[Providing the first comprehensive description of a key theory in modern geometry and mathematical physics]

“Lagrangian Floer Theory and its Deformations,” a book written by Professor Yong-Geun Oh from the Department of Mathematics at Pohang University of Science and Technology (POSTECH) and Director for Center for Geometry and Physics at IBS, has been published by the international publisher Springer Nature.

Professor Oh is a worldly renowned scholar in symplectic geometry and mirror symmetry, key areas of research in modern mathematics and theoretical physics. He is at the forefront of the research on “Lagrangian Floer theory” which describes the mathematical and physical properties of symplectic topology.

Lagrangian Floer theory^*1 is a mathematical theory that addresses complex physical and geometric problems by examining the intersections of two shapes within a specific mathematical space and analyzing the properties of these intersections. A crucial concept in this theory for understanding intricate dynamical interactions is the “A-infinity structure^*2.”

In his book, Professor Yong-Geun Oh offers a synergetic exposition of A-infinity structures and Lagrangian Floer theory based thereon. The book explains fine details of the elements of this sophisticated mathematical theory,and provides both advanced students and new researchers with coherent understanding of the relevant geometry, analysis, and algebra.

Professor Yong-Geun Oh, the book’s author, said, “I hope that this book offers researchers a synergetic perspective on symplectic geometry and mirror symmetry which explore the dynamic interaction of space and time, and that it will inspire new breakthroughs in their research.”

Professor Oh has previously published books in the “Lagrangian Intersection Floer Theory I & II” series (AMS-International Press) in 2009.

1. Lagrangian Floer theory
An essential theory in symplectic geometry, primarily studying the intersection of Lagrangian submanifolds within a symplectic manifold. It is applied in solid mechanics, fluid mechanics, and quantum mechanics to find paths of motion that minimize a system’s energy

2. A-infinity structure
A framework that formalizes the rules of various operations in symmetric spaces, particularly when the commutative law does not strictly apply. This structure is utilized in numerous mathematical theories and applications including Lagrangian Floer theory