Geometric Methods for Analyzing Discrete Shapes

Attend a comprehensive workshop exploring the intersection of continuous and discrete geometry through advanced mathematical methods for analyzing discrete shapes. Delve into cutting-edge research presentations covering geometry processing with intrinsic triangulations, deformation spaces of geodesic triangulations, and canonical cell decompositions for punctured real projective surfaces. Explore discrete uniformization theory, including new approaches to discrete Gaussian curvature and convergence of discrete uniformization factors on closed surfaces. Examine rigidity and deformation properties of discrete conformal structures on polyhedral surfaces, alongside orientation-preserving vectorized distance measures between curves. Investigate the theoretical foundations and practical applications of the Bilaplacian on polyhedral surfaces, geometric persistent homology for networks and hypernetworks, and nonrigidity phenomena in flat ribbons. Learn about minimal Delaunay triangulations of hyperbolic surfaces, parameterization-based remeshing techniques for mesh realization, and discrete spherical Laplacian operators. Gain insights into convergence results for discrete conformal maps based on conformally equivalent triangular lattices and computational theory applications to graphs, sets, and rigid sets, presented by leading researchers in geometric analysis and computational geometry.