Random Sparse Polynomial Systems

Tuesday, September 8, 2020 - 3:00pm
Alperen Ergur
UT San Antonio

For starters (like myself) the first question seems to be how many real zeros are there? We will start by recalling Descartes rule of signs from your high school algebra class, then give a quick review of decades long efforts to generalize it to more variables, and conclude with presenting our probabilistic contribution to the quest. I will not assume any background in algebraic geometry, anyone with a taste for combinatorics, probability, or geometry is welcome to see our humble contribution and plenty of open problems. Joint work with Peter Burgisser and Josue Tonelli-Cueto.

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