January - April 2009
Organizers: D.R. Heath-Brown, A. MacIntyre, Yu.I. Manin, Yu.V. Matiyasevich, and B.Z. Moroz
Description: The study of Diophantine equations is one of the oldest branches of pure mathematics, and is still flourishing. The 20th century saw great progress: the proof of Siegel’s theorem on integer points of algebraic curves, the negative solution of Hilbert’s 10th problem, the proof of Mordell’s conjecture, and the proof of Fermat’s Last Theorem.
This Hausdorff Trimester Program brought together specialists from different areas of the theory of Diophantine equations and provided an excellent opportunity for interactions between them. A proceedings volume of the workshop was published which is conceived as a survey of the modern theory of Diophantine equations. The four month program culminated in a week long research conference, from the 23rd until the 29th of April.
Associated Events: Workshop on new methods in Hilbert’s 10th problem
© HIM
| No. | Author(s) | Title | Preprint | Publication |
| 2009a01 | Alvanos, P.; Bilu, Y.; Poulakis, D. | Characterizing algebraic curves with infinitely many integral points | 0907.2097 | Int. J. Number Theory. 5(4) (2009), 585–590. https://doi.org/10.1142/S1793042109002274 |
| 2009a02 | Bandman, T.; Grunewald, F.; Kunyavski, B. | Geometry and arithmetic of verbal dynamical systems on simple groups | 0809.0369 | Groups Geom. Dyn. 4(4) (2010), 607–655. https://doi.org/10.4171/GGD/98 |
| 2009a03 | Billerey, N. | Critères d'irréductibilité pour les représentations des courbes elliptiques | 0908.1084 | Int. J. Number Theory. 7(4) (2011), 1001–1032. https://doi.org/10.1142/S1793042111004538 |
| 2009a04 | Bilu, Y.; Strambi, M.; Surroca, A. | Quantitative Chevalley-Weil theorem for curves | 0908.1233 | Monatsh. Math. 171(1) (2013), 1–32. https://doi.org/10.1007/s00605-013-0507-0 |
| 2009a05 | Bilu, Y.; Illengo, M. | Effective Siegel's theorem for modular curves | 0905.0418 | Bull. Lond. Math. Soc. 43(4) (2011), 673–688. https://doi.org/10.1112/blms/bdq130 |
| 2009a06 | Bilu, Y.; Parent, P. | Runge's method and modular curves | 0907.3306 | Int. Math. Res. Not. IMRN. 2011(9) (2011), 1997–2027. https://doi.org/10.1093/imrn/rnq141 |
| 2009a07 | Bilu, Y.; Strambi, M. | Quantitative Riemann existence theorem over a number field | 0809.0345 | Acta Arith. 145(4) (2010), 319–339. https://doi.org/10.4064/aa145-4-2 |
| 2009a08 | Bilu, Y.; Parent, P. | Serre's uniformity problem in the split Cartan case | 0807.4954 | Ann. of Math. 173(1) (2011), 569–584. https://doi.org/10.4007/annals.2011.173.1.13 |
| 2009a09 | Browning, T. D. | The divisor problem for binary cubic forms | 1006.3476 | J. Théor. Nombres Bordeaux. 23(3) (2011), 579–602. https://doi.org/10.5802/jtnb.778 |
| 2009a10 | Brüdern, J.; Kawada, K.; Wooley, T. D. | Additive representation in thin sequences, VIII: Diophantine inequalities in review | Number theory, 20–79. https://doi.org/10.1142/9789814289924_0002 |
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| 2009a11 | Brüdern, J.; Dietmann, R.; Liu, J. Y.; Wooley, T. D | A Birch-Goldbach theorem | Arch. Math. (Basel). 94(1) (2010), 53–58. https://doi.org/10.1007/s00013-009-0086-4 |
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| 2009a12 | Brüdern, J.; Wooley, T. D. | Sparse variance for primes in arithmetic progression | Q. J. Math. 62(2) (2011), 289–305. https://doi.org/10.1093/qmath/hap029 |
