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## Representation Theory and Algebraic Geometry

The conference “Interactions between Representation Theory and Algebraic Geometry” was held at the University of Chicago on August 21–25, 2017. It brought together about 150 participants from several major universities in the USA and abroad, more than half of whom were junior mathematicians. It featured 21 talks by eminent mathematicians from the USA, Europe, and Asia on topics at the cutting edge of mathematical research. Some junior participants gave introductory talks in the evening to try to make the presentations by the main speakers more accessible to the general audience, in addition to giving poster presentations of their research. The research articles in these proceedings are dedicated, as was the conference, to Alexander Beilinson and Victor Ginzburg, two visionaries in the fields of Representation Theory and Algebraic Geometry, in honor of their 60th birthdays. Their work and mentoring has influenced a great number of researchers and will continue to shape the development of those branches of mathematics for many years to come. Their influence can be perceived throughout this volume, for instance where important roles are played by D-modules and perverse sheaves, Grassmannians and their affine and loop group analogues, categorical approaches to representation theory, versions of Hecke algebras, symplectic algebraic geometry, and many other topics. The chapters have been organized thematically as follows: the first three deal with

the subjects of groups, algebras, and categories and their representation theory; the next four deal with D-modules and perverse sheaves, particularly on flag varieties and their generalizations; the final two deal with analogous varieties defined by quivers and their relationships to representation theory, cohomology theories, and symplectic geometry.