Many mathematicians are aware of some of the dramatic interactions between ergodic
theory and other parts of the subject, notably Ramsey theory, infinite combinatorics, and …

The importance of recurrence sequences hardly needs to be explained. Their study is
plainly of intrinsic interest and has been a central part of number theory for many years …

" This book by a leading researcher and masterly expositor of the subject studies
diophantine approximations to algebraic numbers and their applications to diophantine …

In this paper, we look at the problem of expressing a term of a given nondegenerate binary
recurrence sequence as a linear combination of a factorial and an S S-unit whose …

The origin of Nevanlinna theory comes from the fundamental theorem of algebra which says
that every complex polynomial equation P (z)= 0 has d number of roots counting …

Diophantine number theory is an active area that has seen tremendous growth over the past
century, and in this theory unit equations play a central role. This comprehensive treatment …

Let K be a field of characteristic 0 and let n be a natural number. Let Γ be a subgroup of the
multiplicative group (K*) n of finite rank r. Given a1,..., an∈ K* write A (a1,..., an, Γ) for the …

In topological quantum computing, information is encoded in “knotted” quantum states of
topological phases of matter, thus being locked into topology to prevent decay. Topological …

This series is devoted to the publication of research monographs, lecture notes, and other
material arising from programs of the Institut de Recherche Mathématique Avancée …

We prove a rank-finiteness conjecture for modular categories: up to equivalence, there are
only finitely many modular categories of any fixed rank. Our technical advance is a …