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| 2009a13 | Brüdern, J.; Wooley, T. D. | On Waring´s problem: three cubes and a minicube | Nagoya Math. J. 200 (2010), 59–91. https://doi.org/10.1215/00277630-2010-012 |
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| 2009a14 | Bruin, N.; Stoll, M. | The Mordell-Weil sieve: proving non-existence of rational points on curves | 0906.1934 | LMS J. Comput. Math. 13 (2010), 272–306. https://doi.org/10.1112/S1461157009000187 |
| 2009a15 | Chan, P-S.; Flicker, Y. Z. | Cyclic odd degree base change lifting for unitary groups in three variables | 0708.4397 | Int. J. Number Theory. 5(7) (2009), 1247–1309. https://doi.org/10.1142/S1793042109002687 |
| 2009a16 | Cojocaru, A-C.; Grant, D.; Jones, N. | One-parameter families of elliptic curves over Q with maximal Galois representations | Proc. Lond. Math. Soc. 103(4) (2011), 654–675. https://doi.org/10.1112/plms/pdr001 |
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| 2009a17 | Colliot-Thélène, J-L.; Wittenberg, O. | Groupe de Brauer et points entiers de deux familles de surfaces cubiques affines | 0911.3539 | Amer. J. Math. 134(5) (2012), 1303–1327. https://doi.org/10.1353/ajm.2012.0036 |
| 2009a18 | D'Aquino, P.; Macintyre, A. | Quadratic forms in models of ΙΔ0+Ω1, Part II: local equivalence | Ann. Pure Appl. Logic. 162(6) (2011), 447–456. https://doi.org/10.1016/j.apal.2010.12.003 |
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| 2009a19 | Davis, M. | Representation theorems for r.e. sets and a conjecture related to Poonen's larges subring of Q | J. Math. Sci. (transl.). 171(6) (2010), 728–730. https://doi.org/10.1007/s10958-010-0176-7 |
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| 2009a20 | Derenthal, U.; Loughran, D. | Singular del Pezzo surfaces that are equivariant compactifications | 0910.2717 | J. Math. Sci. (transl.) 171(6) (2010), 714–724. https://doi.org/10.1007/s10958-010-0174-9 |
| 2009a21 | Dieulefait, L. | On the modularity of rigid Calabi-Yau threefolds: epilogue | 0908.1210 | J. Math. Sci. (transl.). 171(6) (2010), 725–727. https://doi.org/10.1007/s10958-010-0175-8 |
| 2009a22 | Ieronymou, E.; Skorobogatov, A. N.; Zarhin, Y. G. | On the Brauer group of diagonal quartic surfaces | 0912.2865 | J. Lond. Math. Soc. 83(3) (2011), 659–672. https://doi.org/10.1112/jlms/jdq083 |
| 2009a23 | Evertse, J-H. | On the quantitative subspace theorem | 1008.2268 | J. Math. Sci. (transl.). 171(6) (2010), 824–837. https://doi.org/10.1007/s10958-010-0185-6 |
| 2009a24 | Flenner, J. | Relative decidability and definability in Henselian valued fields | 0910.2682 | J. Symbolic Logic. 76(4) (2011), 1240–1260. https://doi.org/10.2178/jsl/1318338847 |
| 2009a25 | Flicker, Y. Z. | Base change for Hilbert eigenvarieties of unitary groups | J. Math. Sci. (transl.). 171(6) (2010), 786–812. https://doi.org/10.1007/s10958-010-0183-8 |
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| 2009a26 | Györy, K.; Hajdu, L.; Tijdeman, R. | Irreducibility criteria of Schur-type and Pólya-type | Monatsh. Math. 163(4) (2011), 415–443. https://doi.org/10.1007/s00605-010-0241-9 |
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| 2009a27 | Heath-Brown, D. R. | Zeros of systems of p-adic quadratic forms | 0810.1122 | Compos. Math. 146(2) (2010), 271–287. https://doi.org/10.1112/S0010437X09004497 |
| 2009a28 | Heath-Brown, D. R. | Bounds for the cubic Weyl sum | 0905.1869 | J. Math. Sci. (transl.). 171(6) (2010), 813–823. https://doi.org/10.1007/s10958-010-0184-7 |
| 2009a29 | Helfgott, H. A.; de Roton, A. | Improving Roth's theorem in the primes | 0912.1842 | Int. Math. Res. Not. IMRN. 2011(4) (2011), 767–783. https://doi.org/10.1093/imrn/rnq108 |
