Random real algebraic geometry is a rapidly developing area of mathematics, addressing questions such as "What is the expected number of connected components of a randomly chosen algebraic curve in real projective plane?" In this talk, I will first outline some results from the literature. Afterwards, I will report on the results of our joint work with Turgay Bayraktar on the expected depth of random real algebraic curves and the expected area of the amoeba of a random complex algebraic curve. 

Link to the seminar is:

https://teams.microsoft.com/l/meetup-join/19%3a0ae91f7b86a24e8fa1d818a6f74b22a1%40thread.tacv2/1649582338192?context=%7b%22Tid%22%3a%22066690f2-a8a6-4889-852e-124371dcbd6f%22%2c%22Oid%22%3a%22a343f6fd-86f8-4abe-95cf-3c7f4ad5f0ca%22%7d