January 2 - April 19, 2013
Organizers: Gerhard Faltings, Roger Heath-Brown, Yuri I. Manin, and Boris Moroz
Description: The main theme of the trimester was the interplay of different methods used in modern number theory. We emphasised the new results and conjectures in arithmetic geometry, having direct bearing on the classical numbertheoretic problems. The proceedings volume, which we published, summarised investigations and discussions during the trimester. Two sessions, on the recently proved Serre conjecture from the 15th of January until the 14th of February (organisers: L. Dieulefait and J-P. Wintenberger) and on counting rational points on algebraic varieties from the 15th of March until the 14th of April (organiser: D.R. Heath-Brown), as well as a couple of shorter workshops, several seminars, and mini-courses were organised. The trimester culminated in a research conference from the 15th until the 19th of April.
Associated Events:
- Trimester Seminar
- Session on the Serre conjecture
- Workshop on the Serre conjecture
- Session on counting rational points on algebraic varieties
- Research Conference
© Wikimedia Commons
| No. | Author(s) | Title | Preprint | Publication |
| 2013a01 | Bandman, T.; Garion, S.; Kunyavskii, B. | Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics | 1302.4667 | Cent. Eur. J. Math. 12(2) (2014), 175–211. https://doi.org/10.2478/s11533-013-0335-4 |
| 2013a02 | Brüdern, J.; Wooley, T. D. | The Hasse principle for systems of diagonal cubic forms | 1304.5165 | Math. Ann. 364(3-4) (2016), 1255–1274. https://doi.org/10.1007/s00208-015-1249-1 |
| 2013a03 | Kuzmin, L. | On a new type of l-adic regulator for algebraic number fields | 1402.1504 | Izv. Math (transl.).79(1) (2015), 109–144. https://doi.org/10.4213/im8177 |
| 2013a04 | Guitart, X.; Masdeu, M.; Sengun, M. H. | Darmon points on elliptic curves over number fields of arbitrary signature | 1404.6650 | Proc. Lond. Math. Soc. 111(2) (2015), 484–518. https://doi.org/10.1112/plms/pdv033 |
| 2013a05 | Buium, A.; Dupuy, T. | Arithmetic differential equations on GLn, I: differential cocycles | 1308.0748 | J. Algebra. 45(4) (2016), 273–291. https://doi.org/10.1016/j.jalgebra.2016.01.026 |
| 2013a06 | Buium, A.; Dupuy, T. | Arithmetic differential equations on GLn, II: arithmetic Lie-Cartan theory | 1308.0744 | Selecta Math. 22(2) (2016), 447–528. https://doi.org/10.1007/s00029-015-0194-x |
| 2013a07 | Buium, A.; Dupuy, T. | Arithmetic differential equations on GLn, III: Galois groups | 1308.0747 | Selecta Math. (N.S.) 22(2) (2016), 529–552. https://doi.org/10.1007/s00029-015-0197-7 |
| 2013a08 | Buium, A.; Manin, Y. I. | Arithmetic differential equations of Painlevé VI type | 1307.3841 | London Math. Soc. Lecture Note Ser., 420 https://doi.org/10.1017/CBO9781316106877.010 |
| 2013a09 | Browning, T. D.; Heath-Brown, D. R. | Forms in many variables and differing degrees | 1403.5937 | J. Eur. Math. Soc. 19(2) (2017), 357–394. https://doi.org/10.4171/JEMS/668 |
| 2013a10 | Browning, T. D.; Dietmann, R.; Heath-Brown, D. R. | Rational points on intersections of cubic and quadric hypersurfaces | 1309.0147 | J. Inst. Math. Jussieu. 14(4) (2015), 703–749. https://doi.org/10.1017/S1474748014000127 |
| 2013a11 | Colliot-Thélène, J-L.; Pál, A.; Skorobogatov, A. N. | Pathologies of the Brauer-Manin obstruction | 1310.5055 | Math. Z. 282(3-4) (2016), 799–817. https://doi.org/10.1007/s00209-015-1565-x |
| 2013a12 | Guitart, X.; Masdeu, M. | Overconvergent cohomology and quaternionic Darmon points | 1307.2556 | J. Lond. Math. Soc. 90(2) (2014), 495–524. https://doi.org/10.1112/jlms/jdu036 |
| 2013a13 | Budylin, R.; Gorchinskiy, S. | Intersections of adelic groups on a surface | 1310.2092 | Sb. Math (transl.). 204(11-12) (2013), 1701–1711. https://doi.org/10.1070/sm2013v204n12abeh004356 |