| 2009a30 | Jones, N. | GL2-representations with maximal image | Math. Res. Lett. 22(3) (2015), 803–839. https://doi.org/10.4310/MRL.2015.v22.n3.a10 |
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| 2009a31 | Jones, N. | Pairs of elliptic curves with maximal Galois representations | J. Number Theory. 133(10) (2013), 3381–3393. https://doi.org/10.1016/j.jnt.2013.03.002 |
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| 2009a32 | Marmon, O. | A generalization of the Bombieri-Pila determinant method | 0905.4443 | J. Math. Sci. (transl.). 171(6) (2010), 736–744. https://doi.org/10.1007/s10958-010-0178-5 |
| 2009a33 | Matiyasevich, Y. | Towards finite-fold Diophantine representations | J. Math. Sci. (transl.). 171(6) (2010), 745–752. https://doi.org/10.1007/s10958-010-0179-4 |
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| 2009a34 | Pasten, H.; Pheidas, T.; Vidaux, X. | A survey on Büchi's problem: new presentations and open problems | J. Math. Sci. (transl.). 171(6) (2010), 765–781. https://doi.org/10.1007/s10958-010-0181-x |
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| 2009a35 | Poonen, B. | Curves over every global field violating the local-global principle | 0902.3965 | J. Math. Sci. (transl.). 171(6) (2010), 782–785. https://doi.org/10.1007/s10958-010-0182-9 |
| 2009a36 | Poonen, B. | Multivariable polynomial injections on rational numbers | 0902.3961 | Acta Arith. 145(2) (2010), 123–127. https://doi.org/10.4064/aa145-2-2 |
| 2009a37 | Pupyrev, Y. A. | Rational approximations of the number 3√3 | Math. Notes (transl.). 86(5-6) (2009), 693–703. https://doi.org/10.1134/S0001434609110121 |
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| 2009a38 | Salberger, P.; Wooley, T. D. | Rational points on complete intersections of higher degree, and mean values of Weyl sums | J. Lond. Math. Soc. 82(2) (2010), 317–342. https://doi.org/10.1112/jlms/jdq027 |
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| 2009a39 | Shlapentokh, A.; Vidaux, X. | The analogue of Büchi's problem for function fields | 1004.0731 | J. Algebra. 330 (2011), 482–506. https://doi.org/10.1016/j.jalgebra.2011.01.008 |
| 2009a40 | Sirokofskich, A. | Decidability of sub-theories of polynomials over a finite field | Mathematical theory and computational practice, 437–446. https://doi.org/10.1007/978-3-642-03073-4_45 |
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| 2009a41 | Sirokofskich, A. | On an exponential predicate in polynomials over finite fields | Proc. Amer. Math. Soc. 138(7) (2010), 2569–2583. https://doi.org/10.1090/S0002-9939-10-10258-5 |
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| 2009a42 | Skorobogatov, A. N.; Zarhin, Y. G. | The Brauer group of Kummer surfaces and torsion of elliptic curves | 0911.2261 | J. Reine Angew. Math. 666 (2012), 115–140. https://doi.org/10.1515/CRELLE.2011.121 |
| 2009a43 | Zahid, J. | Non-singular points on hypersurfaces over Fq | 1001.0684 | J. Math. Sci. (transl.). 171(6) (2010), 731–735. https://doi.org/10.1007/s10958-010-0177-6 |
| 2009a44 | Flicker, Y. Z. | On level-raising congruences | 0811.4094 | Asian J. Math. 13(2) (2009), 151–180. https://doi.org/10.4310/AJM.2009.v13.n2.a1 |
| 2009a45 | Harari, D.; Voloch, J. F. | The Brauer-Manin obstruction for integral points on curves | - | Math. Proc. Cambridge Philos. Soc. 149(3) (2010), 413–421. https://doi.org/10.1017/S0305004110000381 |
