January 3 - April 20, 2018
Organizers: Spencer Bloch (Chicago), Herbert Gangl (Durham), Vasily Golyshev (Moscow), Fernando Rodriguez Villegas (Trieste), Don Zagier (Bonn)
Description: The word "period" is used to designate any number represented by the integral of an algebraic differential form over a cycle in an algebraic variety over Q (or Q^cl). These include many numbers of interest in number theory and mathematical physics (multiple zeta values, Mahler measures, superstring amplitudes, ...), and also have deep connections with special values of motivic L-functions.
Associated Events: The trimester will be divided into five "activities", each concentrating on one topic and including one or several introductory courses, and also three one-week workshops featuring lectures on current work:
- Motives and Periods (Jan 3 - Jan 14)
- Workshop: Periods and Regulators (Jan 15 - Jan 19)
- Regulators (Jan 20 - Feb 4)
- Amplitudes (Feb 5 - Feb 25)
- Workshop: Amplitudes and Periods (Feb 26 - Mar 2)
- Picard-Fuchs Equations and Geometry (Mar 3 - Mar 25)
- Workshop: Picard-Fuchs Equations and Hypergeometric Motives (Mar 26 - Mar 30)
- Hypergeometric Motives (Mar 31 - Apr 20)
Those planning to participate include:
Yves André, Joseph Ayoub, Alexander Beilinson, David Broadhurst, Francis Brown, José Burgos Gil, Henri Cohen, Christopher Deninger, Charles Doran, Hélène Esnault, Javier Fresán, Alexander Goncharov, Benedict Gross, Richard Hain, Annette Huber-Klawitter, Matt Kerr, Dirk Kreimer, Marc Levine, Steve Lichtenbaum, Madhav Nori, Dinakar Ramakrishnan, David Roberts, Jan Stienstra, Tomohide Terasoma, Pierre Vanhove, Wadim Zudilin
The trimester program is supported by the Max Planck Institute for Mathematics. We are grateful for this support.
No. |
Author(s) |
Title |
Preprint |
Publication |
2018a01 | Deninger, C.; Mellit, A. | ZR and Rings of Witt Vectors WS(R) | 1803.00812 | Rend. Sem. Mat. Univ. Padova, 142 (2019), 93–102 DOI 10.4171/RSMUP/32 |
2018a02 | Broedel, J.; Schlotterer, O.; Zerbini, F. | From Elliptic Multiple Zeta Values to Modular Graph Functions: Open and Closed Strings at One Loop | 1803.00527 | J. High Energ. Phys. 2019(155) (2019) https://doi.org/10.1007/JHEP01(2019)155 |
2018a03 | Caron-Huot, S.; Dixon, L.J.; von Hippel, M.; McLeod, J.A.; Papathanasiou, G. | The Double Pentaladder Integral to All Orders | 1806.01361 | J. High Energ. Phys. 2018(170) (2018). https://doi.org/10.1007/JHEP07(2018)170 |
2018a04 | Enriquez, B.; Furusho, H. | The Betti Side of the Double Shuffle Theory. I. The Harmonic Coproduct | 1803.10151 | Sel. Math. New Ser. 27(79) (2021) https://doi.org/10.1007/s00029-021-00659-w |
2018a05 | Enriquez, B.; Furusho, H. | The Betti Side of the Double Shuffle Theory. II. Torsor Structures | 1807.07786 | Sel. Math. New Ser. 29(3) (2023). https://doi.org/10.1007/s00029-022-00807-w |
2018a06 | Schlotterer, O.; Schnetz, O. | Closed Strings as Single-Valued Open Strings: A Genus-Zero Derivation | 1808.00713 | J. Phys. A: Math. Theor. 52(4) 045401 DOI 10.1088/1751-8121/aaea14 |
2018a07 | Zudilin, W. | Some Hypergeometric Integrals for Linear Forms in Zeta Values | 1804.04129 | Bulletin of the Australian Mathematical Society. 98(3) (2018), 372-375, doi:10.1017/S0004972718000503 |
