This is the video of the lecture by Kirsten Wickelgren entitled "Some results in A^1-enumerative geometry". The talk was given on June 28, 2018 at the TU Berlin as part of the Homotopy Theory Summer Berlin.
Abstract:
This talk will discuss enrichments of classical results in enumerative geometry to equalities of stable isomorphism classes of bilinear forms or, equivalently, equalities in pi_0(sphere) by a theorem of Morel. For example, in joint work with Padmavathi Srinivasan, we enrich the result that over the complex numbers, the number of lines meeting 4 general lines in P^3 is 2. Over the real numbers, the Shapiro Conjecture on the Wronski map implies that the two lines meeting four lines tangent to the moment curve are both real. However, in general, the two lines may be a complex conjugate pair of lines defined over C. Using ideas from A1-homotopy theory and joint work with Jesse Kass, we will explain an invariant count over a general field of the lines combined with information on their geometry and field of definition.
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