Includes bibliographical references.

Generalizations of $Q$-systems and orthogonal polynomials from representation theory / Darlayne Addabbo and Maarten Bergvelt -- Some applications and constructions of intertwining operators in Logarithmic Conformal Field Theory / Dražen Adamović and Antun Milas -- Kac-Moody groups and automorphic forms in low dimensional supergravity theories / Ling Bao and Lisa Carbone -- The Lusztig-Macdonald-Wall polynomial conjectures and $q$-difference equations / Kathrin Bringmann, Karl Mahlburg and Antun Milas -- Uniqueness of representation-theoretic hyperbolic Kac-Moody groups over $\mathbb {Z}$ / Lisa Carbone and Frank Wagner -- Coends in conformal field theory / Jürgen Fuchs and Christoph Schweigert -- Remarks on $\phi $-coordinated modules for quantum vertex algebras / Haisheng Li -- The classification of chiral WZW models by $H^4_+(BG,\mathbb {Z})$ / André Henriques -- Some open problems in mathematical two-dimensional conformal field theory / Yi-Zhi Huang -- On realization of some twisted toroidal Lie algebras / Naihuan Jing, Chad R. Mangum and Kailash C. Misra -- Twisted generating functions incorporating singular vectors in Verma modules and their localizations, I / James Lepowsky and Jinwei Yang -- Characterization of the simple Virasoro vertex operator algebras with 2 and 3-dimensional space of characters / Yusuke Arike, Kiyokazu Nagatomo and Yuichi Sakai -- Quasiconformal Teichmüller theory as an analytical foundation for two-dimensional conformal field theory / David Radnell, Eric Schippers and Wolfgang Staubach -- Centralizing the centralizers / A. M. Semikhatov -- On Neeman's gradient flows / Nolan R. Wallach --

This volume contains the proceedings of the conference on Lie Algebras, Vertex Operator Algebras, and Related Topics, celebrating the 70th birthday of James Lepowsky and Robert Wilson, held from August 14-18, 2015, at the University of Notre Dame, Notre Dame, Indiana. Since their seminal work in the 1970s, Lepowsky and Wilson, their collaborators, their students, and those inspired by their work, have developed an amazing body of work intertwining the fields of Lie algebras, vertex algebras, number theory, theoretical physics, quantum groups, the representation theory of finite simple groups.