CLAUDIO BARTOCCI - Böcker

Integral transforms, such as the Laplace and Fourier transforms, have been major tools in mathematical physics for at least two centuries. In the last 25 years, the development of gauge theory has been closely related to new generalizations of integral transforms of a more geometric character. "Nahm and Fourier--Mukai Transforms in Geometry and Mathematical Physics" examines the differential-geometric constructions (Nahm) as well as the algebro-geometric approach (Fourier--Mukai functors). Also included is a considerable amount of material scattered in the literature and not systematically organized in any existing textbook or monograph. Key features: * Basic constructions and definitions are presented in preliminary background chapters so that the work is self-contained * Applications are presented * Open questions for graduate students and researchers * Good bibliography and index The book provides an introduction to current research in mathematical physics and is particularly useful to graduate students or researchers just entering this field.

This volume focuses on the interactions between mathematics, physics, biology and neuroscience by exploring new geometrical and topological modelling in these fields. Among the highlights are the central roles played by multilevel and scale-change approaches in these disciplines.The integration of mathematics with physics, as well as molecular and cell biology and the neurosciences, will constitute the new frontier of 21st century science, where breakthroughs are more likely to span across traditional disciplines.

Steps forward in mathematics often reverberate in other scientific disciplines, and give rise to innovative conceptual developments or find surprising technological applications. This volume brings to the forefront some of the proponents of the mathematics of the twentieth century, who have put at our disposal new and powerful instruments for investigating the reality around us. The portraits present people who have impressive charisma and wide-ranging cultural interests, who are passionate about defending the importance of their own research, are sensitive to beauty, and attentive to the social and political problems of their times. What we have sought to document is mathematics’ central position in the culture of our day. Space has been made not only for the great mathematicians but also for literary texts, including contributions by two apparent interlopers, Robert Musil and Raymond Queneau, for whom mathematical concepts represented a valuable tool for resolving the struggle between ‘soul and precision.’

Steps forward in mathematics often reverberate in other scientific disciplines, and give rise to innovative conceptual developments or find surprising technological applications.