Enumerative geometry is the branch of algebraic geometry concerned with counting numbers of solutions to geometric questions. A famous problem in this area is counting plane rational curves of degree d passing through 3d-1 given points.

Tropical geometry has been a powerful tool in tackling enumerative geometry problems, notably marked by Mikhalkin's correspondence theorem. This theorem translates the count of plane curves into the count of their tropical counterparts, for which there are elegant solutions using only combinatorics.

Results from A1-homotopy theory allow to ask questions in enumerative geometry over arbitrary base fields, not just algebraically closed ones, and still get meaningful answers, leading to a new area called A1-enumerative geometry.

In the talk I will give an introduction to A1-enumerative geometry and explain how tropical geometry can be used to solve problems in this area.

Tropical methods in A1-enumerative geometry Sponsored by the Meyer Fund

Enumerative geometry is the branch of algebraic geometry concerned with counting numbers of solutions to geometric questions. A famous problem in this area is counting plane rational curves of degree d passing through 3d-1 given points.

Tropical geometry has been a powerful tool in tackling enumerative geometry problems, notably marked by Mikhalkin's correspondence theorem. This theorem translates the count of plane curves into the count of their tropical counterparts, for which there are elegant solutions using only combinatorics.

Results from A1-homotopy theory allow to ask questions in enumerative geometry over arbitrary base fields, not just algebraically closed ones, and still get meaningful answers, leading to a new area called A1-enumerative geometry.

In the talk I will give an introduction to A1-enumerative geometry and explain how tropical geometry can be used to solve problems in this area.