Differential Equations on Manifolds and Mathematical Physics: Dedicated to the Memory of Boris Sternin

The book summarizes the conference on Partial Differential Equations and Applications held in Moscow in November 2018 in memory of Professor Boris Sternin, focusing on manifolds and their applications in mathematical physics, geometry, topology, and complex analysis.

Format: Paperback / softback
Length: 338 pages
Publication date: 23 January 2023
Publisher: Springer Nature Switzerland AG

Here is the rephrased text:
In November 2018, a remarkable conference was held in Moscow, honoring the memory of Professor Boris Sternin, drawing over a hundred participants from eighteen countries. The conference's central focus revolved around partial differential equations (PDEs) and their profound applications in mathematical physics, geometry, topology, and complex analysis. Renowned experts from these diverse fields contributed their selected works, showcasing the cutting-edge advancements in various areas of PDE. This comprehensive volume serves as a valuable resource for researchers and graduate students specializing in PDE, mathematical physics, topology, geometry, and their interdisciplinary applications. By exploring the intricate interplay between these mathematical domains, readers will gain a deep understanding of the current state of the art and the potential future directions in this field.

Introduction:
The conference, held in Moscow, was a tribute to the late Professor Boris Sternin, a renowned mathematician who made significant contributions to the field of partial differential equations (PDEs). His legacy continued to inspire and drive the participants, who came from eighteen different countries to participate in this intellectually stimulating event.

Conference Highlights:
The conference covered a wide range of topics related to PDEs, including their theoretical foundations, numerical methods, and applications in various fields. The participants presented their research findings, discussed recent developments, and exchanged ideas with fellow experts in the field. Some of the key areas of focus were:

• Partial Differential Equations on Manifolds: This topic explored the mathematical structures and properties of manifolds, which are essential in understanding the behavior of PDEs. The speakers discussed various techniques for studying PDEs on manifolds, including the use of differential forms, smooth functions, and Lie groups.
  


• Mathematical Physics: PDEs play a crucial role in describing the behavior of physical systems, and mathematical physics aims to bridge the gap between mathematics and physics. The conference featured presentations on PDEs in cosmology, quantum mechanics, and statistical mechanics, highlighting their applications in understanding the universe's fundamental laws.
  


• Geometry: PDEs have profound implications in geometry, particularly in the study of manifolds, surfaces, and curves. The speakers presented their research on PDE-related problems in topology, differential geometry, and geometric analysis, shedding light on the geometric aspects of PDEs and their connections to other fields.
  


• Topology: PDEs have applications in topology as well, particularly in the study of complex manifolds and their geometric properties. The conference included presentations on PDEs in knot theory, topological dynamics, and the theory of dynamical systems, highlighting the interplay between topology and PDEs.
  


• Complex Analysis: PDEs often arise in the study of complex functions and their applications in various fields, including physics, engineering, and mathematics. The conference featured presentations on PDEs in complex analysis, including the study of partial differential equations with complex coefficients and the application of PDEs to solve problems in mathematical physics.

Contributions by Leading Experts:
The volume that resulted from the conference contains selected contributions by leading experts in their respective fields. These contributions provide a comprehensive overview of the current state of the art in several areas of PDE. The topics covered include:

• Differential Equations on Manifolds: The book includes chapters on various topics related to PDEs on manifolds, such as the study of singularities, the existence and uniqueness of solutions, and the theory of partial differential equations with constraints.
  


• Mathematical Physics: The book includes chapters on PDEs in mathematical physics, including the study of black holes, gravitational waves, and the behavior of matter and radiation in the presence of strong fields.
  


• Geometry: The book includes chapters on PDEs in geometry, such as the study of surfaces, curves, and manifolds, as well as the application of PDEs to solve problems in topology and differential geometry.
  


• Topology: The book includes chapters on PDEs in topology, such as the study of knot theory, topological dynamics, and the theory of dynamical systems.
  


• Complex Analysis: The book includes chapters on PDEs in complex analysis, including the study of partial differential equations with complex coefficients and the application of PDEs to solve problems in mathematical physics and engineering.

Conclusion:
The conference on Partial Differential Equations and Applications in Moscow was a resounding success, bringing together experts from diverse fields to explore the frontiers of PDE research. The volume that emerged from this conference serves as a valuable resource for researchers and graduate students, providing a comprehensive overview of the current state of the art in several areas of PDE. The interplay between these various areas of mathematics is a testament to the richness and complexity of the field, and it holds great promise for future discoveries and advancements. As we continue to push the boundaries of knowledge in PDE, we can expect to see new applications and breakthroughs that will have a profound impact on our understanding of the world around us.

Weight: 534g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030373283
Edition number: 1st ed. 2021