Organizers
Fengchun Lei(雷逢春), BIMSA
Guowei Wei(魏国卫), Michigan State University
Jie Wu(吴杰), BIMSA
Abstract
Data analysis has an extremely wide range of applications in science and engineering. Topological data analysis has emerged as an important analytical tool. As a new branch of algebraic topology, persistent homology is able to incorporate certain geometric features into topological invariants, narrowing the gap between traditional topology and geometry. Computational topology, particularly topological deep learning, holds the potential to provide revolutionary methods for scientific research. For instance, persistent homology has achieved great success in extracting and simplifying the complexity of macromolecular structures and in drug discovery. Topological descriptions provide an excellent foundation for machine learning on large-scale complex datasets and images. In computational science, algebraic topology has also been applied to concurrent, distributed, sequential computing, and networks. In summary, computational topology has found numerous valuable applications in fields such as physics, chemistry, biology, materials science, fluid mechanics, computer graphics, control theory, geometric design, shape analysis, and computational science. This success has also greatly spurred the development of related mathematical areas, including computational geometry, differential geometry, spectral geometry, geometric topology, geometric algebra, combinatorics, partial differential equations, optimization theory, inverse problems, and statistics. The upcoming workshop on data analysis and topological statistics will bring together researchers from mathematics, physics, chemistry, biology, computational science, and other fields to explore new methods connecting different disciplines and to promote the application of topology in mathematics and various applied fields.
The proposed workshop will pursue the following primary objectives:
To promote the development of topology and its applications in science and engineering.
To advance mathematical analysis and topological tools that can effectively leverage modern computational power to deepen our understanding of the complexity of chemical, biological, and computational systems.
To stimulate the flow of information from experiment to mathematics, encouraging the emergence of new mathematically inspired scientific frameworks--similar to the way quantum physics in the twentieth century inspired significant developments in mathematics.
To foster new connections, interactions, and collaborations between mathematicians and data scientists.
To provide a platform for communication and exchange, where researchers can share ideas and discuss topological results related to data science and computer science.
To introduce graduate students, postdoctoral researchers, and early-career faculty to this rapidly developing field and its related disciplines, while contributing to the training of the next generation of researchers in computational topology.
