Geometry helps us see and shape the world, bringing insights to complex and diverse shapes generated by 3D scanning, computer animation, additive manufacturing, medical imaging, and more. Modern geometry research builds on centuries of mathematical foundations to assemble unstructured and noisy signals about shape into robust models describing digital and physical worlds. Geometric techniques in two and three dimensions used in computer graphics, medical imaging, and autonomous driving also can prove valuable in higher dimensions: Geometric measurements like distances and flows make sense when analyzing abstract data, from corpora of text to clicks on a website, suggesting that geometry applies far beyond shapes gathered from robotic sensors or virtual reality environments.
Professor Justin Solomon, who leads the Geometric Data Processing group in MIT CSAIL, sees a broadly applicable, versatile toolbox for applied geometry as the solution to these and other problems. To solve growing challenges in shape analysis, his work advances the theory and practice of geometric data processing.
Before joining the MIT faculty as a professor of EECS, Prof. Solomon received a PhD in computer science from Stanford University and worked at Pixar Animation Studios; he also completed postdoctoral research in the Princeton Program in Applied and Computational Mathematics. His textbook Numerical Algorithms covers numerical methods for geometry, graphics, robotics, and other computational areas.
His group aims to widen the scope of applied geometry to benefit anyone using computers to analyze complex shapes, networks, maps, datasets, and other modalities. Central areas of his research include transitioning optimal transport from theory to practice, addressing both theoretical and algorithmic challenges in 3D shape analysis, and developing architectures for learning from geometric data.
Prof. Solomon and his group respond to challenges at the intersection of geometry and computation in a broad range of applications as technology emerges – making sure that robots and autonomous vehicles can navigate their environments safely and reliably, that political redistricting practices are established fairly, that physical systems can be simulated virtually with high fidelity, and that medical diagnoses are responsive to subtle changes in shape.
Gerrymandering is a direct threat to our democracy, undermining founding principles like equal protection under the law and eroding public confidence in elections.
Data often has geometric structure which can enable better inference; this project aims to scale up geometry-aware techniques for use in machine learning settings with lots of data, so that this structure may be utilized in practice.
The shared mission of Visual Computing is to connect images and computation, spanning topics such as image and video generation and analysis, photography, human perception, touch, applied geometry, and more.
Justin Solomon, MIT associate professor of electrical engineering and computer science and leader of the CSAIL Geometric Data Processing Group, has been named one of eight 2025 Schmidt Polymaths. He will explore problems in acoustics, climate, and other fields that require digital simulation of physical phenomena.
By visualizing Escher-like optical illusions in 2.5 dimensions, the “Meschers” tool could help scientists understand physics-defying shapes and spark new designs.
A new algorithm solves complicated partial differential equations by breaking them down into simpler problems, potentially guiding computer graphics and geometry processing.