| 2013a14 | Browning, T. D.; Matthiesen, L. | Norm forms for arbitrary number fields as products of linear polynomials | 1307.7641 | Ann. Sci. Éc. Norm. Supér. 50(6) (2017), 1383–1446. https://doi.org/10.24033/asens.2348 |
| 2013a15 | Brüdern, J.; Wooley, T. D. | Cubic moments of Fourier coefficients and pairs of diagonal quartic forms | 1307.1393 | J. Eur. Math. Soc. 17(11) (2015), 2887–2901. https://doi.org/10.4171/JEMS/574 |
| 2013a16 | Brüdern, J.; Wooley, T. D. | Correlation estimates for sums of three cubes | 1404.3846 | Ann. Sc. Norm. Super. Pisa Cl. Sci. 16(3) (2016), 789–816. https://doi.org/10.2422/2036-2145.201409_013 |
| 2013a17 | Diamond, F.; Savitt, D. | Serre weights for locally reducible two-dimensional Galois representations | 1304.7649 | J. Inst. Math. Jussieu. 14(3) (2015), 639–672. https://doi.org/10.1017/S1474748014000164 |
| 2013a18 | Loughran, D. | The number of varieties in a family which contain a rational point | 1310.6219 | J. Eur. Math. Soc. 20(10) (2018), 2539–2588. https://doi.org/10.4171/JEMS/818 |
| 2013a19 | Kumar, N.; Purkait, S. | A note on the Fourier coefficients of half-integral weight modular forms | 1304.6586 | Arch. Math. 102(4) (2014), 369–378. https://doi.org/10.1007/s00013-014-0622-8 |
| 2013a20 | Grishkov, A. N.; Logachev, D. | Resultantal varieties related to zeroes of L-functions of Carlitz modules | 1205.2900 | Finite Fields Appl. 38 (2016), 116–176. https://doi.org/10.1016/j.ffa.2015.12.004 |
| 2013a21 | Galkin, S.; Katzarkov, L.; Mellit, A.; Shinder, E. | Derived categories of Keum's fake projective planes | Adv. Math. 278 (2015), 238–253. https://doi.org/10.1016/j.aim.2015.03.001 |
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| 2013a22 | Gun, S.; Kumar, N. | A note on Fourier-Jacobi coefficients of Siegel modular forms | 1302.0410 | Arch. Math. 101(6) (2013), 519–524. https://doi.org/10.1007/s00013-013-0586-0 |
| 2013a23 | Harpaz, Y.; Skorobogatov, A. N.; Wittenberg, O. | The Hardy-Littlewood conjecture and rational points | 1304.3333 | Compos. Math. 150(12) (2014), 2095–2111. https://doi.org/10.1112/S0010437X14007568 |
| 2013a24 | Akhtari, S. | Representation of small integers by binary forms | 1508.03602 | Q. J. Math. 66(4) (2015), 1009–1054. https://doi.org/10.1093/qmath/hav026 |
| 2013a25 | Dieulefait, L.; Zenteno, A. | Constructing Hilbert modular forms whithout exceptional primes | 1402.5905 |
Math. Z. 288 (2018), 199–215. |
| 2013a26 | Abrashkin, V. | Galois groups of local fields, Lie algebras and ramification | Arithmetic and Geometry. (2015), 1 – 23. https://doi.org/10.1017/CBO9781316106877.006 |
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| 2013a27 | Adibhatla, R.; Tsaknias, P. | A characterisation of ordinary modular eigenforms with CM | 1206.0177 | Arithmetic and Geometry. (2015), 24 – 35. https://doi.org/10.1017/CBO9781316106877.007 |
| 2013a28 | Benois, D. | Selmer complexes and p-adic Hodge theory | 1404.7386 | Arithmetic and Geometry. (2015), 36 – 88. https://doi.org/10.1017/CBO9781316106877.008 |
| 2013a29 | Browning, T. D. | A survey of applications of the circle method to rational points | Arithmetic and Geometry. (2015), 89 – 113. https://doi.org/10.1017/CBO9781316106877.009 |
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| 2013a30 | Buium, A. | Differential calculus with integers | 1308.5194 | Arithmetic and Geometry. (2015), 139 – 187. https://doi.org/10.1017/CBO9781316106877.011 |
| 2013a31 | Colliot-Thélène, J-L. | Un calcul de groupe de Brauer et une application arithmétique | Arithmetic and Geometry. (2015), 188 – 192. https://doi.org/10.1017/CBO9781316106877.012 |
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| 2013a32 | Dieulefait, L.; Pacetti, A. | Connectedness of Hecke algebras and the Rayuela conjecture: a path to functoriality and modularity | 1402.6270 | Arithmetic and Geometry. (2015), 193 – 216. https://doi.org/10.1017/CBO9781316106877.013 |
