I am a student in first year of masters degree in mathematics. My backround in analysis consists of Real and Complexe Analysis, Measure Theory, ODEs and stability,Optimization, Numerical Analysis, Functionnal Analysis, i will also study more Functionnal analysis and Optimization this year as well as PDEs, Dynamical Systems, multi-scale modeling and Evolution Problems.
I absolutely love mathematics and especially analysis, but i have to start thinking about what area to specialise in and i am very lost at the moment. I want to become a researcher in analysis and applied mathematics in a domain that is active and where there are oportunities, Optimization adn PDEs seems like very interesting and active fields but i have no idea what the research landscape looks like. I heard that there is less research in PDEs than there used to be but i don't have anything more precise than that, i have heard about shape otimization as well as computational geometry and geometric data analysis (seems very exiting) but i don't know if there are a lot of research in those areas. I also heard that there is a lot of research in machine learning and that it involves a lot of Optimization but i dont know if the mathematical content in this area is enough to satisfy me.
If anyone has information, advice or maybe one area they would like to bring my attention to i would be very grateful, also if anyone knows where i can find up to date and reliable data on this it would be perfect.
Thank you very much.