Course Geometry of amoebas
Grigory Mikhalkin (University of Geneva), 2013 Research chaire of excellence laureate, gave from october to december 2013 a course entitled Geometry of amoebas. The course took place at the Institut Henri Poincaré (11 rue Pierre et Marie Curie 75005 Paris) from 11:00 to 12:30:
Thursday 10 october: amphithéâtre Hermite
Thursday 17 october: amphithéâtrei Darboux
Thursday 31 october: amphithéâtre Hermite
Thursday 14 november: amphithéâtre Hermite
Thursday 21 november: amphithéâtre Hermite
Thursday 28 november: amphithéâtre Darboux
Thursday 12 december: amphithéâtre Hermite
In this lecture series we give an introduction to amoebas andthe role they play in complex and real geometry. In the first two or three lectures we treat the following subjects.
Introduction: use of polar coordinates in complex geomtry; definitions of amoebae and algae (coamoebas); first examples: lines, planes, hyperplanes. Area and volume of amoebas and coamoebas; computation of zeta(2) due to Passare; degrees and bounds for amoeba volumes. More examples: amoebas of planar curves and their tropical limit; Ronkin's function and its thermodynamical interpretation. Further topics are to include Monge-Ampère measure; holes (vacuoles); amoeba's contours; connections to real geometry; simple Harnack curves; generalized amoebas and amoeba-like objects.
A more detailed further plan is to be announced after the beginning of the first couple of lectures.