This course, led by Meera Sitharam, will feature a number of lecturers and cover kinematics and those aspects of real algebraic geometry relevant to geometric constraint systems. The course should be accessible to any graduate student in mathematics and the only background assumed will be in basic linear algebra, Euclidean geometry and commutative algebra.

The meeting times for the course are Tuesday 10am-Noon (with a 20min break), and Thursday 10am-11am. The first two weeks of the course will  include guest lectures  on several of these topics.  Additionally, the course will cross-coordinate with the winter school, companion graduate course on combinatorial rigidity, distinguished lectures, and selected other lectures during workshops and other events that will run in parallel during this Fields thematic program.

Logistics
This is a 3-credit, semester long graduate course offered in Spring 2021 as part of the Fields Institute Thematic Program on Geometric Constraint Systems.  
 
The course is free and open to all graduate students worldwide. Prerequisites for the course are: a proof-based, upper-division, undergraduate course in discrete mathematics,  basic exposure to algorithms and complexity and mathematical maturity. Registration is through the above Fields institute link.  Course credit  is available through participating institutions.
 
Grading will be S/U, and likely based on preparing, critiquing and editing high quality lecture notes, Wikipedia articles of key topics, and/or a substantial project (paper and presentation) that can be theory or software-implementation based. Active class participation is also encouraged.
 
Syllabus
Geometric constraint systems are polynomial systems that underlie discrete structures arising in diverse pure and applied mathematical areas  including algorithmic foundations.  They are also widely employed in modeling and design in the sciences and engineering, from kinematics, robotics, molecular and materials modeling, computer aided mechanical design,  and virtual reality.
 
This course concerns the principles of geometric constraint systems,  and will touch briefly upon applications.
The course will use both mathematical  and algorithmic foundational perspectives for analyzing geometric constraint systems and their solutions;  and  for solving them.  
 
The course will employ diverse techniques  from combinatorial rigidity, graphs and matroids, complexity theory, discrete geometry, real algebraic geometry,  and convex and distance geometry.
 
Most of the material to be covered will come from the Instructor's recently edited volume Handbook of Geometric Constraint Systems Principles (not a required textbook for the course), her previous   lecture notes ( here, here and here), some of her research articles and relevant others.

Talks will be posted on Fields' YouTube Channel.