Time: 9:30 - 11:30,  January 20, 2021

Venue: Room 612, A6, Institute of Mathematics, VAST

Abstract: In this talk, we review some results on the expected number of zeros of random polynomials in two cases: real and p-adic. For the real case, we present the Kac-Rice formula and its geometric meaning through Integral Geometry . To extend these ideas to the p-adic case, we discuss the works of Evans; Kulkarni and Lerario.

References:

1. Alan Edelman and Eric Kostlan. How many zeros of a random polynomial are real? Bull. Amer. Math. Soc. (N.S.), 32(1):1–37, 1995.
2. Steven N. Evans. The expected number of zeros of a random system of p-adic polynomials. Electron. Comm. Probab., 11:278–290, 2006.
3. Avinash Kulkarni and ANtonio Lerario. p–adic Integral Geometry. Preprint arXiv:1908.04775v1