Spring 2009, Thursdays, Milner 216, 4:00-4:50 PM

Date: April 2

"  Experimentation at the Frontiers of Reality in Schubert Calculus. "
  Dr. Zachariah Teitler  


Given four random blue lines in 3-space, how many red lines meet all four of them? I will explain with pictures why the answer is two. Classical (nineteenth-century) Schubert calculus gives the answer to a much wider family of similar problems about configurations of linear subspaces---as long as we are using an algebraically closed field such as complex numbers. I will explain with pictures why the answer is not so simple over the real numbers. In the last 15 years, a series of conjectures, computational experiments, and theorems has investigated this situation. Currently, a team led by Frank Sottile and consisting of current and former postdocs and graduate students has been studying one of these conjectures, which of course I will explain with pictures. We have amassed overwhelming computational evidence for the conjecture. In fact, the computation has used over 260 GigeHertz-years of CPU time on the calclabs in Blocker! If you have ever wondered what the computers are up to after class is done for the day, I will show you.