Explore advanced mathematical concepts in this comprehensive workshop covering real algebraic geometry and algorithms for geometric constraint systems. Delve into cutting-edge research topics including framework snappability and singularity-distance analysis, hinge mechanisms and Kempe's theorem, and room reconstruction from noisy echoes. Learn about globally optimal solutions for inverse kinematics problems, pure conditions computation in edge coordinates, and challenges in discrete geometry focusing on convex polytopes. Examine convex forms that are not sums of squares, geodesic interior-point methods for linear optimization over symmetric cones, and numerical computation of monodromy actions. Discover new directions in cylindrical algebraic decomposition, global optimization via dual SONC cones and linear programming, and flexible quad-surfaces with elliptic functions. Investigate zero-sum cycles as necessary conditions for polyhedra flexibility, invariant theory for maximum likelihood estimation, and determinantal representations with principal minor mapping. Study Helly type problems in discrete geometry, line-symmetric mobile infinity-pods, and sum-of-squares proofs of logarithmic Sobolev inequalities on finite Markov chains. Master rigidity concepts with few locations, polynomial time guarantees for the Burer-Monteiro method, and construction of weakly infeasible semidefinite programs. Analyze the central path of semidefinite optimization including degree and worst-case convergence rates, and explore framework challenges in discrete geometry through expert presentations and discussions.

Syllabus

Snappability and singularity-distance of frameworks
On the geometric definition of hinge mechanisms and Kempe's theorem
Reconstructing a room from noisy echoes
Globally optimal solution to inverse kinematics of a serial manipulator with 7 degrees of freedom
Computing Pure Conditions in Edge Coordinates
Challenges in Discrete Geometry - Part I: Convex polytopes
A convex form that is not a sum of squares
A geodesic interior-point method for linear optimization over symmetric cones
Numerical computation of monodromy action over R
New Directions in Cylindrical Algebraic Decomposition
Global Optimization via the Dual SONC Cone and Linear Programming
Flexible quad-surfaces and elliptic functions
Zero-sum cycles: a necessary condition for the flexibility of polyhedra
Invariant Theory for Maximum Likelihood Estimation
Determinantal representations and the principal minor map
Challenges in Discrete Geometry - Part II: Helly type problems
A new line-symmetric mobile infinity-pod
Sum-of-Squares proofs of logarithmic Sobolev inequalities on finite Markov chains
Rigidity with few locations
Polynomial time guarantees for the Burer-Monteiro method
How to construct any weakly infeasible semidefinite program and bad projection of the psd cone?
On the central path of semidefinite optimization: degree and worst-case convergence rate
Challenges in Discrete Geometry - Part III: Frameworks