Helfgott, Harald Andrés

[["dc.bibliographiccitation.firstpage","1"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","Journal of Algebraic Combinatorics"],["dc.bibliographiccitation.lastpage","22"],["dc.bibliographiccitation.volume","40"],["dc.contributor.author","Bamberg, John"],["dc.contributor.author","Gill, Nick"],["dc.contributor.author","Hayes, Thomas P."],["dc.contributor.author","Helfgott, Harald Andrés"],["dc.contributor.author","Seress, Ákos"],["dc.contributor.author","Spiga, Pablo"],["dc.date.accessioned","2017-09-07T11:54:20Z"],["dc.date.available","2017-09-07T11:54:20Z"],["dc.date.issued","2013"],["dc.description.abstract","In this paper we are concerned with the conjecture that, for any set of generators S of the symmetric group Sym(n), the word length in terms of S of every permutation is bounded above by a polynomial of n. We prove this conjecture for sets of generators containing a permutation fixing at least 37 % of the points."],["dc.identifier.arxiv","1205.1596"],["dc.identifier.doi","10.1007/s10801-013-0476-3"],["dc.identifier.gro","3146554"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4334"],["dc.notes.intern","mathe"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.publisher","Springer Nature"],["dc.relation.eissn","1572-9192"],["dc.relation.issn","0925-9899"],["dc.subject","Cayley graph Diameter Babai’s conjecture Babai-Seress conjecture"],["dc.title","Bounds on the diameter of Cayley graphs of the symmetric group"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","333"],["dc.bibliographiccitation.issue","321"],["dc.bibliographiccitation.journal","Mathematics of Computation"],["dc.bibliographiccitation.lastpage","350"],["dc.bibliographiccitation.volume","89"],["dc.contributor.author","Helfgott, Harald Andrés"],["dc.date.accessioned","2021-04-14T08:27:47Z"],["dc.date.available","2021-04-14T08:27:47Z"],["dc.date.issued","2020"],["dc.identifier.doi","10.1090/mcom/3438"],["dc.identifier.eissn","1088-6842"],["dc.identifier.issn","0025-5718"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/82402"],["dc.language.iso","en"],["dc.notes.intern","DOI Import GROB-399"],["dc.relation.eissn","1088-6842"],["dc.relation.issn","0025-5718"],["dc.title","An improved sieve of Eratosthenes"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.journal","The Electronic Journal of Combinatoric"],["dc.bibliographiccitation.volume","6"],["dc.contributor.author","Helfgott, Harald Andrés"],["dc.contributor.author","Gessel, Ira M."],["dc.date.accessioned","2017-09-07T11:47:59Z"],["dc.date.available","2017-09-07T11:47:59Z"],["dc.date.issued","1999"],["dc.description.abstract","We show how to count tilings of Aztec diamonds and hexagons with defects using determinants. In several cases these determinants can be evaluated in closed form. In particular, we obtain solutions to open problems 1, 2, and 10 in James Propp's list of problems on enumeration of matchings [22]."],["dc.identifier.gro","3146821"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4625"],["dc.notes.intern","mathe"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.title","Enumeration of Tilings of Diamonds and Hexagons with Defects"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","357"],["dc.bibliographiccitation.issue","3"],["dc.bibliographiccitation.journal","Bulletin of the American Mathematical Society"],["dc.bibliographiccitation.lastpage","413"],["dc.bibliographiccitation.volume","52"],["dc.contributor.author","Helfgott, Harald Andrés"],["dc.date.accessioned","2017-09-07T11:54:22Z"],["dc.date.available","2017-09-07T11:54:22Z"],["dc.date.issued","2015"],["dc.identifier.doi","10.1090/s0273-0979-2015-01475-8"],["dc.identifier.gro","3146548"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4330"],["dc.notes.intern","Not valid abstract: This is a survey of methods developed in the last few years to prove results on growth in non-commutative groups. These techniques have their roots in both additive combinatorics and group theory, as well as other fields. We discuss linear algebraic groups, with $ \\\\\\\\.athrm {SL}_2(\\\\\\\\.athbb{Z}/p\\\\\\\\.athbb{Z})$ as the basic example, as