ABHYANKAR 82nd BIRTHDAY CONFERENCE SPEAKER: Sudhir Ghorpade (Mumbai) TITLE: Two miracles about 1-jets of determinantal varieties Abstract: I will talk about what appears to me as a little miracle and a not-so-little miracle. These concern the multiplicity and the Hilbert series of the so called principal component of 1-jets of the affine algebraic variety given by the vanishing of 2 x 2 minors of a generic m x n matrix. I will explain what these objects are, discuss related background and results, which include a beautiful formula of Abhyankar for the Hilbert function of classical determinantal varieties, and attempt to give an idea of the two miracles. This is a joint work with Boyan Jonov and Bharath Sethuraman.