Robert Williams
Published 2017-08-07Version 1
The Galois group of a Schubert problem encodes some structure of its set of solutions. Galois groups are known for a few infinite families and some special problems, but what permutation groups may appear as a Galois group of a Schubert problem is still unknown. We expand the list of Schubert problems with known Galois groups by fully exploring the Schubert problems on $\text{Gr}(4,9)$, the smallest Grassmannian for which they are not currently known. We also discover sets of Schubert conditions for any sufficiently large Grassmannian that imply the Galois group of a Schubert problem is much smaller than the full symmetric group.
Comments: Doctoral dissertation, Texas A&M University 2017
Numerical computation of Galois groups
On realizability of $p$-groups as Galois groups
Galois groups of Schubert problems of lines are at least alternating
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