Antonio Lerario and I have started writing a book titled
Lectures on Random Algebraic Geometry
The file under this link is the most recent, but still work in progress.
The last update was on July 8, 2019.
Here is the list of chapters we are thinking of.
1. How many zeros of a random polynomial are real?
2. Counting formulas
3. Volume and degree
4. Topology of random submanifolds
5. Invariant measures
6. Random quadrics
7. Random tensors
8. Probabilistic Schubert calculus
9. Singularity theory
10. Central limit theorems
11. Further directions
