Extreme forms of real algebraic varieties

April 6 to April 9, 2006

at the

American Institute of Mathematics, San Jose, California

organized by

Ilia Itenberg, Grigory Mikhalkin, and Oleg Viro

Original Announcement

This workshop will focus on real loci of algebraic varieties, and more specifically, their extreme geometrical and topological forms. Here are 3 groups of examples that have appeared particularly many times in recent research:

Harnack and anti-Harnack curves; maximal real projective hypersurfaces and complete intersections.
Varieties with extremal behavior of their amoebas or co-amoebas; varieties close to the tropical limit,
Extreme real forms for some specific classes of varieties: Grassmannians, Fano, Calabi-Yau, etc.

A common point of all these examples is that the real locus alone there can be used in a purely geometric way to reconstruct the corresponding complex variety.

There are some quite diverse areas of Mathematics where such extreme real varieties have recently appeared. The workshop will bring together researchers from these diverse areas in an attempt to answer the ill-posed question "What is the best real form for an algebraic variety?" at least in some simple cases.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A concise description of Harnack curves.
(This is a section of an introductory text concerning topology of real algebraic curves. Other parts of this text also can be used, although they are less relevant.)

An introduction to amoebas.

An elementary introduction to patchworking, including patchworking construction of Harnack curves.