Real Algebraic Geometry for Applications.
Real algebraic geometry is a fundamental input for many
applications of algebraic geometry. Its goals and methods
are distinct from classical algebraic geometry, and it may
be studied independent of other courses in algebraic geometry.
I expect to cover topics such as real solutions to systems
of equations, including upper and lower bounds and algorithms
for real solutions. Another topic I will cover particular
to real algebraic geometry is positivity and sums of squares,
which is important for optimization, and I expect to also
discuss real toric varieties, which underly some objects
in several different application areas.
This would be based on parts of my book "Real solutions
to Equations from Geometry" and three relevant chapters
in another book "Algebraic Geometry for Applications"
that is now a completed manuscript. Both texts will be available
to class participants in .pdf form. The expected background
would be a graduate course in algebra.