## Speaker: Dr. Antonio Lerario, SISSA (Trieste) and FAU

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Venue: | GL 132 |

Dr. Antonio Lerario, SISSA (Trieste) and FAU will speak

Nov. 19, 3.30 pm, rm. GL 132

Title: "Statistics on Hilbert's Sixteenth Problem"

Abstract: The degree d of a polynomial equals the number of its complex zeroes (counted with multiplicity), but the number of real zeros can range anywhere from zero to d, and determining that number is difficult even case by case. The situation is even more complicated for the zero set of a polynomial in several variables and Hilbert's Sixteenth Problem asks to study the “number, shape, and position” of the connected components of a real algebraic hypersurface in R^n. In this talk I will present a probabilistic approach to this problem, discussing new exciting questions related to the topology of random hypersurfaces. (This is joint work with E. Lundberg)