Journal: Bulletin of the London Mathematical Society

Abbreviation

Bull. Lond. Math. Soc.

Publisher

Wiley

Journal Volumes

ISSN

0024-6093
1469-2120

Description

Filters

2018 - 201932020 - 202618
Reset filters

Search Results

Publications 1 - 10 of 21
  • Stability estimates for the Vlasov-Poisson system in p-kinetic Wasserstein distances
    Item type: Journal Article
    Iacobelli, Mikaela; Junne, Jonathan (2024)
    Bulletin of the London Mathematical Society
  • A generalized pseudo-rotation with positive topological entropy
    Item type: Journal Article
    Çineli, Erman (2025)
    Bulletin of the London Mathematical Society
    In this note, we give examples of Hamiltonian diffeomorphisms which are on one hand dynamically complicated, for instance, with positive topological entropy, and on the other hand minimal from the perspective of Floer theory. The minimality is in the sense that the barcode of the Floer complex of all iterates of these maps consists of only infinite bars. In particular, the maps have zero barcode entropy.
  • A Faber-Krahn inequality for Wavelet transforms
    Item type: Journal Article
    Ramos, João P.G.; Tilli, Paolo (2023)
    Bulletin of the London Mathematical Society
    For some special window functions psi alpha is an element of H2(C+)$\psi _{\alpha } \in H<^>2(\mathbb {C}<^>+)$, we prove that, over all sets Delta subset of C+$\Delta \subset \mathbb {C}<^>+$ of fixed hyperbolic measure nu(Delta)$\nu (\Delta )$, those for which the Wavelet transform W psi alpha$W_{\psi _{\alpha }}$ with window psi alpha$\psi _{\alpha }$ concentrates optimally are exactly the discs with respect to the pseudo-hyperbolic metric of the upper half space. This answers a question raised by Abreu and Dorfler in Abreu and Dorfler (Inverse Problems 28 (2012) 16). Our techniques make use of a framework recently developed by Nicola and Tilli in Nicola and Tilli (Invent. Math. 230 (2022) 1-30), but in the hyperbolic context induced by the dilation symmetry of the Wavelet transform. This leads us naturally to use a hyperbolic rearrangement function, as well as the hyperbolic isoperimetric inequality, in our analysis.
  • The size-Ramsey number of cubic graphs
    Item type: Journal Article
    Conlon, David; Nenadov, Rajko; Trujić, Miloš (2022)
    Bulletin of the London Mathematical Society
    We show that the size-Ramsey number of any cubic graph with n vertices is O (n^(8/5)), improving a bound of n^(5/3+o(1)) due to Kohayakawa, Rödl, Schacht, and Szemerédi. The heart of the argument is to show that there is a constant C such that a random graph with C n vertices where every edge is chosen independently with probability p ⩾ C n^(−2/5) is with high probability Ramsey for any cubic graph with n vertices. This latter result is best possible up to the constant.
  • The inertia bound is far from tight
    Item type: Journal Article
    Kwan, Matthew; Wigderson, Yuval (2024)
    Bulletin of the London Mathematical Society
    The inertia bound and ratio bound (also known as the Cvetković bound and Hoffman bound) are two fundamental inequalities in spectral graph theory, giving upper bounds on the independence number α(G) of a graph (G) in terms of spectral information about a weighted adjacency matrix of G. For both inequalities, given a graph G, one needs to make a judicious choice of weighted adjacency matrix to obtain as strong a bound as possible. While there is a well-established theory surrounding the ratio bound, the inertia bound is much more mysterious, and its limits are rather unclear. In fact, only recently did Sinkovic find the first example of a graph for which the inertia bound is not tight (for any weighted adjacency matrix), answering a longstanding question of Godsil. We show that the inertia bound can be extremely far from tight, and in fact can significantly underperform the ratio bound: for example, one of our results is that for infinitely many n, there is an n-vertex graph for which even the unweighted ratio bound can prove α(G) ≤ 4n³/⁴, but the inertia bound is always at least n/4. In particular, these results address questions of Rooney, Sinkovic, and Wocjan–Elphick–Abiad.
  • Longest cycles in vertex-transitive and highly connected graphs
    Item type: Journal Article
    Groenland, Carla; Longbrake, Sean; Steiner, Raphael; et al. (2025)
    Bulletin of the London Mathematical Society
    We present progress on three old conjectures about longest paths and cycles in graphs. The first pair of conjectures, due to Lovász from 1969 and Thomassen from 1978, respectively, states that all connected vertex-transitive graphs contain a Hamiltonian path, and that all sufficiently large such graphs even contain a Hamiltonian cycle. The third conjecture, due to Smith from 1984, states that for r ≥2 in every r-connected graph any two longest cycles intersect in at least r vertices. In this paper, we prove a new lemma about the intersection of longest cycles in a graph, which can be used to improve the best known bounds toward all the aforementioned conjectures: First, we show that every connected vertex-transitive graph on n≥3 vertices contains a cycle (and hence path) of length at least Ω(n^(13/21)), improving on Ω(n^(3/5)) from DeVos [arXiv:2302:04255, 2023]. Second, we show that in every r-connected graph with r≥2, any two longest cycles meet in at least Ω(r^(5/8)) vertices, improving on Ω(r^(3/5)) from Chen, Faudree, and Gould [J. Combin. Theory, Ser. B, 72 (1998) no. 1, 143-149]. Our proof combines combinatorial arguments, computer search, and linear programming.
  • Traces of reciprocal singular moduli
    Item type: Journal Article
    Alfes-Neumann, Claudia; Schwagenscheidt, Markus (2020)
    Bulletin of the London Mathematical Society
    We show that the generating series of traces of reciprocal singular moduli is a mixed mock modular form of weight 3/2 whose shadow is given by a linear combination of products of unary and binary theta functions. To prove these results, we extend the Kudla–Millson theta lift of Bruinier and Funke to meromorphic modular functions.
  • Minimum saturated families of sets
    Item type: Journal Article
    Bucić, Matija; Letzter, Shoham; Sudakov, Benny; et al. (2018)
    Bulletin of the London Mathematical Society
  • Quasi-Mobius Homeomorphisms of Morse boundaries
    Item type: Journal Article
    Charney, Ruth; Cordes, Matthew; Murray, Devin (2019)
    Bulletin of the London Mathematical Society
  • Acyclic subgraphs of tournaments with high chromatic number
    Item type: Journal Article
    Fox, Jacob; Kwan, Matthew; Sudakov, Benny (2021)
    Bulletin of the London Mathematical Society
    We prove that every n-vertex tournament G has an acyclic subgraph with chromatic number at least n5/9-o(1), while there exists an n-vertex tournament G whose every acyclic subgraph has chromatic number at most n3/4+o(1). This establishes in a strong form a conjecture of Nassar and Yuster and improves on another result of theirs. Our proof combines probabilistic and spectral techniques together with some additional ideas. In particular, we prove a lemma showing that every tournament with many transitive subtournaments has a large subtournament that is almost transitive. This may be of independent interest.
Publications 1 - 10 of 21