It is classically known that there exist (n+1)(d-1)n singular hypersurfaces of degree d in complex projective n-space passing through a prescribed set of points (of the correct size). In this talk we will deal with the analogous problem over the real numbers and construct, using tropical geometry, Ω(dn) real singular hypersurfaces through a collection of points in ℝℙn. We will also consider the enumeration of hypersurfaces with more than one singular point. No prior knowledge of tropical geometry will be assumed.
This video was produced by Tel Aviv University as part of its algebra seminar.
