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Open algebraic surfaces are a synonym for algebraic surfaces that are not necessarily complete. An open algebraic surface is understood as a Zariski open set of a projective algebraic surface. This book contains an account of the theory of open algebraic surfaces, as well as several applications, in particular to the study of affine surfaces.

Addresses an important recurrent theme of modern mathematics: the various compactifications of moduli spaces, which have a large number of applications. This book treats the case of thin Schubert varieties, which are natural subvarieties of Grassmannians. It develops the theory that exhibits similarities with the case of moduli of stable curves.

Examines the well-posedness of boundary value problems of Dirichlet and Neumann type for elliptic systems on the upper half-space with coefficients independent of the transversal variable and with boundary data in fractional Hardy-Sobolev and Besov spaces. The authors use the so-called "first order approach" which uses minimal assumptions on the coefficients.

Presents a comprehensive introduction to free probability theory, a highly noncommutative probability theory with independence based on free products instead of tensor products. This title provides basic examples of this kind of theory by convolution operators on free groups and by the asymptotic behavior of large Gaussian random matrices.

Topics related to the differentiation of real functions have received considerable attention during the last few decades. This book provides an account of the state of the subject. It addresses the problems that arise when dealing with the class $\Delta '$ of derivatives, a class that is difficult to handle for a number of reasons.

Integrating ideas from category theory, algebra and combinatorics, this monograph is organised into three parts: category theory; combinatorics and geometry; and an examination of how ideas in Parts I and II lead to a unified approach to Hopf algebras.