2018a08 | Bachmann, H.; Tanaka, T. | Rooted Tree Maps and the Kawashima Relations for Multiple Zeta Values | 1801.05381 | Kyushu J. Math. 74 (2020), 169–176 doi:10.2206/kyushujm.74.169 |
2018a09 | Emery, V.; Kim, I. | Quaternionic Hyperbolic Lattices of Minimal Covolume | 1802.07776 | Forum of Mathematics, Sigma 10 (2022): e68. https://doi.org/10.1017/fms.2022.43. |
2018a10 | Adams, L.; Chaubey, E.; Weinzierl, S. | Planar Double Box Integral for Top Pair Production with a Closed Top Loop to all orders in the Dimensional Regularization Parameter |
1804.11144 | PHYSICAL REVIEW LETTERS 121, 142001 (2018) DOI: 10.1103/PhysRevLett.121.142001 |
2018a11 | Adams, L.; Chaubey, E.; Weinzierl, S. | Analytic Results for the Planar Double Box Integral Relevant to Top-Pair Production with a Closed Top Loop | 1806.04981 | J. High Energ. Phys. 2018, 206 (2018). https://doi.org/10.1007/JHEP10(2018)206 |
2018a12 | Colmez, P.; Nizioł, W. | On p-Adic Comparison Theorems for Rigid Analytic Varieties, I | 1905.04721 | Münster J. of Math. 13 (2020), 445–507, DOI 10.17879/90169648511 |
2018a13 | Osburn, R.; Straub, A. | Interpolated Sequences and Critical L-Values of Modular Forms | 1806.05207 | Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory. Texts & Monographs in Symbolic Computation. Springer, Cham. https://doi.org/10.1007/978-3-030-04480-0_14 |
2018a14 | Belmans, P.; Galkin, S.; Mukhopadhyay, S. | Examples Violating Golyshev's Canonical Strip Hypotheses | 1806.07648 | Experimental Mathematics 31 (1): 233–37. doi:10.1080/10586458.2019.1602571. |
2018a15 | Dembélé, L.; Panchishkin, A.; Voight, J.; Zudilin, W. | Special Hypergeometric Motives and their L-Functions: Asai Recognition | 1906.07384 | Experimental Mathematics 31 (4): 1278–90. doi:10.1080/10586458.2020.1737990. |
2018a16 | Kedlaya, K.S. | Frobenius Structures on Hypergeometric Equations | 1912.13073 | Arithmetic, Geometry, Cryptography, and Coding Theory 2021 Contemporary Mathematics, 2022, p. 133-158, https://doi.org/10.1090/conm/779/15673 |
2018a17 | Caron-Huot, S.; Dixon, L.J.; Dulat, F.; von Hippel, M.; McLeod, A.J.; Papathanasiou, G. | Six-Gluon Amplitudes in Planar N=4 Super-Yang-Mills Theory at Six and Seven Loops | 1903.10890 | J. High Energ. Phys. 2019, 16 (2019). https://doi.org/10.1007/JHEP08(2019)016 |
2018a18 | Caron-Huot, S.; Dixon, J.L.; Dulat, F.; von Hippel, M.; McLeod, A.J.; Papathanasiou, G. | The Cosmic Galois Group and Extended Steinmann Relations for Planar N=4 SYM Amplitudes | 1906.07116 | J. High Energ. Phys. 2019, 61 (2019). https://doi.org/10.1007/JHEP09(2019)061 |
2018a19 | Ahlén, O.; Kleinschmidt, A. | D6 R4 Curvature Corrections, Modular Graph Functions and Poincaré Series | 1803.10250 | J. High Energ. Phys. 2018, 194 (2018). https://doi.org/10.1007/JHEP05(2018)194 |
2018a20 | Iritani, H. | Quantum D-Modules of Toric Varieties and Oscillatory Integrals | preprint (not on arxiv) | to appear in the volume "Handbook for Mirror Symmetry of Calabi-Yau and Fano manifolds" by higher education press and international press |
2018a21 | Unver, S. | Infinitesimal Bloch Regulator | 1904.06694 | Journal of Algebra. 559(1) (2020), 203-225, https://doi.org/10.1016/j.jalgebra.2020.05.003 |
