Universität Bonn

Trimester Program: "Periods in Number Theory, Algebraic Geometry and Physics"


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.


Publications

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?

Recorded talk  Lecture notes

Yves André (Institut de Mathématiques de Jussieu): Periods of relative 1-motives

Recorded talk 

Joseph Ayoub (University of Zurich): The conservativity conjecture for Chow motives in characteristic zero 

Recorded talk  Lecture notes

Henrik Bachmann (MPIM): Multiple harmonic q-series at roots of unity and finite & symmetrized multiple zeta values

Recorded talk   Lecture notes

Spencer Bloch (The University of Chicago / MPIM): Periods and regulators

Recorded talk

Mikhail Bondarko (MPIM): Mixed motivic sheaves and weights for them

Slides

David Broadhurst (Open University): Eta quotients, Eichler integrals and L-series

Slides

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 

Recorded talk

Steven Charlton (MPIM): Bowman-Bradley type relations for symmetrized multiple zeta values

Lecture notes

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?

Lecture notes

Michael Hoffman (U.S. Naval Academy): Multiple zeta values and alternating MZVs arising from a combinatorial problem

Slides

Dirk Kreimer (Humboldt-Universität zu Berlin) Amplitudes: a few conundrums

Slides   Recorded Talk

Marianne Leitner (Dublin Institute for Advanced Studies): The modular forms of the simplest quantum field theory

Lecture notes

Andrey Levin (LMS NRU HSE): Modular arrangements

Lecture notes I   Lecture notes II

Marc Levine (Universität Duisburg-Essen): Chow-Witt groups, ramification and quadratic forms

Lecture notes

Nils Matthes (Kyushu University): Rational associator in small depths

Lecture notes

Nils Matthes (Kyushu University): Elliptic analogs of multiple zeta values

Lecture notes

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

Lecture notes

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

Lecture notes 

Sinan Unver (Koc University): Infinitesimal Chow Dilogarithm

Recorded talk

Pierre Vanhove (CEA Saclay): Feynman integrals and Mirror symmetry

Slides

Masha Vlasenko (Institute of Mathematics of the Polish Academy of Sciences): What is... a motivic gamma function?

Lecture notes

Guangyu Zhu  (Yale University): The Galois group of the category of mixed Hodge-Tate structures

Slides


Participants

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.

Poster TP_2018_01.jpg
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