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The next Open Neighborhood Seminar will be held in the Science Center
on Wednesday, September 11th, 2019 at 4:30 PM in SC 507.
The speaker is Joe Harris with the title:
How many lines meet each of 4 given lines in 3-space, and why it matters
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Basic linear algebra tells us how pairs of subspaces of a vector space can intersect. It says less about intersections of multiple subspaces. For example, given four lines in a three-dimensional vector space, we can ask whether there are any lines that have nonzero intersection with all four. In the late 19th century, Hermann Schubert developed a "calculus of conditions" to answer these questions. It's a beautiful theory, which is still an object of research today, but beyond that it's had an enormous impact on the development of geometry, for example inspiring Poincare to introduce the notions of cohomology and cup product. In this talk I'll give a very brief overview both of the Schubert calculus and the developments to which it gave rise.
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