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Research in differential equations is usually oriented toward explicit results and motivated by applications. Many clever methods have been discovered in this way, but, when …
In a very broad sense, 'spaces' are objects of study in geometry, and 'functions' are objects of study in analysis. There are, however, deep relations between functions defined on …
The word 'moduli' in the sense of this book first appeared in the epoch-making paper of B. Riemann, Theorie der Abel'schen Funktionen, published in 1857. Riemann defined a Riemann …
Masaki Kashiwara is undoubtedly one of the masters of the theory of $D$-modules, and he has created a good, accessible entry point to the subject. The theory of $D$-modules is a …
This book studies a large class of topological spaces, many of which play an important role in differential and homotopy topology, algebraic geometry, and catastrophe theory. These …
Algebraic geometry plays an important role in several branches of science and technology. This is the last of three volumes by Kenji Ueno algebraic geometry. This, in together with …
Stochastic analysis is often understood as the analysis of functionals defined on the Wiener space, i.e., the space on which the Wiener process is realized. Since the Wiener space …
Modern algebraic geometry is built upon two fundamental notions: schemes and sheaves. The theory of schemes was explained in "Algebraic Geometry 1: From Algebraic Varieties to …