Counting Conics -- Rebecca Bellovin
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How many conics lie tangent to five given conics?  This is known as Steiner's problem, and for suitable assumptions on the given conics, the answer is 3264.  More generally, how many conics contain p given points, are tangent to l given lines, and are tangent to q given conics?  I won't fully answer this question, but I'll talk about some general counting techniques from algebraic geometry that give a partial solution.  The talk should be broadly accessible.