2018a22 | Unver, S. | A Survey of the Additive Dilogarithm | 1904.05409 | Arithmetic L-Functions and Differential Geometric Methods . Progress in Mathematics, vol 338. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-65203-6_10 |
2018a23 | Broedel, J.; Duhr, C.; Dulat, F.; Penante, B.; Tancredi, L. | Elliptic Symbol calculus: From Elliptic Polylogarithms to Iterated Integrals of Eisenstein Series | 1803.10256 | J. High Energ. Phys. 2018, 14 (2018). https://doi.org/10.1007/JHEP08(2018)014 |
2018a24 | Bachmann, H.; Charlton, S. | Generalized Jacobi-Trudi Determinants and Evaluations of Schur Multiple Zeta Values | 1908.05061 | European Journal of Combinatorics, 87 (2020), 103133, ISSN 0195-6698, https://doi.org/10.1016/j.ejc.2020.103133. |
2018a25 | Bruggeman, R.; Choie, Y. | Modular Cocycles and Cup Product | Advances in Mathematics. 351 (2019), 296-342, https://doi.org/10.1016/j.aim.2019.05.008 | |
2018a26 | Tarasov, V.; Varchenko, A. | q-Hypergeometric Solutions of Quantum Differential Equations, Quantum Pieri Rules, and Gamma Theorem | 1710.03177 | Journal of Geometry and Physics. 142 (2019), 179-212, https://doi.org/10.1016/j.geomphys.2019.04.005 |
2018a27 | Fresán, J.; Sabbah, C.; Yu, J.-D. | Hodge Theory of Kloosterman Connections | 1810.06454 | Duke Math. J. 171(8): 1649-1747 (1 June 2022). DOI: 10.1215/00127094-2021-0036 |
2018a28 | Luo, M. | Algebraic de Rham Theory for Relative Completion of SL_2(Z) | 1804.06977 | Trans. Amer. Math. Soc. 376 (2023), 7743-7782DOI: https://doi.org/10.1090/tran/9014 |
2018a29 | Bitoun, T.; Bogner, C.; Klausen, R.P.; Panzer, E. | Feynman Integral Relations from Parametric Annihilators | 1712.09215 | Lett Math Phys 109, 497–564 (2019). https://doi.org/10.1007/s11005-018-1114-8 |
2018a30 | Banks, P.; Panzer, E.; Pym, B. | Multiple Zeta Values in Deformation Quantization | 1812.11649 | Invent. math. 222, 79–159 (2020). https://doi.org/10.1007/s00222-020-00970-x |
2018a31 | Matthes, N.; Tasaka, K. | On Ecalle's and Brown's Polar Solutions to the Double Shuffle Equations Modulo Products | 1805.09500 | Kyushu J. Math. 73 (2019), 337–356 doi:10.2206/kyushujm.73.337 |
2018a32 | Beukers, F.; Vlasenko, M. | Dwork Crystals I | 1903.11155 | International Mathematics Research Notices, 2021(12) (2021), 8807–8844, https://doi.org/10.1093/imrn/rnaa119 |
2018a33 | Bloch, S.; Vlasenko, M. | Gamma Functions, Monodromy and Apéry Constants | 1908.07501 | |
2018a34 | Mafra, C.R.; Schlotterer, O. | Towards the n-Point One-Loop Superstring Amplitude III: One-Loop Correlators and their Double-Copy Structure | 1812.10971 | J. High Energ. Phys. 2019(92) (2019). https://doi.org/10.1007/JHEP08(2019)092 |
2018a35 | Radchenko, D.; Villegas, F.R. | Goursat Rigid Local Systems of Rank Four | 1803.08379 |
Res Math Sci 5, 38 (2018). https://doi.org/10.1007/s40687-018-0156-y |
2018a36 | Bajpai, J.; Harder, G.; Horozov, I.; Giusti, M.M. | Boundary and Eisenstein Cohomology of SL_3(Z) | 1812.03734 | Math. Ann. 377 (2020), 199–247, https://doi.org/10.1007/s00208-020-01976-9 |
2018a37 | Banerjee, A. | A Topological Nullstellensatz for Tensor-Triangulated Categories | Comptes Rendus Mathematique. 356(4) (2018), 365-375, https://doi.org/10.1016/j.crma.2018.02.012 | |
2018a38 | Movasati, H.; Loyola, R.V. | Periods of Linear Algebraic Cycles | 1705.00084 | |
