Real-Number Complexity

This workshop will explore complexity-theoretic and probabilistic aspects of real number computations, with a focus on numerical equation solving, optimization, and the geometry of solution sets. Topics include condition numbers, random real algebraic systems, and the distribution of points on manifolds. We will also address new directions involving effective o-minimality and positive, hyperbolic and Lorentzian polynomials.

Our workshop naturally connects with Computational Algebraic Geometry, particularly around shared interests in solution structure and symbolic-numeric techniques. There is also strong overlap with Numerical Linear Algebra, especially regarding condition numbers, optimization, and the stability of algorithms. Joint sessions or panels could explore the interplay between algebraic structure, numerical behavior, and computational complexity, enriching discussions across disciplines.