In the Netherlands, PhD students (promovendi) are formally considered academic researchers rather than students.
If you are independently funded (your own funds, student loan, grant from your home country etc.), you can apply directly to the "Graduate Programme in Mathematics and Statistics" to become a PhD student. For this, you use the KdVI-PhD Application Form at the bottom of this page.
You need a Dutch Masters degree in mathematics or stochastics, or a degree in an adjacent field with sufficient mathematics. Foreign degrees which are equivalent to such a Dutch master degree also give access to the PhD Programme. The Doctorate Board of the University decides whether a foreign degree is equivalent to a Dutch one. Furthermore a good command of the English and/or Dutch language is important for communication with your advisor.
The tuition fee is € 4000 euro per year. For this, PhD students will have the status of KdVI researcher with a desk at the Institute and access to the library and computing facilities. In addition, PhD students have access to a travel budget for conferences and research visits comparable to the travel budget of hired PhD students (aio's). Note that PhD students do not have student status in the Netherlands! In special cases the department may decide to waive the fee.
Students with a good command of Dutch (or English) can apply for teaching assistantships, if these are available.
Each accepted student will be assigned an academic mentor, who will guide the student through the first year and makes a precise assessment of the level and quality of the student. Depending on the outcome he will help the student finding the right advisor, or suggest the student to attend certain courses in the first year. The mentor will also play a crucial role in the evaluation. This mentor is not to be confused with a PhD thesis supervisor (even though the mentor can become the PhD thesis supervisor).
In the first year, PhD students either start already with their PhD-project, or start by taking courses from the graduate programme (or advanced courses from our master programmes) and start smaller research projects with various staff members. In the meantime they are actively looking for a PhD thesis supervisor and topic, for which the mentor can play a helpful role.
After the first year, the PhD student will be evaluated by the mentor and the director of KdVI. The evaluation is based on the general performance of the student. A student can only be positively evaluated if he or she has found a PhD thesis supervisor or topic. Positively evaluated PhD students are accepted for three more years.
After the evaluation, the main emphasis is on the independent research in the PhD thesis project. To get an impression of possible PhD thesis topics, you can look in UvA Dare. See the link below.