2018a39 | Loyola, R.V. | Periods of Complete Intersection Algebraic Cycles | 1812.03964 | Manuscripta math. 167 (2022), 765–792, https://doi.org/10.1007/s00229-021-01290-x |
2018a39 | André, Y.; Corvaja, P.; Zannier, U. | The Betti map Associated to a Section of an Abelian Scheme (with an appendix by Z. Gao) | 1802.03204 | Invent. math. 222 (2020), 161–202. https://doi.org/10.1007/s00222-020-00963-w |
2018a40 | André, Y. | Groupes de Galois Motiviques et Périodes | 1606.03714 | Séminaire Bourbaki. Vol. 2015/2016. Exposés 1104–1119 Astérisque(2017), no.390, Exp. No. 1104, 1–26.ISBN:978-2-85629-855-8 |
2018a41 | Burns, D.; de Jeu, R.; Gangl, H.; Rham, A.D.; Yasaki, D. | Hyperbolic Tessellations and Generators of K_3 for Imaginary Quadratic Fields | 1909.09091 | Forum of Mathematics, Sigma 9 (2021): e40. https://doi.org/10.1017/fms.2021.9 |
2018a42 | Charlton, S.; Gangl, H.; Radchenko, D. | On Functional Equations for Nielsen Polylogarithms | 1908.04770 | Commun.Num.Theor.Phys. 15(2) (2021), 363-454, DOI: 10.4310/CNTP.2021.v15.n2.a4 |
2018a43 | Charlton, S. | Analogues of Cyclic Insertion Type Identities for Multiple Zeta Star Values | 1806.10053 | Kyushu J. Math. 74 (2020), 337–352 doi:10.2206/kyushujm.74.337 |
2018a44 | Špenko, S.; Van den Bergh, M. | Tilting Bundles on Hypertoric Varieties | 1805.05285 | International Mathematics Research Notices, 2021(2) (2021), 1034–1042, https://doi.org/10.1093/imrn/rnz218 |
2018a45 | Charlton, S.; Gangl, H.; Radchenko, D. | Explicit Formulas for Grassmannian Polylogarithms | 1909.13869 | |
2018a46 | Sikirić, M.; Dutour; Elbaz-Vincent, P.; Kupers, A.; Martinet, J. | Voronoi Complexes in Higher Dimensions, Cohomology of GLN(Z)for N≥8 and the Triviality of K8(Z) | 1910.11598 | |
2018a47 | D'Hoker, E. Schlotterer, O. | Fay Identities for Polylogarithms on Higher-Genus Riemann Surfaces | 2407.11476 |
Repository
Yves André (Institut de Mathématiques de Jussieu): What is… a motivic Galois group?
Yves André (Institut de Mathématiques de Jussieu): Periods of relative 1-motives
Joseph Ayoub (University of Zurich): The conservativity conjecture for Chow motives in characteristic zero
Henrik Bachmann (MPIM): Multiple harmonic q-series at roots of unity and finite & symmetrized multiple zeta values
Spencer Bloch (The University of Chicago / MPIM): Periods and regulators
Mikhail Bondarko (MPIM): Mixed motivic sheaves and weights for them
David Broadhurst (Open University): Eta quotients, Eichler integrals and L-series
Johannes Brödel: From elliptic multiple zeta values to modular graph functions: open and closed strings at one loop
Further information (preprint on arXiv)
Francis Brown (University of Oxford): Motivic periods: applications
Francis Brown (University of Oxford): A guide to motivic periods
Steven Charlton (MPIM): Bowman-Bradley type relations for symmetrized multiple zeta values
Steven Charlton (MPIM): Motivic MZV's and the cyclic insertion conjecture
slides with notes
Lance J. Dixon (SLAC): Cosmic Galois Theory and Amplitudes in N=4 Super-Yang-Mills Theory
Lecture notes
Clement Dupont (Université de Montpellier): Mixed Tate motives, bi-arrangements, and irrationality proofs
Lecture notes
Richard Hain (Duke University): What is... relative completion?
