Takahiro Kawai Livres

Taking into account the various criss-crossing among mathematical subject, Physical Combinatorics presents new results and exciting ideas from three viewpoints; representation theory, integrable models, and combinatorics. This work is concerned with combinatorial aspects arising in the theory of exactly solvable models and representation theory. Recent developments in integrable models reveal an unexpected link between representation theory and statistical mechanics through combinatorics.

Focusing on microlocal analysis, this treatise delves into the local study of differential equations on cotangent bundles, offering a comprehensive exploration from foundational concepts. It introduces hyperfunctions and develops microfunction theory, highlighting its applications in differential equations and theoretical physics. The text also covers microdifferential equations and the microlocalization of linear differential equations, culminating in structure theorems for systems of microdifferential equations, utilizing quantized contact transformations as a key tool.