Tropical Machinery

algebraic-geometry tropical-geometry

Recently I heard of a recent field in mathematics called tropical geometry. Having read the wiki page on it it seems like it is combinatorial algebraic geometry.

My question is what are the benefits of applying tropical geometry to problems in algebraic geometry? Are there examples of theorems in algebraic geometry where a proof was made much simpler using tropical geometry? Or are there any conjectures in algebraic geometry that was proved using tropical geometry?

Also does anyone know the motivation behind why it was developed?


Solution 1:

Here is a link to a Mathoverflow thread that gives several references for someone wanting to learn tropical algebraic geometry, including to the recent book of Maclagan and Sturmfels. Much of the motivation for tropical algebraic geometry can be found by perusing the papers mentioned there.

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