| 2013a33 | Hida, H.; Tilouine, J. | Big image of Galois representations and congruence ideals | Arithmetic and Geometry. (2015), 217 – 254. https://doi.org/10.1017/CBO9781316106877.014 |
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| 2013a34 | Kunyavskiĭ, B. | Equations in matrix groups and algebras over number fields and rings: prolegomena to a lowbrow noncommutative Diophantine geometry | Arithmetic and Geometry. (2015), 264 – 282. https://doi.org/10.1017/CBO9781316106877.016 |
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| 2013a35 | Paranjape, K.; Ramakrishnan, D. | Modular forms and Calabi-Yau varieties | 1404.1154 | Arithmetic and Geometry. (2015), 351 – 372. https://doi.org/10.1017/CBO9781316106877.019 |
| 2013a36 | Rosso, G. | Derivative of symmetric square p-adic L-functions via pull-back formula | 1401.1431 | Arithmetic and Geometry. (2015), 373 – 400. https://doi.org/10.1017/CBO9781316106877.020 |
| 2013a37 | Salberger, P. | Uniform bounds for rational points on cubic hypersurfaces | Arithmetic and Geometry. (2015), 401 – 421. https://doi.org/10.1017/CBO9781316106877.021 |
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| 2013a38 | Van Order, J. | On the dihedral Euler characteristics of Selmer groups of abelian varieties | 1112.3825 | Arithmetic and Geometry. (2015), 458 – 492. https://doi.org/10.1017/CBO9781316106877.024 |
| 2013a39 | Viazovska, M. | CM values of higher Green's functions and regularized Petersson products | Arithmetic and Geometry. (2015), 493 – 503. https://doi.org/10.1017/CBO9781316106877.025 |
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| 2013a40 | Ivanov, M. A.; Vostokov, S. V. | The skew-symmetric pairing on the Lubin-Tate formal module | Arithmetic and Geometry. (2015) 255 – 263. https://doi.org/10.1017/CBO9781316106877.015 |
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| 2013a41 | Kuz'min, L. V. | On the l-adic regulator as an ingredient of Iwasawa theory | Arithmetic and Geometry. (2015), 283 – 317. https://doi.org/10.1017/CBO9781316106877.017 |
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| 2013a42 | Tuan, N. D. | On a counting problem for G-shtukas | Arithmetic and Geometry. (2015), 318 – 350. https://doi.org/10.1017/CBO9781316106877.018 |
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| 2013a43 | Skorobogatov, A. N. | Descent on toric fibrations | 1312.7539 | Arithmetic and Geometry. (2015), 422 – 435. https://doi.org/10.1017/CBO9781316106877.022 |
| 2013a44 | Smirnov, A. L. | On filtrations of vector bundles over PZ1 | Arithmetic and Geometry. (2015), 436 – 457. https://doi.org/10.1017/CBO9781316106877.023 |
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| 2013a45 | Smeets, A. | Principes locaux-globaux pour certaines fibrations en torseurs sous un tore | 1305.0756 | Math. Proc. Cambridge Philos. Soc. 158(1) (2015), 131–145. https://doi.org/10.1017/S0305004114000577 |
| 2013a46 | Rosso, G. | Derivative at s=1 of the p-adic L-function of the symmetric square of a Hilbert modular form | 1306.4935 | Israel J. Math. 215(1) (2016), 255–315. https://doi.org/10.1007/s11856-016-1379-5 |
| 2013a47 | Rosso, G. | A formula for the derivative of the p-adic L-function of the symmetric square of a finite slope modular form | 1310.6583 | Amer. J. Math. 138(3) (2016), 821–878. https://doi.org/10.1353/ajm.2016.0023 |
| 2013a48 | Grishkov, A. N.; Logachev, D. | Lattice map for Anderson t-motives: first approach | 1109.0679 | J. Number Theory. 180 (2017), 373–402. https://doi.org/10.1016/j.jnt.2017.04.004 |
| Name | Affiliation |
| Victor Abrashkin | University of Durham |
| Rajender Adibhatla | Universität Regensburg |
| Shabnam Akhtari | University of Oregon |
| Paloma Bengoechea | Collège de France |
| Denis Benois | Université Bordeaux 1 |
| Tobias T. Berger | University of Sheffield |
| Yuri Bilu | IMB Université Bordeaux I |
| Marco Boggi | University of Los Andes |
| Régis de la Bretèche | Institut de Mathématiques de Jussieu - Université Paris Diderot |
