Representation Theory and Algebraic Geometry

A Conference Celebrating the Birthdays of Sasha Beilinson and Victor Ginzburg
1. Auflage 2022
ISBN: 978-3-030-82009-1
Verlag: Springer International Publishing

Buch, Englisch, 459 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 703 g

Reihe: Trends in Mathematics

The chapters in this volume explore the influence of the Russian school on the development of algebraic geometry and representation theory, particularly the pioneering work of two of its illustrious members, Alexander Beilinson and Victor Ginzburg, in celebration of their 60th birthdays. Based on the work of speakers and invited participants at the conference “Interactions Between Representation Theory and Algebraic Geometry”, held at the University of Chicago, August 21-25, 2017, this volume illustrates the impact of their research and how it has shaped the development of various branches of mathematics through the use of D-modules, the affine Grassmannian, symplectic algebraic geometry, and other topics. All authors have been deeply influenced by their ideas and present here cutting-edge developments on modern topics. Chapters are organized around three distinct themes:

• Groups, algebras, categories, and representation theory
• D-modules and perverse sheaves
• Analogous varieties defined by quivers

Representation Theory and Algebraic Geometry will be an ideal resource for researchers who work in the area, particularly those interested in exploring the impact of the Russian school.

Zielgruppe

Research

Autoren/Hrsg.

Baranovsky, Vladimir

Schedler, Travis

Guay, Nicolas

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

Part I: Groups, algebras, categories, and their representation theory.- On semisimplification of tensor categories.- Total aspherical parameters for Cherednik algebras.- Microlocal approach to Lusztig's symmetries.- Part II: D-modules and perverse sheaves, particularly on flag varieties and their generalizations.- Fourier-Sato Transform on hyperplane arrangements.- A quasi-coherent description of the category D-mod(Gr ).- The semi-infinite intersection cohomology sheaf--II: the Ran space version.- A topological approach to Soergel theory.- Part III: Varieties associated to quivers and relations to representation theory and symplectic geometry.- Loop Grassmannians of quivers and affine quantum groups.- Symplectic resolutions for multiplicative quiver varieties and character varieties for punctured surfaces.