This book features a series of lectures that explores three different fields in which functor homology (short for homological algebra in functor categories) has recently played a significant role. For each of these applications, the functor viewpoint provides both essential insights and new methods for tackling difficult mathematical problems.
In the lectures by Aurelien Djament, polynomial functors appear as coefficients in the homology of infinite families of classical groups, e.g. general linear groups or symplectic groups, and their stabilization. Djament's theorem states that...
This book features a series of lectures that explores three different fields in which functor homology (short for homological algebra in functor ca...
The book provides the proof of a complex geometric version of a well-known result in algebraic geometry: the theorem of Riemann Roch Grothendieck for proper submersions. It gives an equality of cohomology classes in Bott Chern cohomology, which is a refinement for complex manifolds of de Rham cohomology. When the manifolds are Kahler, our main result is known. A proof can be given using the elliptic Hodge theory of the fibres, its deformation via Quillen's superconnections, and a version in families of the 'fantastic cancellations' of McKean Singer in local index theory. In the general case,...
The book provides the proof of a complex geometric version of a well-known result in algebraic geometry: the theorem of Riemann Roch Grothendieck for ...
Over the last forty years, David Vogan has left an indelible imprint on the representation theory of reductive groups. His groundbreaking ideas have lead to deep advances in the theory of real and p-adic groups, and have forged lasting connections with other subjects, including number theory, automorphic forms, algebraic geometry, and combinatorics.
Representations of Reductive Groups is an outgrowth of the conference of the same name, dedicated to David Vogan on his 60th birthday, which took place at MIT on May 19-23, 2014. This volume highlights the depth and...
Over the last forty years, David Vogan has left an indelible imprint on the representation theory of reductive groups. His groundbreaking id...
This book focuses on finding all ordinary differential equations that satisfy a given set of properties. It is dedicated to inverse problems of ordinary differential equations, with the Nambu bracket acting as the central tool to the authors approach. The authors start with a characterization of ordinary differential equations in R DEGREESN which have a given set of M N partial and first integrals, before addressing planar polynomial differential systems with a given set of polynomial partial integrals. They continue solving the 16th Hilbert problem (restricted to algebraic limit cycles)...
This book focuses on finding all ordinary differential equations that satisfy a given set of properties. It is dedicated to inverse problems of ord...
This book presents a consistent development of the Kohn-Nirenberg type global quantization theory in the setting of graded nilpotent Lie groups in terms of their representations.
This book presents a consistent development of the Kohn-Nirenberg type global quantization theory in the setting of graded nilpotent Lie groups in ter...
This book provides an overview of the latest developments concerning the moduli of K3 surfaces. It is aimed at algebraic geometers, but is also of interest to number theorists and theoretical physicists, and continues the tradition of related volumes like "The Moduli Space of Curves" and "Moduli of Abelian Varieties," which originated from conferences on the islands Texel and Schiermonnikoog and which have become classics.
K3 surfaces and their moduli form a central topic in algebraic geometry and arithmetic geometry, and have recently attracted a lot of attention from both...
This book provides an overview of the latest developments concerning the moduli of K3 surfaces. It is aimed at algebraic geometers, but is also of ...
Ce travail en deux volumes donne la preuve de la stabilisation de la formule des trace tordue.
Stabiliser la formule des traces tordue est la methode la plus puissante connue actuellement pour comprendre l'action naturelle du groupe des points adeliques d'un groupe reductif, tordue par un automorphisme, sur les formes automorphes de carre integrable de ce groupe. Cette comprehension se fait en reduisant le probleme, suivant les idees de Langlands, a des groupes plus petits munis d'un certain nombre de donnees auxiliaires; c'est ce que l'on appelle les donnees endoscopiques....
Ce travail en deux volumes donne la preuve de la stabilisation de la formule des trace tordue.
This text introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of the most recent developments in the field. For the second edition the context has been extended to general surfaces with hyperbolic ends, which provides a natural setting for development of the spectral theory while still keeping technical difficulties to a minimum. All of the material from the first edition is included and updated, and new sections have been added.
Topics covered include an introduction to the geometry of hyperbolic surfaces, analysis...
This text introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of the most rece...