| Christophe Breuil | Université Paris-Sud |
| Tim Browning | University of Bristol |
| Jörg Brüdern | Universität Göttingen |
| Roman Budylin | Steklov Mathematical Institute |
| Alexandru Buium | University of New Mexico |
| Henri Carayol | L'Université de Strasbourg et du CNRS |
| Magnus Carlson | University of Stockholm |
| Tommaso Centeleghe | Universität Heidelberg |
| Huan Chen | Ecole normale superieure ENS |
| Narasimha Kumar Cheraku | Universität Heidelberg |
| Przemyslaw Chojecki | Institut Mathématique de Jussieu |
| Przemyslaw Chojecki | Institut Mathématique de Jussieu |
| Laurent Clozel | Université de Paris Sud 11 |
| Jean-Louis Colliot-Thélène | Université Paris-Sud |
| Alberto Cámara | University of Nottingham |
| Ulrich Derenthal | Universität München |
| Fred Diamond | King's College London |
| Rainer Dietmann | Royal Holloway, University of London |
| Luis V. Dieulefait | Universitat de Barcelona |
| Gerhard Faltings | Max-Planck-Institut für Mathematik |
| Ivan Fesenko | University of Nottingham |
| Nuno Freitas | Universitat de Barcelona |
| Nuno Freitas | Universitat de Barcelona |
| Wojciech Jerzy Gajda | The Adam Mickiewicz University |
| David Geraghty | Institute for Advanced Study |
| Sergey O. Gorchinskiy | Steklov Mathematical Institute |
| Frank Gounelas | Humboldt University |
| Xavier Guitart | Universität Duisburg-Essen |
| Shuvra Gupta | University of Iowa |
| Shai Haran | Technion - Israel Institute of Technology |
| Michael Harris | Institut de Mathématiques de Jussieu |
| David Rodney Heath-Brown | University of Oxford |
| Florian Herzig | University of Toronto |
| Alexander Ivanov | Universität Heidelberg |
| Mikhail Ivanov | Saint-Petersburg State University |
| Andrew Kresch | Universität Zürich |
| Boris Kunyavskii | Bar-Ilan University |
| Leonid V. Kuzmin | National Research Center Kurchatov Institute |
| Lars Kühne | SNS Pisa |
| Kai-Wen Lan | University of Minnesota |
| Pierre Le Boudec | Institut of Advanced Study |
| Dmitry Logachev | Universidad Simon Bolivar |
| Oliver Lorscheid | IMPA |
| Daniel Loughran | Leibniz Universität Hannover |
| Yuri I. Manin | Universität Bonn |
| Lilian Matthiesen | University of Bristol |
| David Mendes da Costa | University of Bristol |
| Boris Moroz | Universität Bonn |
| Tuan Ngo Dac | Université de Paris 13 |
| Denis Osipov | Steklov Mathematical Institute |
| Ambrus Pal | Imperial College London |
| Aftab Pande | Cidade Universitária Ilha do Fundao |
| Alexej N. Parshin | Steklov Mathematical Institute |
| Florian Pop | University of Pennsylvania |
| Dinakar Ramakrishnan | Caltech |
| Giovanni Rosso | Université Paris 13 |
| Mohamed Saidi | Exeter University |
| Per Salberger | Chalmers University of Technology |
| Cecília Salgado Guimaraes da Silva | UFRJ |
| Mehmet Haluk Sengun | University of Warwick |
| Evgeny Shinder | Max-Planck-Institut für Mathematik |
| Alexei Skorobogatov | Imperial College London |
| Arne Smeets | Université Paris-Sud 11 |
| Aleksander Leonidovich Smirnov | Steklov Institute of Mathematics |
| Efthymios Sofos | University of Bristol |
| Cesar Alejandro Soto Posada | Universität Tübingen |
| Mike Swarbrick Jones | University of Bristol |
| Jack Thorne | Harvard University |
| Jacques Tilouine | Université Paris 13 |
| Yuri Tschinkel | New York University |
| Jeanine Marie Van Order | The Hebrew University of Jerusalem |
| Pankaj Hemant Vishe | University of York |
| Sergei Vostokov | University of St.Petersburg |
| Yosuhiro Wakabayashi | Kyoto University |
| Nicholas Williams | University of Exeter |
| Jean-Pierre Wintenberger | Université Strasbourg |
| Trevor Wooley | Univeristy of Bristol |
| Yanhong Yang | Universität Mainz |
| Adrián Zenteno | Universidad Nacional Autónoma de México |
This list does not include people who only participated in the workshops.
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