Abstract
We describe a large-scale computational experiment study- ing structure in the numbers of real solutions to osculating instances of Schubert problems. This investigation uncovered Schubert problems whose computed numbers of real solutions variously exhibit nontriv- ial upper bounds, lower bounds, gaps, and a congruence modulo four. We present a family of Schubert problems, one in each Grassmannian, and prove that their real osculating instances have the observed lower bounds and gaps.
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