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Integral geometry and an application: computing the expected number of real roots of a random polynomial

Marco Caporaletti
Institution: 
SISSA
Location: 
A-134
Schedule: 
Thursday, July 25, 2019 - 14:30
Abstract: 

The fundamental formula of integral geometry relates the measures of random manifolds and their intersections. We state and prove it in the case of a smooth curve and a great circle in the euclidean sphere, and we apply it to compute (expected values of) relevant quantities in real algebraic geometry, such as the number of real roots of a random polynomial or real eigenvalues of a random matrix.

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