Michael Hoffman (U.S. Naval Academy): Multiple zeta values and alternating MZVs arising from a combinatorial problem
Dirk Kreimer (Humboldt-Universität zu Berlin) Amplitudes: a few conundrums
Marianne Leitner (Dublin Institute for Advanced Studies): The modular forms of the simplest quantum field theory
Andrey Levin (LMS NRU HSE): Modular arrangements
Marc Levine (Universität Duisburg-Essen): Chow-Witt groups, ramification and quadratic forms
Nils Matthes (Kyushu University): Rational associator in small depths
Nils Matthes (Kyushu University): Elliptic analogs of multiple zeta values
Erik Panzer (University of Oxford): Multiple zeta values in deformation quantization
Oliver Schlotterer (Max Planck Institut für Gravitationsphysik): Moduli-space integrals in string tree-level amplitudes
Leila Schneps (Institut de Mathématiques de Jussieu): What is... an associator?
Oliver Schnetz (FAU Erlangen-Nürnberg): Graphical hyperlogs
Oliver Schnetz (FAU Erlangen-Nürnberg): What is... the connection between motivic coaction and QFT?
Lecture notes
Oliver Schnetz (FAU Erlangen-Nürnberg): Talk at Bethe Forum
Lecture notes
Anthony Scholl (University of Cambridge)/Jan Nekovar (Universite Pierre et Marie Curie): Plectic cohomology
Tatsushi Tanaka (Kyoto Sangyo University): Rooted tree maps
Tomohide Terasoma (The University of Tokyo): Period integrals of open Fermat surfaces and special values of hypergeometric functions
Sinan Unver (Koc University): Infinitesimal Chow Dilogarithm
Pierre Vanhove (CEA Saclay): Feynman integrals and Mirror symmetry
Masha Vlasenko (Institute of Mathematics of the Polish Academy of Sciences): What is... a motivic gamma function?
Guangyu Zhu (Yale University): The Galois group of the category of mixed Hodge-Tate structures
Name |
Affiliation |
Piotr Achinger | Instytut Matematyczny PAN |
Xiaohua Ai | Université Pierre Marie Curie (Paris 6) |
Bill Allombert | University of Bordeaux |
Yves André | Institut de Mathématiques de Jussieu |
Joseph Ayoub | University of Zurich |
Henrik Bachmann | MPIM |
Jitendra Bajpai | TU Dresden |
Abhishek Banerjee | Indian Institute of Science |
Hohto Bekki | The University of Tokyo |
Frits Beukers | Utrecht University |
Spencer Bloch | The University of Chicago / MPIM |
David Broadhurst | Open University |
Francis Brown | University of Oxford |
Johannes Brödel | Humboldt-Universität zu Berlin |
José Ignacio Burgos Gil | ICMAT |
Jin Cao | Tsinghua University |
Ozgur Ceyhan | University of Luxembourg |
Steven Charlton | Universität Tübingen |
YoungJu Choie | POSTECH (Pohang University of Science and Technology) |
Henri Cohen | Université de Bordeaux |
Henri Cohen | Université de Bordeaux |
John Alexander Cruz Morales | Max Planck Institute for Mathematics |
Ishai Dan-Cohen | Ben Gurion University |
Christopher Deninger | Universität Münser |
Lance Dixon | SLAC |
Keremcan Dogan | Koc University |
Dmitry Doryn | IBS Center for Geometry and Physics |
Claude Duhr | CERN |
Falko Dulat | SLAC National Accelerator |
Clément Dupont | Université de Montpellier |
Philippe Elbaz-Vincent | Université Grenoble Alpes |
Vincent Emery | Universität Bern |
Hélène Esnault | Freie Universität Berlin |
Hélène Esnault | Freie Universität Berlin |
Matthias Flach | California Institute of Technology |
Javier Fresán | École polytechnique |
Hidekazu Furusho | Nagoya University |
Sergey Galkin | National Research University, Higher School of Economics |
Herbert Gangl | Durham University |
Vasily Golyshev | IITP RAS Moscow |
Richard Hain | Duke University |
Minoru Hirose | Kyushu University |
R. Paul Horja | University of Miami |
Annette Huber-Klawitter | Universtität Freiburg |
Hiroshi Iritani | Kyoto University |
David Jarossay | University of Geneva |
Rob de Jeu | Vrije Universiteit Amsterdam |
