Real Algebraic Geometry for Applications. 

   Real algebraic geometry is a fundamental input for many
applications of algebraic geometry.  Its goals and methods 
are also distinct from classical algebraic geometry.  
I expect to cover topics such as real solutions to systems 
of equations, including upper and lower bounds, positivity
and sums of squares, real toric varieties, and non-standard
real structures.

  This would be based on parts of my book "Real solutions
to Equations from Geometry" and three relevant chapters 
in Theobald's book "Algebraic Geometry for Applications".  
The expected background is a graduate course in algebra,
possibly concurrent.