Geometry, Algebra, and Topology are pure mathematics and essential to modern mathematical research. In the MAST programme, we study topics such as Riemannian geometry, algebraic topology, and ...

TripoSF represents a significant leap forward in 3D shape modeling, combining high-resolution capabilities with arbitrary topology support. Our approach enables: ...

Researchers have solved a long-standing problem in topology by helping classify four-dimensional shapes (4-manifolds) that ...

A powerful mathematical technique is used to model melting ice and other phenomena. But it has long been imperiled by certain ...

Topology optimization is a process that aims to achieve reduce a part to its most minimal possible geometry. To do this, an initial concept of a part is optimized using computer-based calculations so ...

ABSTRACT: Geometric gauge theory provides a mathematical foundation for the most successful innovations in twentieth-century theoretical physics. The theories use symmetry groups, connections on fiber ...

Fierro is a C++ code designed to aid the research and development of numerical methods, testing of user-specified models, and creating multi-scale models related to quasi-static solid mechanics and ...

The surface of a torus (the shape of our breakfast donut), for example, offers another perspective of what a 2D space could be. Mathematicians, through geometric topology, explore these spaces in ...

Network topology is the "shape" of a network of biological interactions and shows how the nodes — the parts of the network where elements interact — are connected to each other. Common ...