Current Trends in Analysis, its Applications and Computation: Proceedings of the 12th ISAAC Congress, Aveiro, Portugal, 2019

This volume contains the contributions of the 12th ISAAC congress, held at the University of Aveiro, Portugal, in 2019. The congress covered various topics in mathematics, including dynamical systems theory, complex analysis, partial differential equations, and more.

Format: Paperback / softback
Length: 699 pages
Publication date: 04 October 2022
Publisher: Springer Nature Switzerland AG

The 12th ISAAC Congress, held at the University of Aveiro, Portugal, from July 29 to August 3, 2019, brought together a diverse group of scholars from around the world to explore the latest developments in Dynamical Systems Theory. This congress, which featured a wide range of sessions covering various topics, showcased the cutting-edge research and innovative ideas that are shaping the field.

The first session, titled "Applications of Dynamical Systems Theory in Biology," aimed to bridge the gap between theoretical biology and dynamical systems theory. Researchers presented their work on modeling biological systems, such as gene expression networks and population dynamics, using tools from dynamical systems theory. The session highlighted the importance of understanding complex biological processes through the lens of mathematical models and emphasized the potential of dynamical systems theory to provide insights into disease outbreaks, ecological dynamics, and other biological phenomena.

The second session, titled "Complex Analysis and Partial Differential Equations," focused on the study of complex functions and their applications in mathematics and physics. Researchers presented their work on topics such as harmonic analysis, partial differential equations, and mathematical physics, exploring the rich mathematical structures and analytical techniques that arise in these fields. The session emphasized the importance of interdisciplinary collaboration and the use of complex analysis to solve problems in diverse areas, such as signal processing, quantum mechanics, and cosmology.

The third session, titled "Complex Geometry," explored the geometric properties of complex spaces and their applications in mathematics and physics. Researchers presented their work on topics such as hyperbolic geometry, Riemann surfaces, and string theory, exploring the connections between these mathematical structures and the physical world. The session highlighted the importance of geometric thinking in understanding complex phenomena and emphasized the role of complex geometry in advancing our understanding of the universe.

The fourth session, titled "Complex Variables and Potential Theory," focused on the study of complex functions and their applications in mathematics and physics. Researchers presented their work on topics such as complex analysis, differential equations, and quantum mechanics, exploring the rich mathematical structures and analytical techniques that arise in these fields. The session emphasized the importance of understanding complex systems and their behavior through the lens of potential theory and highlighted the potential applications of complex variables in fields such as quantum computing and cosmology.

The fifth session, titled "Constructive Methods in the Theory of Composite and Porous Media," explored the use of constructive methods to solve problems in the theory of composite and porous media. Researchers presented their work on topics such as finite element methods, mesh refinement, and optimization, exploring the computational techniques and theoretical foundations that underpin these methods. The session emphasized the importance of developing efficient and accurate models for complex systems and highlighted the potential applications of these methods in fields such as materials science, engineering, and geosciences.

The sixth session, titled "Function Spaces and Applications," explored the study of function spaces and their applications in mathematics and physics. Researchers presented their work on topics such as Banach spaces, Hilbert spaces, and operator theory, exploring the mathematical structures and analytical techniques that arise in these fields. The session emphasized the importance of function spaces in understanding complex systems and their behavior and highlighted the potential applications of these methods in fields such as signal processing, quantum mechanics, and cosmology.

The seventh session, titled "Generalized Functions and Applications," explored the study of generalized functions and their applications in mathematics and physics. Researchers presented their work on topics such as analytic functions, smooth functions, and differential equations, exploring the mathematical structures and analytical techniques that arise in these fields. The session emphasized the importance of generalized functions in understanding complex systems and their behavior and highlighted the potential applications of these methods in fields such as mathematical physics, quantum mechanics, and cosmology.

The eighth session, titled "Geometric & Regularity Properties of Solutions to Elliptic and Parabolic PDEs," focused on the study of geometric and regularity properties of solutions to elliptic and parabolic partial differential equations. Researchers presented their work on topics such as boundary value problems, partial differential equations, and mathematical physics, exploring the mathematical techniques and theoretical foundations that underpin these methods. The session emphasized the importance of understanding the behavior of complex systems and their solutions through the lens of partial differential equations and highlighted the potential applications of these methods in fields such as fluid dynamics, solid mechanics, and geosciences.

The ninth session, titled "Geometries Defined by Differential Forms," explored the study of geometries defined by differential forms and their applications in mathematics and physics. Researchers presented their work on topics such as differential geometry, symplectic geometry, and geometric analysis, exploring the mathematical structures and analytical techniques that arise in these fields. The session emphasized the importance of understanding the geometry of complex systems and their behavior through the lens of differential forms and highlighted the potential applications of these methods in fields such as theoretical physics, cosmology, and mathematical biology.

