Some ideas concerning doctoral programs and initiation in research in Mathematics

Abstract: In the first part of this talk, I will try to present some ideas that, in my opinion, are crucial for the success of a Doctoral Program in mathematics. I will begin with some claims: the need of auto criticism, the recognition of our limits and the convenience of diffusion. Then, I will make some comments on the (positive and negative) best known peculiarities of mathematicians. I will also speak of the “teaching style”, a controversial subject that has led to many discussions. In the second part, I will mention several mathematical problems (in a few cases connected to real world phenomena) that have served as motivation and starting point for some recent PhD Theses. I will describe the chosen strategies and the corresponding results, paying special attention to the main difficulties found in their analysis. Finally, particular and nontrivial questions on the control and inverse problems for linear and nonlinear PDEs will be reviewed from both the theoretical and numerical viewpoints.

SpanishMathematics

Audience: general audience

Seminários de Matemática da UFPB