Mahler Measuring the Genetic Code of Amoebae

Understand

Amoebae from tropical geometry and the Mahler measure from number theory play important roles in quiver gauge theories and dimer models.

• Their dependencies on the coefficients of the Newton polynomial closely resemble each other, and they are connected via the Ronkin function.
• Genetic symbolic regression methods are employed to extract the numerical relationships between the 2d and 3d amoebae components and the Mahler measure.
• We find that the volume of the bounded complement of a d-dimensional amoeba is related to the gas phase contribution to the Mahler measure by a degree-d polynomial, with d = 2 and 3.