2019-20 MATRIX Annals

MATRIX is Australias international and residential mathematical research institute, which facilitates new collaborations and mathematical advances through intensive residential research programs. This book is a scientific record of the ten programs held at MATRIX in 2019 and the two programs held in January 2020, including topics such as topology of manifolds, ergodic theory, and spatial statistics.

Format: Paperback / softback
Length: 803 pages
Publication date: 11 February 2022
Publisher: Springer Nature Switzerland AG

MATRIX, Australia's esteemed international and residential mathematical research institute, plays a pivotal role in fostering new collaborations and advancing mathematical knowledge through its rigorous residential research programs. These programs, spanning 1 to 4 weeks in duration, provide a dynamic platform for scholars to delve into cutting-edge research topics. This book serves as a scientific record, encapsulating the ten programs conducted at MATRIX in 2019 and the two programs held in January 2020.

The first program, titled "Topology of Manifolds: Interactions Between High and Low Dimensions," delved into the intricate interplay between different dimensions, offering insights into the fundamental structures and properties of manifolds.

The second program, titled "Australian-German Workshop on Differential Geometry in the Large," brought together experts from both countries to explore the latest developments in differential geometry, a branch of mathematics that plays a crucial role in understanding the universe's complex structures.

The third program, titled "Aperiodic Order meets Number Theory," brought together researchers from various fields to explore the connections between aperiodic order and number theory, a branch of mathematics that deals with the study of integers and their properties.

The fourth program, titled "Ergodic Theory, Diophantine Approximation, and Related Topics," focused on the study of ergodic theory, a branch of mathematics that examines the behavior of dynamical systems, and diophantine approximation, a technique used to solve complex mathematical problems.

The fifth program, titled "Influencing Public Health Policy with Data-informed Mathematical Models of Infectious Diseases," explored the use of mathematical models to predict and control the spread of infectious diseases, highlighting the importance of data-driven approaches in public health policy.

The sixth program, titled "International Workshop on Spatial Statistics," brought together researchers from around the world to discuss the latest developments in spatial statistics, a branch of mathematics that analyzes data in spatial contexts.

The seventh program, titled "Mathematics of Physiological Rhythms," explored the mathematical foundations of physiological rhythms, a field that plays a crucial role in understanding the functioning of biological systems.

The eighth program, titled "Conservation Laws, Interfaces, and Mixing," delved into the study of conservation laws, a fundamental concept in physics that describes the behavior of matter and energy, and their interactions at interfaces.

The ninth program, titled "Structural Graph Theory Downunder," showcased the vibrant structural graph theory community in Australia, highlighting the latest research developments in this field.

The tenth program, titled "Tropical Geometry and Mirror Symmetry," explored the geometric properties of tropical spaces and their connections to mirror symmetry, a branch of mathematics that studies the symmetry of objects and spaces.

The eleventh program, titled "Early Career Researchers Workshop on Geometric Analysis and PDEs," aimed at providing a nurturing environment for early career researchers to develop their skills in geometric analysis and partial differential equations.

The twelfth program, titled "Harmonic Analysis and Dispersive PDEs: Problems and Progress," focused on the study of harmonic analysis, a branch of mathematics that examines the properties of functions defined on a complex manifold, and dispersive PDEs, a class of equations that arise in various physical and mathematical contexts.

The articles in this book are organized into two sections: peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or comprehensive reviews on topics closely related to the MATRIX program. On the other hand, the other contributions primarily consist of lecture notes or short articles derived from talks or activities conducted at MATRIX.

MATRIX's residential research programs not only facilitate scientific advancements but also foster a vibrant community of scholars, enabling them to exchange ideas, collaborate, and push the boundaries of mathematical knowledge. This book serves as a testament to the institute's commitment to promoting excellence in mathematics and advancing the field globally.

Weight: 1282g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030624996
Edition number: 1st ed. 2021