Geometric Shape

Geometric shape research spans diverse fields, focusing on understanding, manipulating, and generating shapes across various scales and contexts. Current research emphasizes efficient algorithms for shape optimization (e.g., co-optimization of design and control in robotics, geometric artifact correction in tomography), leveraging machine learning (e.g., neural networks for classifying Fano varieties, surrogate modeling for physics simulations) and generative models (e.g., GANs for design under uncertainty, shape-to-cartoon translation) to address complex problems. These advancements have significant implications for diverse applications, including robotics, medical imaging, computer graphics, and engineering design, by enabling more efficient and accurate shape analysis and manipulation.