastic Processes (A+); Stochastic Processes II (A+); Probability Theory (A); Stochastic Calculus (A+); Stochastic Processes III (A+); Probability Theory II (A+);
Calculus I–III (A+); Real Analysis (A+); Complex Analysis (A+); Topological and Metric Spaces (A+); Measure Theory (B)
Linear Algebra (A+); Group Theory (A+); Rings and Fields (A+); Commutative Algebra (B+)
Statistics Grades: Mathematical Statistics I (A+); Linear Models (A); Survival Analysis for Actuaries (A); Generalised Linear Models (A); Mathematical Statistics II (B+); High-Dimensional Statistics (A+) Any Miscellaneous Points that Might Help: About 1/4 of those subjects listed above were masters-level courses here, which roughly corresponds to upper-division undergrad classes or first-year graduate classes in the US.