Dr Erik Panzer

Royal Society University Research Fellow
Mathematical Institute
University of Oxford
Woodstock Road
OX2 6GG, Oxford
United Kingdom

ORCID: 0000-0002-9897-5812

Office N1.07
Andrew Wiles Building



Research interests

Feynman integrals, hyperlogarithms, (elliptic) polylogarithms, (elliptic) multiple zeta values, motivic periods, combinatorial Hopf algebras, renormalization, Dyson-Schwinger equations

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Selected Publications

  1. Cusp and collinear anomalous dimensions in four-loop QCD from form factors (arXiv), Physics Review Letters, Vol. 124, 162001 - 24 April 2020
    with Andreas von Manteuffel and Robert M. Schabinger
  2. Hepp's bound for Feynman graphs and matroids, August 2019
  3. Manifestly dual-conformal loop integration (arXiv), Nuclear Physics B, 942 (May, 2019) pp. 251-302,
    with Jacob Bourjaily and Falko Dulat
  4. Multiple zeta values in deformation quantization (arXiv), Inventiones Mathematicae 222 (2020), pp. 79-159.
    with Peter Banks and Brent Pym
    Introduction: Research case study
    Software: kontsevint and starproducts
  5. Lambert-W solves the noncommutative φ4-model (arXiv), Communications in Mathematical Physics (October 2019)
    with Raimar Wulkenhaar
    The story: Mathematician discusses solving a seemingly unsolvable equation
  6. Feynman integral relations from parametric annihilators (arXiv), Letters in Mathematical Physics, August 2018
    with Thomas Bitoun, Christian Bogner and René Pascal Klausen
  7. Minimally subtracted six loop renormalization of O(n)-symmetric φ4 theory and critical exponents (arXiv), Phys. Rev. D 96:036016 (2017)
    with Mikhail Kompaniets
  8. The Galois coaction on ϕ4 periods (arXiv), Communications in Number Theory and Physics, Vol. 11, 3:657-705 (2017)
    with Oliver Schnetz
  9. The parity theorem for multiple polylogarithms (arXiv), Journal of Number Theory, March 2017, 172:93-113
  10. Computation of Form Factors in Massless QCD with Finite Master Integrals (arXiv), Physical Review D, June 2016, 93:125014
    with Andreas von Manteuffel and Robert M. Schabinger
  11. Graphical functions in parametric space (arXiv), Letters in Mathematical Physics (2017) 107:1177-1192
    with Marcel Golz and Oliver Schnetz
  12. A quasi-finite basis for multi-loop Feynman integrals (arXiv), Journal of High Energy Physics, February 2015, 2015:120
    with Andreas von Manteuffel and Robert M. Schabinger
  13. Feynman integrals and hyperlogarithms (also on arXiv), PhD thesis (Humboldt-Universität zu Berlin, supervisor Dirk Kreimer)
    submitted 26th August 2014, defended 5th February 2015, last updated 24th June 2015
  14. Renormalization, Hopf algebras and Mellin transforms (arXiv), pages 169-202 in Feynman Amplitudes, Periods and Motives, Contemporary Mathematics 648 (AMS, 2015)
  15. Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals (arXiv), Computer Physics Communications 188 (2015), pages 148-166
    Latest version of the program: HyperInt
  16. On hyperlogarithms and Feynman integrals with divergences and many scales (arXiv), Journal of High Energy Physics, March 2014, 2014:71
    Text file: explicit results (format compatbile with Maple™)
  17. On the analytic computation of massless propagators in dimensional regularization (arXiv), Nuclear Physics, Section B 874 (2013), pp. 567-593
    Maple™ files with epsilon-expansions of three- and some four-loop massless propagators: raw data, utilities, illustrative Maple worksheet
  18. Renormalization and Mellin Transforms (arXiv), pp. 195-223 in Computer Algebra in Quantum Field Theory, Texts & Monographs in Symbolic Computation (Springer, 2013)
    with Dirk Kreimer
  19. Hopf algebraic Renormalization of Kreimer's toy model, Master's thesis, June 2011

Selected talks

  1. Multiple Zeta Values in Deformation Quantization
  2. Feynman periods - on graphs, integrals, polytopes and tropical physics
    (TU Kaiserslautern, June 18th, 2019)
  3. Modular graph functions as iterated Eisenstein integrals
    (Durham, November 2019)
  4. Feynman integral relations from parametric annihilators
    (Loops & Legs in Quantum Field Theory, May 3rd, 2018, St Goar)
  5. 6-loop φ4 theory in 4-2ε dimensions
    (Worksop on multi-loop calculations: Methods and applications, June 7th, 2017, Paris)
  6. Feynman integrals, graph polynomials and zeta values
    (North meets South Colloquium, May 26th, 2017, Oxford)
  7. Conical sums and multiple polylogarithms
    (The 5th International Congress on Mathematical Software, July 14th, 2016, Berlin)
  8. Feynman integrals and hyperlogarithms
    (5th Itzykson Colloquium, IHES, April 07th, 2016)
  9. Parametric Feynman integrals with hyperlogarithms
    (Trinity College Dublin, February 15th, 2016)
  10. Symbolic integration of multiple polylogarithms
    (ACA 2015, Kalamata, July 22nd, 2015)
  11. Multiple polylogarithms and Feynman integrals
    (Amplitudes 2015, Zürich, July 7th, 2015)
  12. Master integrals without subdivergences
    (HOCTOOLS NNLO meeting, Athens, January 18th, 2015)
  13. Renormalization by kinematic subtraction and Hopf algebras
    ( Renormalisation from Quantum Field Theory to Random and Dynamical Systems, November 07-09, 2013, Potsdam)
  14. Relations among multiple zeta values
    (Multiple Zeta Values in Mathematics and Physics, October 1-5, 2013, Berlin)
  15. Parametric Feynman integrals and hyperlogarithms
    (Feynman Graphs and Motives, March 18-22, 2013, Bingen)