Journal: Proceedings of the American Mathematical Society

Abbreviation

Proc. Am. Math. Soc.

Publisher

American Mathematical Society

Journal Volumes

ISSN

0002-9939
1088-6826

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Publications 1 - 10 of 44
  • On the local structure of rank-one convex hulls
    Item type: Journal Article
    Székelyhidi, László Jr. (2006)
    Proceedings of the American Mathematical Society
  • From Newton's second law to Euler's equations of perfect fluids
    Item type: Journal Article
    Han-Kwan, Daniel; Iacobelli, Mikaela (2021)
    Proceedings of the American Mathematical Society
    Vlasov equations can be formally derived from $ N$-body dynamics in the mean-field limit. In some suitable singular limits, they may themselves converge to fluid dynamics equations. Motivated by this heuristic, we introduce natural scalings under which the incompressible Euler equations can be rigorously derived from $ N$-body dynamics with repulsive Coulomb interaction. Our analysis is based on the modulated energy methods of Brenier and [Comm. Partial Differential Equations 25 (2000), pp. 737-754] Serfaty [Duke Math. J. 169 (2020), pp. 2887-2935].
  • On the topology of nested set complexes
    Item type: Journal Article
    Feichtner, Eva M.; Müller, Irene (2005)
    Proceedings of the American Mathematical Society
  • Gowers' dichotomy for asymptotic structure
    Item type: Journal Article
    Wagner, Roy (1996)
    Proceedings of the American Mathematical Society
    In this article Gowers' dichotomy is extended to the context of weaker forms of unconditionality, most notably asymptotic unconditionality. A general dichotomic principle is demonstrated; a Banach space has either a subspace with some unconditionality property, or a subspace with a corresponding 'proximity of subspaces' property.
  • Turán numbers of sunflowers
    Item type: Journal Article
    Bradac, Domagoj; Bucić, Matija; Sudakov, Benny (2023)
    Proceedings of the American Mathematical Society
    A collection of distinct sets is called a sunflower if the intersection of any pair of sets equals the common intersection of all the sets. Sunflowers are fundamental objects in extremal set theory with relations and applications to many other areas of mathematics as well as to theoretical computer science. A central problem in the area due to Erdős and Rado from 1960 asks for the minimum number of sets of size r needed to guarantee the existence of a sunflower of a given size. Despite a lot of recent attention including a polymath project and some amazing breakthroughs, even the asymptotic answer remains unknown. We study a related problem first posed by Duke and Erdős in 1977 which requires that in addition the intersection size of the desired sunflower be fixed. This question is perhaps even more natural from a graph theoretic perspective since it asks for the Turán number of a hypergraph made by the sunflower consisting of k edges, each of size r and with common intersection of size t. For a fixed size of the sunflower k, the order of magnitude of the answer has been determined by Frankl and Füredi. In the 1980’s, with certain applications in mind, Chung, Erdős and Graham considered what happens if one allows k, the size of the desired sunflower, to grow with the size of the ground set. In the three uniform case, r = 3, the correct dependence on the size of the sunflower has been determined by Duke and Erdős and independently by Frankl and in the four uniform case by Bucić, Draganić, Sudakov and Tran. We resolve this problem for any uniformity, by determining up to a constant factor the n-vertex Turán number of a sunflower of arbitrary uniformity r, common intersection size t and with the size of the sunflower k allowed to grow with n.
  • Simplicial shellable spheres via combinatorial blowups
    Item type: Journal Article
    Cukic, Sonja Lj.; Delucchi, Emanuele (2007)
    Proceedings of the American Mathematical Society
  • Induced Ramsey problems for trees and graphs with bounded treewidth
    Item type: Journal Article
    Hunter, Zach; Sudakov, Benny (2025)
    Proceedings of the American Mathematical Society
    The induced q-color size-Ramsey number r̂_(ind)(H; q) of a graph H is the minimal number of edges a host graph G can have so that every q-edge-coloring of G contains a monochromatic copy of H which is an induced subgraph of G. A natural question, which in the non-induced case has a very long history, asks which families of graphs H have induced Ramsey numbers that are linear in |H|. We prove that for every k, w, q, if H is an n-vertex graph with maximum degree k and treewidth at most w, then r̂_(ind)(H; q) = O_(k,w,q)(n). This extends several old and recent results in Ramsey theory. Our proof is quite simple and relies upon a novel reduction argument.
  • Induced Ramsey problems for trees and graphs with bounded treewidth
    Item type: Journal Article
    Hunter, Zach; Sudakov, Benny (2025)
    Proceedings of the American Mathematical Society
    The induced q-color size-Ramsey number r̂ind(H; q) of a graph H is the minimal number of edges a host graph G can have so that every q-edge-coloring of G contains a monochromatic copy of H which is an induced subgraph of G. A natural question, which in the non-induced case has a very long history, asks which families of graphs H have induced Ramsey numbers that are linear in |H|. We prove that for every k, w, q, if H is an n-vertex graph with maximum degree k and treewidth at most w, then r̂ind(H; q) = Ok,w,q(n). This extends several old and recent results in Ramsey theory. Our proof is quite simple and relies upon a novel reduction argument.
  • Characterization of optimal Transport Plans for the Monge-Kantorovich-Problem
    Item type: Journal Article
    Schachermayer, Walter; Teichmann, Josef (2009)
    Proceedings of the American Mathematical Society
  • Optimal Hamilton covers and linear arboricity for random graphs
    Item type: Journal Article
    Draganić, Nemanja; Glock, Stefan; Munhá Correia, David; et al. (2025)
    Proceedings of the American Mathematical Society
    In his seminal 1976 paper, P´osa showed that for all p ≥ C log n/n, the binomial random graph G(n, p) is with high probability Hamiltonian. This leads to the following natural questions, which have been extensively studied: How well is it typically possible to cover all edges of G(n, p) with Hamilton cycles? How many cycles are necessary? In this paper we show that for p ≥ C log n/n, we can cover G ∼ G(n, p) with precisely Δ(G)/2 Hamilton cycles. Our result is clearly best possible both in terms of the number of required cycles, and the asymptotics of the edge probability p, since it starts working at the weak threshold needed for Hamiltonicity. This resolves a problem of Glebov, Krivelevich and Szab´o [Random Structures Algorithms 44 (2014), pp. 183–200] and improves upon previous work of Hefetz, K¨uhn, Lapinskas and Osthus [Combinatorica 34 (2014), pp. 573–596], and of Ferber, Kronenberg and Long [Israel J. Math. 220 (2017), pp. 57–87], essentially closing a long line of research on Hamiltonian packing and covering problems in random graphs.
Publications 1 - 10 of 44