well as permutation groups. The emphasis will lie on the ideas behind the methods."],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.publisher","American Mathematical Society (AMS)"],["dc.relation.eissn","1088-9485"],["dc.relation.issn","0273-0979"],["dc.title","Growth in groups: ideas and perspectives"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","135"],["dc.bibliographiccitation.journal","Astérisque"],["dc.bibliographiccitation.lastpage","182"],["dc.bibliographiccitation.volume","407"],["dc.contributor.author","Helfgott, Harald Andrés"],["dc.date.accessioned","2020-12-10T18:43:48Z"],["dc.date.available","2020-12-10T18:43:48Z"],["dc.date.issued","2019"],["dc.description.abstract","Not valid abstract: Soient donn'es deux graphes $, $ `a $ sommets. Sont-ils isomorphes? S'ils le sont, l'ensemble des isomorphismes de $ `a $ peut ^etre identifi'e avec une classe pi$ du groupe sym'etrique sur $ 'el'ements. Comment trouver $ et des g'en'erateurs de 0 Le d'efi de donner un algorithme toujours efficace en r'eponse `a ces questions est rest'e longtemps ouvert. Babai a r'ecemment montr'e comment r'esoudre ces questions -- et d'autres qui y sont li'ees -- en temps quasi-polynomial, c'est-`a-dire en temps (O(log n)^{O(1)})$. Sa strat'egie est bas'ee en partie sur l'algorithme de Luks (1980/82), qui a r'esolu le cas de graphes de degr'e born'e. English translation: Graph isomorphisms in quasipolynomial time [after Babai and Luks, Weisfeiler--Leman,...]. Let $, $ be two graphs with $ vertices. Are they isomorphic? If any isomorphisms from $ to $ exist, they form a coset pi$ in the symmetric group on $ elements. How can we find a representative $ and a set of generators for 0 Finding an algorithm that answers such questions efficiently (in all cases) is a challenge that has long remained open. Babai has recently shown how to solve these problems and related ones in quasipolynomial time, i.e., time (O(log n)^{O(1)})$. His strategy is based in part on an algorithm due to Luks (1980/82), who solved the case of graphs of bounded degree."],["dc.identifier.arxiv","1701.04372"],["dc.identifier.doi","10.24033/ast.1063"],["dc.identifier.eissn","2492-5926"],["dc.identifier.gro","3146794"],["dc.identifier.issn","0303-1179"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/78233"],["dc.notes.intern","DOI Import GROB-354"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.title","Isomorphismes de graphes en temps quasi-polynomial (d’après Babai et Luks, Weisfeiler-Leman, ...)"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","527"],["dc.bibliographiccitation.issue","3"],["dc.bibliographiccitation.journal","Journal of the American Mathematical Society"],["dc.bibliographiccitation.lastpage","550"],["dc.bibliographiccitation.volume","19"],["dc.contributor.author","Helfgott, Harald Andrés"],["dc.contributor.author","Venkatesh, A."],["dc.date.accessioned","2017-09-07T11:47:52Z"],["dc.date.available","2017-09-07T11:47:52Z"],["dc.date.issued","2006"],["dc.description.abstract","We give new bounds for the number of integral points on elliptic curves. The method may be said to interpolate between approaches via diophantine techniques ([BP], [HBR]) and methods based on quasiorthogonality in the Mordell-Weil lattice ([Sil6], [GS], [He]). We apply our results to break previous bounds on the number of elliptic curves of given conductor and the size of the 3-torsion part of the class group of a quadratic field. The same ideas can be used to count rational points on curves of higher genus."],["dc.identifier.doi","10.1090/s0894-0347-06-00515-7"],["dc.identifier.gro","3146787"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4590"],["dc.language.iso","en"],["dc.notes.intern","mathe"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0894-0347"],["dc.title","Integral points on elliptic curves and 3-torsion in class groups"],["dc.type","journal_article"],["dc.type.internalPublication","no"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.contributor.author","Helfgott, Harald Andrés"],["dc.date.accessioned","2017-09-07T11:54:22Z"],["dc.date.available","2017-09-07T11:54:22Z"],["dc.date.issued","2015"],["dc.description.abstract","The