Results 11 to 20 of about 63 (61)
Affine opers and conformal affine Toda
Journal of the London Mathematical Society, Volume 104, Issue 5, Page 2148-2207, December 2021., 2021 Abstract For g a Kac–Moody algebra of affine type, we show that there is an AutO‐equivariant identification between FunOpg(D), the algebra of functions on the space of g‐opers on the disc, and W⊂π0, the intersection of kernels of screenings inside a vacuum Fock module π0.
Charles A. S. Young
wiley +1 more source
Katsura–Exel–Pardo groupoids and the AH conjecture
Journal of the London Mathematical Society, Volume 104, Issue 5, Page 2240-2259, December 2021., 2021 Abstract It is proven that Matui's AH conjecture is true for Katsura–Exel–Pardo groupoids GA,B associated to integral matrices A and B. This conjecture relates the topological full group of an ample groupoid with the homology groups of the groupoid. We also give a criterion under which the topological full group [[GA,B]] is finitely generated.
Petter Nyland, Eduard Ortega
wiley +1 more source
Almost uniform domains and Poincaré inequalities
Transactions of the London Mathematical Society, Volume 8, Issue 1, Page 243-298, December 2021., 2021 Abstract Here we show existence of many subsets of Euclidean spaces that, despite having empty interior, still support Poincaré inequalities with respect to the restricted Lebesgue measure. Most importantly, despite the explicit constructions in our proofs, our methods do not depend on any rectilinear or self‐similar structure of the underlying space ...
Sylvester Eriksson‐Bique, Jasun Gong
wiley +1 more source
Dold sequences, periodic points, and dynamics
Bulletin of the London Mathematical Society, Volume 53, Issue 5, Page 1263-1298, October 2021., 2021 Abstract In this survey we describe how the so‐called Dold congruence arises in topology, and how it relates to periodic point counting in dynamical systems.
Jakub Byszewski +2 more
wiley +1 more source
Quasicircles and width of Jordan curves in CP1
Bulletin of the London Mathematical Society, Volume 53, Issue 2, Page 507-523, April 2021., 2021 Abstract We study a notion of ‘width’ for Jordan curves in CP1, paying special attention to the class of quasicircles. The width of a Jordan curve is defined in terms of the geometry of its convex hull in hyperbolic three‐space. A similar invariant in the setting of anti‐de Sitter geometry was used by Bonsante–Schlenker to characterize quasicircles ...
Francesco Bonsante +3 more
wiley +1 more source
Dimension of ergodic measures projected onto self‐similar sets with overlaps
Proceedings of the London Mathematical Society, Volume 122, Issue 2, Page 191-206, February 2021., 2021 Abstract For self‐similar sets on R satisfying the exponential separation condition we show that the dimension of natural projections of shift invariant ergodic measures is equal to min{1,h−χ}, where h and χ are the entropy and Lyapunov exponent, respectively. The proof relies on Shmerkin's recent result on the Lq dimension of self‐similar measures. We
Thomas Jordan, Ariel Rapaport
wiley +1 more source
The boundary of chaos for interval mappings
Proceedings of the London Mathematical Society, Volume 121, Issue 6, Page 1427-1467, December 2020., 2020 Abstract A goal in the study of dynamics on the interval is to understand the transition to positive topological entropy. There is a conjecture from the 1980s that the only route to positive topological entropy is through a cascade of period doubling bifurcations. We prove this conjecture in natural families of smooth interval maps, and use it to study
Trevor Clark, Sofía Trejo
wiley +1 more source
An aperiodic monotile that forces nonperiodicity through dendrites
Bulletin of the London Mathematical Society, Volume 52, Issue 5, Page 942-959, October 2020., 2020 Abstract We introduce a new type of aperiodic hexagonal monotile; a prototile that admits infinitely many tilings of the plane, but any such tiling lacks any translational symmetry. Adding a copy of our monotile to a patch of tiles must satisfy two rules that apply only to adjacent tiles. The first is inspired by the Socolar–Taylor monotile, but can be
Michael Mampusti, Michael F. Whittaker
wiley +1 more source
F‐Manifolds and geometry of information
Bulletin of the London Mathematical Society, Volume 52, Issue 5, Page 777-792, October 2020., 2020 Abstract The theory of F‐manifolds, and more generally, manifolds endowed with commutative and associative multiplication of their tangent fields, was discovered and formalised in various models of quantum field theory involving algebraic and analytic geometry, at least since the 1990s. The focus of this paper consists in the demonstration that various
Noémie Combe, Yuri I. Manin
wiley +1 more source
Proceedings of the London Mathematical Society, Volume 121, Issue 4, Page 954-1032, October 2020., 2020 Abstract I provide an explicit construction of spectral curves for the affine E8 relativistic Toda chain. Their closed‐form expression is obtained by determining the full set of character relations in the representation ring of E8 for the exterior algebra of the adjoint representation; this is in turn employed to provide an explicit construction of ...
Andrea Brini
wiley +1 more source