TITLE: How to find a topic to do research with as a Post-Doc?
QUESTION [6 upvotes]: I will soon finish my PhD in arithmetic geometry. My advisor told me that I will have to find my next research topic on my own. How do I do that? (Except for "continue where the PhD thesis ends") Can you give me hints/advice?

REPLY [8 votes]: You should read literature in the area of your previous research, in search of interesting unsolved
problems. Also attend conferences and talk to specialists in your field. When I was on this stage
of my career, I found surveys with lists of unsolved problems in my field, and tried to solve them.
Now I make such lists myself, to help young researchers, and I suppose they exist in every field
of mathematics. You have to read a lot to become an expert in your area.