ternary Goldbach conjecture (or three-prime conjecture) states that every odd number greater than 5 can be written as the sum of three primes. The purpose of this book is to give the first proof of the conjecture, in full."],["dc.identifier.arxiv","1501.05438"],["dc.identifier.gro","3146544"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4327"],["dc.notes.intern","mathe"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.title","The ternary Goldbach problem"],["dc.type","preprint"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","433"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","Journal de Théorie des Nombres de Bordeaux"],["dc.bibliographiccitation.lastpage","472"],["dc.bibliographiccitation.volume","19"],["dc.contributor.author","Helfgott, Harald Andrés"],["dc.date.accessioned","2017-09-07T11:47:54Z"],["dc.date.available","2017-09-07T11:47:54Z"],["dc.date.issued","2007"],["dc.identifier.doi","10.5802/jtnb.596"],["dc.identifier.gro","3146785"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4587"],["dc.notes.intern","mathe"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.publisher","Cellule MathDoc/CEDRAM"],["dc.relation.issn","1246-7405"],["dc.title","Power-free values, large deviations, and integer points on irrational curves"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","611"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","Annals of Mathematics"],["dc.bibliographiccitation.lastpage","658"],["dc.bibliographiccitation.volume","179"],["dc.contributor.author","Helfgott, Harald Andrés"],["dc.contributor.author","Seress, Ákos"],["dc.date.accessioned","2017-09-07T11:54:20Z"],["dc.date.available","2017-09-07T11:54:20Z"],["dc.date.issued","2014"],["dc.description.abstract","Given a finite group G and a set A of generators, the diameter diam(Γ(G,A)) of the Cayley graph Γ(G,A) is the smallest ℓ such that every element of G can be expressed as a word of length at most ℓ in A∪A−1. We are concerned with bounding diam(G):=maxAdiam(Γ(G,A)). It has long been conjectured that the diameter of the symmetric group of degree n is polynomially bounded in n, but the best previously known upper bound was exponential in nlogn−−−−−√. We give a quasipolynomial upper bound, namely, diam(G)=exp(O((logn)4loglogn))=exp((loglog"],["dc.identifier.doi","10.4007/annals.2014.179.2.4"],["dc.identifier.gro","3146557"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4337"],["dc.notes.intern","mathe"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.publisher","Princeton University"],["dc.relation.issn","0003-486X"],["dc.subject","Cayley graphs graph diameters permutation groups"],["dc.title","On the diameter of permutation groups"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","3593"],["dc.bibliographiccitation.issue","8"],["dc.bibliographiccitation.journal","Proceedings of the American Mathematical Society"],["dc.bibliographiccitation.lastpage","3602"],["dc.bibliographiccitation.volume","143"],["dc.contributor.author","Gill, Nick"],["dc.contributor.author","Helfgott, Harald Andrés"],["dc.contributor.author","Rudnev, Misha"],["dc.date.accessioned","2017-09-07T11:54:22Z"],["dc.date.available","2017-09-07T11:54:22Z"],["dc.date.issued","2015"],["dc.description.abstract","There is a parallelism between growth in arithmetic combinatorics and growth in a geometric context. While, over R or C, geometric statements on growth often have geometric proofs, what little is known over finite fields rests on arithmetic proofs. We discuss strategies for geometric proofs of growth over finite fields, and show that growth can be defined and proven in an abstract projective plane – even one with weak axioms."],["dc.identifier.doi","10.1090/proc/12309"],["dc.identifier.gro","3146549"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4331"],["dc.notes.intern","mathe"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.publisher","American Mathematical Society (AMS)"],["dc.relation.eissn","1088-6826"],["dc.relation.issn","0002-9939"],["dc.title","On growth in an abstract plane"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]