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This volume contains the proceedings of the International Conference on Vertex Operator Algebras, Number Theory, and Related Topics, held from June 11-15, 2018, at California State University, Sacramento, California.

The mathematics of vertex operator algebras, vector-valued modular forms and finite group theory continues to provide a rich and vibrant landscape in mathematics and physics. The resurgence of moonshine related to the Mathieu group and other groups, the increasing role of algebraic geometry and the development of irrational vertex operator algebras are just a few of the exciting and active areas at present.

The proceedings centre around active research on vertex operator algebras and vector-valued modular forms and offer original contributions to the areas of vertex algebras and number theory, surveys on some of the most important topics relevant to these fields, introductions to new fields related to these and open problems from some of the leaders in these areas.

Vertex Operator Algebras, Number Theory and Related Topics

P. Bantay, Orbifold deconstruction: A computational approach.

K. Barron, N. Vander Werf, and J. Yang, The level one Zhu algebra for the Virasoro vertex operator algebra.

L. Candelori, J. Fogliasso, C. Marks, and S. Moses, Period relations for Riemann surfaces with many automorphisms.

A. Ros Camacho, On the Landau-Ginzburg/conformal field theory correspondence.

J. F. R. Duncan, From the monster to Thompson to O'Nan.

C. Franc and S. Rayan, Nonabelian Hodge theory and vector valued modular forms; R. L. Griess, Jr., Research topics in finite groups and vertex algebras.

C. H. Lam, Automorphism group of an orbifold vertex operator algebra associated with the Leech lattice.

L. Long, Some numeric hypergeometric supercongruences.

K. Nagatomo, G. Mason, and Y. Sakai, Vertex operator algebras with central charge 8 and 16.

K. Nagatomo, Y. Kurokawa, and Y. Sakai, Pseudo-characters of the symplectic fermions and modular linear differential equations.

G. Mason, Five not-so-easy pieces: Open problems with vertex rings.

M. Miyamoto, Vertex operator algebras and modular invariance..