| 2009a46 | Niedermowwe, N. | The circle method with weights for the representation of integers by quadratic forms | 0905.1229 | J. Math. Sci. (transl.). 171(6) (2010), 753–764. https://doi.org/10.1007/s10958-010-0180-y |
| 2009a47 | Poonen, B. | Automorphisms mapping a point into a subvariety | 0902.3571 | J. Algebraic Geom. 20(4) (2011), 785–794. https://doi.org/10.1090/S1056-3911-2011-00543-2 |
| 2009a48 | Schlank, T. M. | On the Brauer-Manin obstruction applied to ramified covers | 0911.5728 | |
| 2009a49 | Browning, T. D.; Heath-Brown, D. R. | Quadratic polynomials represented by norm forms | 1109.0232 | Geom. Funct. Anal. 22(5) (2012), 1124–1190. https://doi.org/10.1007/s00039-012-0168-5 |
Name |
Affiliation |
| Nicolas Billerey | Université Paris VI |
| Yuri Bilu | IMB Université Bordeaux I |
| Régis de la Breteche | Université Paris 7 Denis Diderot |
| Tim Browning | University of Bristol |
| Jörg Brüdern | Universität Stuttgart |
| Maria Carrizosa | Université Paris VI |
| Jean-Louis Colliot-Thélène | Université Paris-Sud |
| Paola D'Aquino | Seconda Università di Napoli |
| Martin Davis | New York University |
| Kirsten Eisenträger | The Pennsylvania State University |
| Jan-Hendrik Evertse | Universiteit Leiden |
| Joseph Flenner | University of California at Berkeley |
| Yuval Flicker | The Ohio State University |
| Kálmán Györy | University of Debrecen |
| Michael Harvey | University of Bristol |
| Roger Heath-Brown | University of Oxford |
| Harald A. Helfgott | University of Bristol |
| Ehud Hrushovski | Hebrew University (Giv'at Ram) |
| Evis Ieronymou | École polytechnique fédérale de Lausanne |
| Moshe Jarden | Tel Aviv University |
| Nathan Conrad Jones | University of Mississippi |
| Andrew Kresch | Universität Zürich |
| Boris Kunyavskii | Bar-Ilan University |
| Daniel Loughran | University of Bristol |
| Angus MacIntyre | Queen Mary University of London |
| Yuri I. Manin | Universität Bonn |
| Oscar Marmon | Chalmers University of Technology and Göteborg University |
| Yuri Matiyasevich | Steklov Institute of Mathematics (POMI) |
| Boris Moroz | Universität Bonn |
| Yuri Nesterenko | Moscow State University |
| Nic Niedermowwe | Exeter College |
| Vladimir Orevkov | Steklov Institute of Mathematics |
| Prem Prakash Pandey | Institute of Mathematical Sciences |
| Athanasios (Thanases) Pheidas | University of Crete |
| Bjorn Poonen | Massachusetts Institute of Technology |
| Florian Pop | University of Pennsylvania |
| Sean Prendiville | University of Bristol |
| Yurii Pupyrev | Moscow Lomonosov State University |
| Wayne Raskind | Arizona State University |
| Per Salberger | Chalmers University of Technology |
| Tomer Schlank | The Hebrew University of Jerusalem |
| Alexandra Shlapentokh | East Carolina University |
| Cecilia Salgado Guimaraes da Silva | Universiteit Leiden |
| Alla Sirokofskich | University of Crete |
| Alexei Skorobogatov | Imperial College London |
| Michael Stoll | Universität Bayreuth |
| Yuri Tschinkel | New York University |
| Alexey Ustinov | Far Eastern Branch of the Russian Academy of Sciences |
| Xavier Vidaux | Universidad de Concepción |
| Bianca Viray | University of California at Berkeley |
| Maxim Vsemirnov | Steklov Institute for Mathematics |
| Anthony Várilly-Alvarado | University of California at Berkeley |
| Trevor Wooley | University of Bristol |
| Jahan Zahid | Jesus College |
This list does not include people who only participated in the workshop or the conference.
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