Office: Blocker 601K
Email:
sottile"at"math.tamu.edu
WWW:
www.math.tamu.edu/~sottile
Frank has an open door office policy;
just walk in when the door is open. You may also schedule an appointment.
Seminars on Monday and Fridays Geometry (MF) and Algebra and Combinatorics (F)
are a good venue for catching faculty members, including Frank.
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". Both texts will be available to class participants in .pdf form. The expected background would be a graduate course in algebra.
- Some geometrical aspects of control points for toric patches
Gheorghe Craciun, Luis Garcia, and Frank Sottile. - Sign conditions for injectivity of generalized polynomial maps with
applications to chemical reaction networks and real algebraic geometry,
S Müller, E Feliu, G Regensburger, C Conradi, A Shiu, A Dickenstein
Foundations of Computational Mathematics 16 (1), 69-97 2016.