I have just completed my 4-year undergraduate studies in mathematics (my overall grade is 9.62/10) in Greece and I'm about to enroll in the M.sc. programme of my current university. I feel like I have what it takes to be admitted in a good institution and I'd like to pursue a Ph.D in pure mathematics somewhere in Europe, however my professors are highly discouraging; they say that it is very hard finding a Ph.D. position in Europe, the vacancies are very few and that the competition is extreme. They advise me to take the GRE exams and consider studying in the U.S. However, I feel that they are a little prejudiced because of their personal choices as students.
I am unsure on how to confirm this information. The sites of the universities that interest me are not very helpful, since they only say that Ph.D. vacancies are anounced when available.
P.S: For those familiar with mathematics academia, my interests currently lie in operator theory, dynamical systems & ergodic theory, complex analysis and harmonic analysis. I have only seen a few things from each subject therefore I have not yet decided precisely what I'd like to focus on. I am also starting a side-project on an algebraic topic, Quiver representations, so this is another possible interest of mine. Also, the universities I've been considering are KU Leuven, Lund University, Stockholm University and NTNU.