Two Methods of Efficiently Approximating Semi-Algebraic Sets Up to Homotopy

Explore two innovative approaches for efficiently approximating semi-algebraic sets up to homotopy in this one-hour lecture by Saugata Basu. Delve into the challenging algorithmic problem of triangulating semi-algebraic subsets of R^n with singly exponential complexity, a significant open question in algorithmic semi-algebraic geometry. Learn about two methods that solve a weaker problem by computing a simplicial complex $\ell$-equivalent to a given semi-algebraic set with singly exponential complexity for any fixed $\ell$. Discover the potential applications of these approaches and gain insights into the collaborative work with Negin Karisani and Sarah Percival. This talk, presented as part of the Applied Algebraic Topology Network, offers a deep dive into cutting-edge research in computational geometry and topology.