Symmetry and Its Application in Differential Geometry and Topology III

Dear Colleagues,

Differential geometry is a branch of mathematics that has many applications not only in mathematics but in many other sciences, e.g., applications of the theory of curves and surfaces in the Euclidean plane and space. Geometry and Topology are quite related to Symmetry. Symmetric spaces commonly occur in differential geometry, representation theory and harmonic analysis. Differential geometry can be defined as the study of the geometry of differential manifolds, as well as of their submanifolds. In recent years, there has been a fast-growing interest in developing theories and tools for studying singular submanifolds. Because singular submanifolds are produced in physics, mechanics, and other application fields and are the breakthrough point to discover new problems. Therefore, it is of great scientific significance to study the geometric and topological properties of singular submanifolds. However, due to the existence of singular sets, the traditional analysis and geometric mathematical tools are no longer applicable, which makes the study of singular submanifolds difficult. In addition, applications of differential geometry and Topology can be found in almost any field of science, from biology to architecture. One of the most important applications of Topology is Topological Data Analysis (TDA). TDA combines ideas from Topology and also algebra, geometry, and analysis, with methods from statistics and computer science, for the purpose of analyzing contemporary data sets for which standard approaches are unsatisfactory. The motivating idea is that there is an underlying ''shape'' to the data and that new variants of some of the sophisticated tools of modern mathematics may be brought to bear to elucidate and learn from this structure. TDA has convincingly proved its utility in a wide range of applications in the life sciences, including in neuroscience, genomics, proteomics, evolution, and cancer biology, among other areas of research.

This Special Issue is intended to provide a series of papers focused on Symmetry and its applications of geometry and Topology, devoted to surveying the remarkable insights into many fields of sciences and exploring promising new developments.

Prof. Dr. Tiehong Zhao
Prof. Dr. Yanlin Li
Guest Editors

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• singularity theory
• morse theory/discrete Morse Theory
• singularities
• singular submanifolds
• lightlike submanifolds
• biharmonic submanifolds
• warped product submanifolds
• differentiable manifolds
• Submanifold Theory
• Legendrian duality
• front and frontal
• physics
• statistics
• topological data analysis
• computational topology
• applied topology and geometry
• topological and geometric methods in data analysis
• spectral and geometric methods in machine learning and data analysis
• persistent homology and cohomology, and applications
• neuroscience
• cancer biology
• genomics
• other sciences