Imperial College London

ProfessorKevinBuzzard

Faculty of Natural SciencesDepartment of Mathematics

Professor of Pure Mathematics
 
 
 
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Contact

 

k.buzzard Website

 
 
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Location

 

660Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
to

26 results found

Buzzard K, Gee T, 2016, Slopes of Modular Forms, FAMILIES OF AUTOMORPHIC FORMS AND THE TRACE FORMULA, Pages: 93-109, ISSN: 2365-9564

JOURNAL ARTICLE

Buzzard K, Lauder A, 2016, A computation of modular forms of weight one and small level, Annales mathématiques du Québec, ISSN: 2195-4755

JOURNAL ARTICLE

Buzzard K, Verberkmoes A, 2016, Stably uniform affinoids are sheafy, Journal für die reine und angewandte Mathematik (Crelles Journal), Vol: 0, ISSN: 0075-4102

JOURNAL ARTICLE

Buzzard K, 2014, Computing Weight One Modular Forms over C and (F)over-bar(p), COMPUTATIONS WITH MODULAR FORMS, Vol: 6, Pages: 129-146

JOURNAL ARTICLE

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.

JOURNAL ARTICLE

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

JOURNAL ARTICLE

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

JOURNAL ARTICLE

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.

JOURNAL ARTICLE

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

JOURNAL ARTICLE

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

JOURNAL ARTICLE

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.

BOOK CHAPTER

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.

JOURNAL ARTICLE

Buzzard K, 2005, Questions about slopes of modular forms, ASTERISQUE, Pages: 1-15, ISSN: 0303-1179

JOURNAL ARTICLE

Buzzard K, Calegari F, 2005, Slopes of overconvergent 2-adic modular forms, COMPOSITIO MATHEMATICA, Vol: 141, Pages: 591-604, ISSN: 0010-437X

JOURNAL ARTICLE

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

JOURNAL ARTICLE

Buzzard K, Calegari F, 2004, A counterexample to the Gouvea-Mazur conjecture, COMPTES RENDUS MATHEMATIQUE, Vol: 338, Pages: 751-753, ISSN: 1631-073X

JOURNAL ARTICLE

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

CONFERENCE PAPER

Buzzard K, 2003, Analytic continuation of overconvergent eigenforms, JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, Vol: 16, Pages: 29-55, ISSN: 0894-0347

JOURNAL ARTICLE

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

JOURNAL ARTICLE

Buzzard K, 2001, Families of modular forms, Journal de Théorie des Nombres de Bordeaux, Vol: 13, Pages: 43-52, ISSN: 1246-7405

JOURNAL ARTICLE

Buzzard K, Dickinson M, Shepherd-Barron N, Taylor Ret al., 2001, On icosahedral Artin representations, DUKE MATHEMATICAL JOURNAL, Vol: 109, Pages: 283-318, ISSN: 0012-7094

JOURNAL ARTICLE

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

BOOK CHAPTER

Buzzard K, 2000, On level-lowering for mod 2 representations, Mathematical Research Letters, Vol: 7, Pages: 95-110, ISSN: 1073-2780

JOURNAL ARTICLE

Buzzard K, Taylor R, 1999, Companion forms and weight one forms, Annals of Mathematics, Vol: 149, Pages: 905-919, ISSN: 0003-486X

JOURNAL ARTICLE

Buzzard K, 1997, Integral models of certain shimura curves, Duke Mathematical Journal, Vol: 87, Pages: 591-612, ISSN: 0012-7094

JOURNAL ARTICLE

Buzzard K, 1996, On the eigenvalues of the Hecke operator T-2, Journal of Number Theory, Vol: 57, Pages: 130-132, ISSN: 0022-314X

JOURNAL ARTICLE

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