Scientists / Open questions
Richard E. Borcherds
Algebra; automorphic forms; vertex algebras
1998 Fields Medal
8 questions
Central extensions and outer derivations of Borcherds-Kac-Moody superalgebras: the super analog of Borcherds's 1991 central-extension theorems
Borcherds' thirteen open problems on automorphic forms with singularities on Grassmannians
Composite-order modular moonshine and the surviving open problems of Borcherds-Ryba's Modular moonshine II: Tate cohomology of the moonshine module for composite-order elements, the 4B compressed algebra, normalizer actions, and generalized Kac-Moody algebras mod p
The Borcherds–Dolgachev family of modular forms on symmetric tube domains: constructing the analogues of the Enriques -function for the remaining quaternionic, exceptional, real, and complex cases
Lattices like the Leech lattice: classification of Lorentzian lattices having a vector with bounded inner product against all simple roots, and the uniqueness of in dimension at least 26
Uniqueness of the lattice-constructed modules L(r) for Kac–Moody algebras (Borcherds, 1986): is L(r) the only irreducible module with weight r of multiplicity one and no weights of larger norm?
Borcherds' Section 15 open problems on monstrous moonshine Lie (super)algebras: natural constructions, denominator identities, embeddings, and replicability
Borcherds' 1990 problem on Lie algebras for the fixed-point lattices of : automorphic-product generalized Kac-Moody algebras and their natural constructions