February 14, Wednesday, 15:30, room 211

Anastasia Bazykina

Schubert calculus and Hilbert’s 15th problem

Enumerative geometry is a branch of mathematics concerned with counting the number of geometric objects with given properties. In the 19th century, German mathematician Hermann Schubert developed the method for solving such problems, which is called Schubert calculus. Its rigorous foundation is a topic of Hilbert’s 15th problem. Via Schubert calculus one can solve the problem of finding a number of lines intersecting four given lines in a three-dimensional complex projective space, which is called Schubert problem. I will demonstrate the method used by Schubert to solve it. Then I am going to present two other ways to solve this problem: via hyperboloid and Grassmannian.