Inaugural speech M.C. Veraar (EWI): applied mathematics

13 September 2019 15:00 - Location: Aula, TU Delft - By: webredactie

Mathematics: hard or soft?

In mathematical analysis one can distinguish between “hard” and “soft” techniques. Soft techniques are more structural and often give deeper insights in a problem. Afterwards they can be combined with hard techniques, such as delicate estimates, to obtain new results. In my inaugural lecture I will use simple analytical examples to demonstrate the difference between hard and soft analysis. Moreover, I will show how with the help of bridges between different subfields in mathematics one can replace hard arguments by soft ones. Also the converse occurs: new results by soft arguments are afterwards improved by using hard arguments. 
The interplay of hard and soft analysis plays an important role in the fields in my research field: the theory of partial differential equations and harmonic analysis. Partial differential equations are of fundamental importance in the understanding of mathematical models in applied sciences. By connecting the fields harmonic analysis, stochastic analysis and functional analysis, I try to prove new properties of solutions to partial differential equations. The combination of hard and soft techniques is often the key in obtaining the best results. This is also what I try to explain my students in my lectures and I believe this is of great importance in a mathematics study at university.