Excuse me if I tickle your fancies.
But it is really on my mind, and what better place could I find than this one to put it upfront!
Can one present or read a mathematics book review at a mathematics conference? Does it happen?
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I have never seen a book review given at a math conference. However, at least in my field in math, people do occasionally give largely expository/survey talks, even as invited speakers. I would say these are quite infrequent, and typically given by more senior researchers who maybe want to showcase their students’ work, or maybe talk about a new topic they’re just getting into.
In the end, unless you agreed something explicit with the organizers (which is less typical), you can talk about basically anything you want. But I think that points to what may be the better question to ask, which is how will it impact others’ views of you if you give such a talk, and how much does that matter to you.
I’ve seen a PhD student give a talk once which consisted of nothing but their failed attempts at finishing their thesis. It was actually a really interesting talk, but of course by design it didn’t impress anyone about their abilities. That was OK for this student, because they were leaving the program and had a job lined up in industry. They just wanted to give a fun talk.
Depending on your career stage and future ambitions, you should consider this. If you’re a student, talk to your advisor. If you’re a postdoc, talk to your mentor. If you’re at a later stage, maybe consider talking to colleagues. For better or worse, talks are a way others form impressions about you so you should consider this carefully.