Rob de Jeu | Vrije Universiteit Amsterdam |
Peter Jossen | ETH Zürich |
Ralph Martin Kaufmann | Purdue University |
Adam Keilthy | University of Oxford |
Matthew Kerr | Washington University in St. Louis |
Hyungseop Kim | POSTECH |
Axel Kleinschmidt | Max Planck Institute for Gravitational Physics |
Dirk Kreimer | Humboldt-Universität zu Berlin |
Robert Kucharczyk | ETH Zürich |
Ulf Kühn | Universität Hamburg |
Nathan Lawless | Caltech University |
Marianne Leitner | Dublin Institute for Advanced Studies |
Francesco Lemma | Université Paris 7 Denis Diderot |
Andrey Levin | NRU HSE |
James Lewis | University of Alberta |
Stephen Lichtenbaum | Brown University |
Pierre Lochak | Institut de Mathématiques de Jussieu |
Oliver Lorscheid | Instituto Nacional de Matematica Pura e Aplicada |
Ma Luo | Mathematical Institute, University of Oxford |
Carlos Mafra | University of Southampton |
Vincent Maillot | Institut de Mathématiques de Jussieu (IMJ-PRG) |
Yuri I. Manin | Universität Bonn |
Olivier Martin | Stony Brook University |
Nils Matthes | University of Oxford |
Anton Mellit | University of Vienna |
Hartmut Monien | Universität Bonn |
V. Kumar Murty | University of Toronto |
Werner Nahm | Dublin Institute for Advanced Studies |
Bartosz Naskrecki | Adam Mickiewicz University |
Jan Nekovar | Universite Pierre et Marie Curie |
Nicola Nesa | Albert-Ludwigs-Universität Freiburg |
Wieslawa Niziol | CNRS, Sorbonne Univ. |
Madhav Nori | The University of Chicago |
Robert Osburn | University College Dublin, Belfield |
Erik Panzer | University of Oxford |
Erik Panzer | University of Oxford |
Owen Patashnick | University of Bristol |
Danylo Radchenko | Max Planck Institute for Mathematics |
Niranjan Ramachandran | University of Maryland |
Dinakar Ramakrishnan | California Institute of Technology |
David Roberts | University of Minnesota Morris |
Fernando Rodriguez Villegas | The Abdus Salam Centre for Theoretical Physics |
Fernando Rodriguez Villegas | The Abdus Salam Centre for Theoretical Physics |
Fernando Rodriguez Villegas | The Abdus Salam Centre for Theoretical Physics |
Damian Rössler | Oxford University |
Alex Saad | University of Oxford |
Nobuo Sato | Kyoto University |
Oliver Schlotterer | Max Planck Institut für Gravitationsphysik |
Leila Schneps | Equipe Analyse Algébrique |
Oliver Schnetz | FAU Erlangen-Nürnberg |
Oliver Schnetz | FAU Erlangen-Nürnberg |
Anthony Scholl | University of Cambridge |
Emre Can Sertöz | Max-Planck-Institute for Mathematics in the Sciences |
Daniel Siebel | California Institute of Technology |
Shehryar Sikander | Abdus Salam International Centre for Theoretical Physics |
Vyacheslav P. Spiridonov | Laboratory of theoretical physics, JINR |
Stephan Stieberger | Max-Planck-Institut für Physik |
Jan Stienstra | Utrecht University |
Duco van Straten | JGU Mainz |
Susumu Tanabe | Galatasaray University |
Tatsushi Tanaka | Kyoto Sangyo University |
Koji Tasaka | Max Planck Institute for Mathematics |
Tomohide Terasoma | The University of Tokyo |
Jean-Baptiste Teyssier | KU Leuven |
Gonzalo Tornaría | Universidad de la República |
Sinan Unver | Koc University |
Pierre Vanhove | CEA Saclay |
Alexander Varchenko | University of North Carolina at Chapel Hill |
Raimundas Vidunas | Osaka University |
Roberto Villaflor Loyola | IMPA |
Masha Vlasenko | Institute of Mathematics of the Polish Academy of Sciences |
John Voight | Dartmouth College |
Vadim Vologodsky | National Research Univeristy |
Mark Watkins | University of Sydney |
Stefan Weinzierl | Universität Mainz |
Don Zagier | MPIM |
Yadollah Zare | IMPA |
Federico Zerbini | Institut de Physique Théorique |
Guangyu Zhu | Yale University |
Wadim Zudilin | The University of Newcastle |
This list does not include people who only participate in workshops.