#
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.