The tenth session, titled "Partial Differential Equations on Curved Spacetimes," focused on the study of partial differential equations on curved physics and their applications in mathematics and physics. Researchers presented their work on topics such as general relativity, black holes, and cosmology, exploring the mathematical techniques and theoretical foundations that underpin these methods. The session emphasized the importance of understanding the behavior of complex systems and their solutions through the lens of partial differential equations and highlighted the potential applications of these methods in fields such as astrophysics, theoretical physics, and mathematical biology.

The eleventh session, titled "Partial Differential Equations with Nonstandard Growth," focused on the study of partial differential equations with nonstandard growth and their applications in mathematics and physics. Researchers presented their work on topics such as singularities, blow-up phenomena, and partial differential equations, exploring the mathematical techniques and theoretical foundations that underpin these methods. The session emphasized the importance of understanding the behavior of complex systems and their solutions through the lens of partial differential equations and highlighted the potential applications of these methods in fields such as mathematical physics, cosmology, and mathematical biology.

The twelfth session, titled "Quaternionic and Clifford Analysis," explored the study of quaternionic and Clifford analysis and their applications in mathematics and physics. Researchers presented their work on topics such as quaternions, Clifford algebras, and geometric analysis, exploring the mathematical structures and analytical techniques that arise in these fields. The session emphasized the importance of understanding the geometry of complex systems and their behavior through the lens of quaternionic and Clifford analysis and highlighted the potential applications of these methods in fields such as theoretical physics, cosmology, and mathematical biology.

The thirteenth session, titled "Recent Progress in Evolution Equations," focused on the study of evolution equations and their applications in mathematics and physics. Researchers presented their work on topics such as differential equations, partial differential equations, and mathematical physics, exploring the mathematical techniques and theoretical foundations that underpin these methods. The session emphasized the importance of understanding the behavior of complex systems and their solutions through the lens of evolution equations and highlighted the potential applications of these methods in fields such as theoretical physics, cosmology, and mathematical biology.

The fourteenth session, titled "Wavelet theory and its Related Topics," explored the study of wavelets and their applications in mathematics and physics. Researchers presented their work on topics such as wavelets, Fourier analysis, and signal processing, exploring the mathematical structures and analytical techniques that arise in these fields. The session emphasized the importance of understanding the behavior of complex systems and their solutions through the lens of wavelets and highlighted the potential applications of these methods in fields such as image processing, signal analysis, and mathematical physics.

In conclusion, the 12th ISAAC Congress was a remarkable event that brought together
together a diverse group of scholars from around the world to explore the latest developments in Dynamical Systems Theory. The congress featured a wide range of sessions covering various topics, from biology to mathematics to physics, and showcased the cutting-edge research and innovative ideas that are shaping the field. The contributions presented at the congress will undoubtedly have a significant impact on the future of Dynamical Systems Theory and will contribute to our understanding of complex systems and their behavior.

The 12th ISAAC Congress, held at the University of Aveiro, Portugal, from July 29 to August 3, 2019, brought together a diverse group of scholars from around the world to explore the latest developments in Dynamical Systems Theory. This congress, which featured a wide range of sessions covering various topics, showcased the cutting-edge research and innovative ideas that are shaping the field.

The first session, titled "Applications of Dynamical Systems Theory in Biology," aimed to bridge the gap between theoretical biology and dynamical systems theory. Researchers presented their work on modeling biological systems, such as gene expression networks and population dynamics, using tools from dynamical systems theory. The session highlighted the importance of understanding complex biological processes through the lens of mathematical models and emphasized the potential of dynamical systems theory to provide insights into disease outbreaks, ecological dynamics, and other biological phenomena.

The second session, titled "Complex Analysis and Partial Differential Equations," focused on the study of complex functions and their applications in mathematics and physics. Researchers presented their work on topics such as harmonic analysis, partial differential equations, and mathematical physics, exploring the rich mathematical structures and analytical techniques that arise in these fields. The session emphasized the importance of interdisciplinary collaboration and the use of complex analysis to solve problems in diverse areas, such as signal processing, quantum mechanics, and cosmology.

The third session, titled "Complex Geometry," explored the geometric properties of complex spaces and their applications in mathematics and physics. Researchers presented their work on topics such as hyperbolic geometry, Riemann surfaces, and string theory, exploring the connections between these mathematical structures and the physical world. The session highlighted the importance of geometric thinking in understanding complex phenomena and emphasized the role of complex geometry in advancing our understanding of the universe.

The fourth session, titled "Complex Variables and Potential Theory," focused on the study of complex functions and their applications in mathematics and physics. Researchers presented their work on topics such as complex analysis, differential equations, and quantum mechanics, exploring the rich mathematical structures and analytical techniques that arise in these fields. The session emphasized the importance of understanding complex systems and their behavior through the lens of potential theory and highlighted the potential applications of complex variables in fields such as quantum computing and cosmology.

The fifth session, titled "Constructive Methods in the Theory of Composite and Porous Media," explored the use of constructive methods to solve problems in the theory of composite and porous media. Researchers presented their work on topics such as finite element methods, mesh refinement, and optimization, exploring the computational techniques and theoretical foundations that underpin these methods. The session emphasized the importance of developing efficient and accurate models for complex systems and highlighted the potential applications of these methods in fields such as materials science, engineering, and geosciences.

