Volume II, on formal (ZFC) set theory, incorporates a self-contained "chapter 0" on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques provides a solid foundation in set theory and a thorough context for the presentation of advanced topics (such as absoluteness, relative consistency results, two expositions of Godel's construstive universe, numerous ways of viewing recursion and Cohen forcing).

Rough path analysis provides a fresh perspective on Ito's important theory of stochastic differential equations. Key theorems of modern stochastic analysis (existence and limit theorems for stochastic flows, Freidlin-Wentzell theory, the Stroock-Varadhan support description) can be obtained with dramatic simplifications. Classical approximation results and their limitations (Wong-Zakai, McShane's counterexample) receive 'obvious' rough path explanations. Evidence is building that rough paths will play an important role in the future analysis of stochastic partial differential equations and...

An introduction to Griffiths' theory of period maps and domains, focused on algebraic, group-theoretic and differential geometric aspects.

Presents contemporary character theory of finite groups from the basics to the state of the art, with new, refined proofs.

A second volume self-contained introduction to the analytical aspects of automorphic forms, featuring proofs of critical results with examples.

Delivers a broad, conceptual introduction to chromatic homotopy theory, focusing on contact with arithmetic and algebraic geometry.

Recent years have seen a flurry of advances in Fourier restriction theory, with significant applications in number theory, PDEs and geometric analysis. This timely text for specialists and graduate students in analysis, written by a leader in the field, brings the reader to the forefront of these exciting developments.

This book covers the spectral theory of Toeplitz forms and Wiener-Hopf integral operators and their applications in harmonic and functional analysis. With exercises and solutions, historical background, and surveys of the latest results, this is an essential source on Toeplitz theory for students and researchers alike.