This is a webpage dedicated to the project that applies methods of numerical algebraic geometry to the problems in enumerative algebraic geometry.
The first part of the project resulted in the paper on Galois groups of Schubert problems via homotopy computation:
"... We use numerical homotopy continuation to investigate the problem of determining Galois groups in the Schubert calculus. For example, we show by direct computation that the Galois group of the Schubert problem of 3-planes in 8-dimensional complex space meeting 15 fixed 5-planes non-trivially is the full symmetric group S6006."
Based on the initial results, we conjecture that the Galois group of every simple Schubert problem is the full symmetric group. As the continuation of the research in this direction we are planning to produce more evidence for this conjecture as well as to go beyond simple Schubert problems.
|Anton Leykin and Frank Sottile, Galois groups of Schubert problems via homotopy computation, 18 pages. ArXiV:0710.4607.|