The sixth session, titled "Function Spaces and Applications," explored the study of function spaces and their applications in mathematics and physics. Researchers presented their work on topics such as Banach spaces, Hilbert spaces, and operator theory, exploring the mathematical structures and analytical techniques that arise in these fields. The session emphasized the importance of function spaces in understanding complex systems and their behavior and highlighted the potential applications of these methods in fields such as signal processing, quantum mechanics, and cosmology.

The seventh session, titled "Generalized Functions and Applications," explored the study of generalized functions and their applications in mathematics and physics. Researchers presented their work on topics such as analytic functions, smooth functions, and differential equations, exploring the mathematical structures and analytical techniques that arise in these fields. The session emphasized the importance of generalized functions in understanding complex systems and their behavior and highlighted the potential applications of these methods in fields such as mathematical physics, quantum mechanics, and cosmology.

The eighth session, titled "Geometric & Regularity Properties of Solutions to Elliptic and Parabolic PDEs," focused on the study of geometric and regularity properties of solutions to elliptic and parabolic partial differential equations. Researchers presented their work on topics such as boundary value problems, partial differential equations, and mathematical physics, exploring the mathematical techniques and theoretical foundations that underpin these methods. The session emphasized the importance of understanding the behavior of complex systems and their solutions through the lens of partial differential equations and highlighted the potential applications of these methods in fields such as fluid dynamics, solid mechanics, and geosciences.

The ninth session, titled "Geometries Defined by Differential Forms," explored the study of geometries defined by differential forms and their applications in mathematics and physics. Researchers presented their work on topics such as differential geometry, symplectic geometry, and geometric analysis, exploring the mathematical structures and analytical techniques that arise in these fields. The session emphasized the importance of understanding the geometry of complex systems and their behavior through the lens of differential forms and highlighted the potential applications of these methods in fields such as theoretical physics, cosmology, and mathematical biology.

The tenth session, titled "Partial Differential Equations on Curved Spacetimes," focused on the study of partial differential equations on curved physics and their applications in mathematics and physics. Researchers presented their work on topics such as general relativity, black holes, and cosmology, exploring the mathematical techniques and theoretical foundations that underpin these methods. The session emphasized the importance of understanding the behavior of complex systems and their solutions through the lens of partial differential equations and highlighted the potential applications of these methods in fields such as astrophysics, theoretical physics, and mathematical biology.

The eleventh session, titled "Partial Differential Equations with Nonstandard Growth," focused on the study of partial differential equations with nonstandard growth and their applications in mathematics and physics. Researchers presented their work on topics such as singularities, blow-up phenomena, and partial differential equations, exploring the mathematical techniques and theoretical foundations that underpin these methods. The session emphasized the importance of understanding the behavior of complex systems and their solutions through the lens of partial differential equations and highlighted the potential applications of these methods in fields such as mathematical physics, cosmology, and mathematical biology.

The twelfth session, titled "Quaternionic and Clifford Analysis," explored the study of quaternionic and Clifford analysis and their applications in mathematics and physics. Researchers presented their work on topics such as quaternions, Clifford algebras, and geometric analysis, exploring the mathematical structures and analytical techniques that arise in these fields. The session emphasized the importance of understanding the geometry of complex systems and their behavior through the lens of quaternionic and Clifford analysis and highlighted the potential applications of these methods in fields such as theoretical physics, cosmology, and mathematical biology.

The thirteenth session, titled "Recent Progress in Evolution Equations," focused on the study of evolution equations and their applications in mathematics and physics. Researchers presented their work on topics such as differential equations, partial differential equations, and mathematical physics, exploring the mathematical techniques and theoretical foundations that underpin these methods. The session emphasized the importance of understanding the behavior of complex systems and their solutions through the lens of evolution equations and highlighted the potential applications of these methods in fields such as theoretical physics, cosmology, and mathematical biology.

The fourteenth session, titled "Wavelet theory and its Related Topics," explored the study of wavelets and their applications in mathematics and physics. Researchers presented their work on topics such as wavelets, Fourier analysis, and signal processing, exploring the mathematical structures and analytical techniques that arise in these fields. The session emphasized the importance of understanding the behavior of complex systems and their solutions through the lens of wavelets and highlighted the potential applications of these methods in fields such as image processing, signal analysis, and mathematical physics.

In conclusion, the 12th ISAAC Congress was a remarkable event that brought together
a diverse group of scholars from around the world to explore the latest developments in Dynamical Systems Theory. The congress featured a wide range of sessions covering various topics, from biology to mathematics to physics, and showcased the cutting-edge research and innovative ideas that are shaping the field. The contributions presented at the congress will undoubtedly have a significant impact on the future of Dynamical Systems Theory and will contribute to our understanding of complex systems and their behavior.

Weight: 1080g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030875015
Edition number: 1st ed. 2022