26 results found
Buzzard K, Verberkmoes A, 2018, Stably uniform affinoids are sheafy, JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, Vol: 740, Pages: 25-39, ISSN: 0075-4102
Buzzard K, Lauder A, 2017, A computation of modular forms of weight one and small level, ANNALES MATHEMATIQUES DU QUEBEC, Vol: 41, Pages: 213-219, ISSN: 2195-4755
Buzzard K, Gee T, 2016, Slopes of Modular Forms, FAMILIES OF AUTOMORPHIC FORMS AND THE TRACE FORMULA, Pages: 93-109, ISSN: 2365-9564
Buzzard K, Ciere M, 2014, Playing simple loony dots and boxes endgames optimally, Integers: electronic journal of combinatorial number theory, Vol: 14, ISSN: 1553-1732
We explain a highly efficient algorithm for playing the simplest type of dotsand boxes endgame optimally (by which we mean "in such a way so as to maximisethe number of boxes that you take"). The algorithm is sufficiently simple thatit can be learnt and used in over-the-board games by humans. The types ofendgames we solve come up commonly in practice in well-played games on a 5x5board and were in fact developed by the authors in order to improve theirover-the-board play.
Buzzard K, 2014, Computing Weight One Modular Forms over C and (F)over-bar(p), COMPUTATIONS WITH MODULAR FORMS, Vol: 6, Pages: 129-146
Buzzard K, Gee T, 2014, The conjectural connections between automorphic representations and Galois representations, AUTOMORPHIC FORMS AND GALOIS REPRESENTATIONS, VOL 1, Vol: 414, Pages: 135-187, ISSN: 0076-0552
Buzzard K, Gee T, 2013, Explicit reduction modulo p of certain 2-dimensional crystalline representations, II, BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, Vol: 45, Pages: 779-788, ISSN: 0024-6093
Buzzard K, 2010, Potential modularity---a survey
A Spitalfields Day at the Newton Institute was organised on the subject ofthe recent theorem that any elliptic curve over any totally real field ispotentially modular. This article is a survey of the strategy of the proof,together with some history.
Buzzard K, Diamond F, Jarvis F, 2010, ON SERRE'S CONJECTURE FOR MOD l GALOIS REPRESENTATIONS OVER TOTALLY REAL FIELDS, DUKE MATHEMATICAL JOURNAL, Vol: 155, Pages: 105-161, ISSN: 0012-7094
Buzzard K, Gee T, 2009, Explicit Reduction Modulo p of Certain Two-Dimensional Crystalline Representations, INTERNATIONAL MATHEMATICS RESEARCH NOTICES, Pages: 2303-2317, ISSN: 1073-7928
Buzzard KM, 2007, Eigenvarieties, L-Functions and Galois Representations, Editors: Burns, Buzzard, Nekovar, Publisher: Cambridge University Press, Pages: 59-120, ISBN: 9780521694155
We axiomatise and generalise the "Hecke algebra" construction of the Coleman-Mazur Eigencurve. In particular we extend the construction to general primes and levels. Furthermore we show how to use these ideas to construct "eigenvarieties" parametrising automorphic forms on totally definite quaternion algebras over totally real fields.
Buzzard K, Calegari F, 2006, The 2-adic Eigencurve is Proper
For p=2 and tame level N=1 we prove that the map from the (Coleman-Mazur)Eigencurve to weight space satisfies the valuative criterion of properness.More informally, we show that the Eigencurve has no "holes"; given a punctureddisc of finite slope overconvergent eigenforms over weight space, the centercan be "filled in" with a finite slope overconvergent eigenform.
Buzzard K, Kilford LJP, 2005, The 2-adic eigencurve at the boundary of weight space, COMPOSITIO MATHEMATICA, Vol: 141, Pages: 605-619, ISSN: 0010-437X
Buzzard K, Calegari F, 2005, Slopes of overconvergent 2-adic modular forms, COMPOSITIO MATHEMATICA, Vol: 141, Pages: 591-604, ISSN: 0010-437X
Buzzard K, 2005, Questions about slopes of modular forms, ASTERISQUE, Pages: 1-15, ISSN: 0303-1179
Buzzard K, Calegari F, 2004, A counterexample to the Gouvea-Mazur conjecture, COMPTES RENDUS MATHEMATIQUE, Vol: 338, Pages: 751-753, ISSN: 1631-073X
Buzzard K, 2004, On p-adic families of automorphic forms, Boston, Modular curves and abelian varieties, Bellaterra, Spain, July 2002, Publisher: Birkhauser Verlag, Pages: 23-44
Buzzard K, 2003, Analytic continuation of overconvergent eigenforms, JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, Vol: 16, Pages: 29-55, ISSN: 0894-0347
Buzzard K, Stein WA, 2002, A mod five approach to modularity of icosahedral Galois representations, PACIFIC JOURNAL OF MATHEMATICS, Vol: 203, Pages: 265-282, ISSN: 0030-8730
Buzzard K, Dickinson M, Shepherd-Barron N, et al., 2001, On icosahedral Artin representations, DUKE MATHEMATICAL JOURNAL, Vol: 109, Pages: 283-318, ISSN: 0012-7094
Buzzard K, 2001, Families of modular forms, Journal de Théorie des Nombres de Bordeaux, Vol: 13, Pages: 43-52, ISSN: 1246-7405
Buzzard K, 2001, A mod l multiplicity one result, appendix to "Lectures on Serre's Conjectures" by K. Ribet and W. Stein, Arithmetic algebraic geometry, Editors: Conrad, Rubin, Publisher: American Mathematical Society Institute for Advanced Study, Pages: 223-225, ISBN: 9780821821732
Buzzard K, 2000, On level-lowering for mod 2 representations, Mathematical Research Letters, Vol: 7, Pages: 95-110, ISSN: 1073-2780
Buzzard K, Taylor R, 1999, Companion forms and weight one forms, Annals of Mathematics, Vol: 149, Pages: 905-919, ISSN: 0003-486X
Buzzard K, 1997, Integral models of certain shimura curves, Duke Mathematical Journal, Vol: 87, Pages: 591-612, ISSN: 0012-7094
Buzzard K, 1996, On the eigenvalues of the Hecke operator T-2, Journal of Number Theory, Vol: 57, Pages: 130-132, ISSN: 0022-314X
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