Dr Erik Panzer

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

Office N1.07
Andrew Wiles Building

ORCID: 0000-0002-9897-5812
CV
When did I know it was maths?

Research interests

Coorganized events

• Tropical and Convex Geometry and Feynman integrals, 05-09 September 2022 at ETH-ITS, Zurich
• Special Values of L-functions, Periods, and Fundamental Groups, 27-28 June 2022 at All Souls College, Oxford
• Algebraic Structures in Perturbative Quantum Field Theory, A conference in honor of Dirk Kreimer's 60th birthday, 16-20 November 2020, online via IHES, Bures-sur-Yvette
  Links: videos, proceedings
• Arithmetic and Geometric Aspects of Modular Forms, 22-23 July 2019 at All Souls College, Oxford
• The Mathematics of Linear Relations between Feynman Integrals, 18-22 March 2019, Mainz
• Modular forms, periods and scattering amplitudes, 11 February - 12 April 2019, ETH Institute for Theoretical Studies

Selected Publications

1. Unstable cohomology of GL_2n(ℤ) and the odd commutative graph complex, June 2024
   with Simone Hu and Francis Brown
2. Regularized integrals and manifolds with log corners, December 2023
   with Clément Dupont and Brent Pym
3. Feynman symmetries of the Martin and c₂ invariants of regular graphs, April 2023
   with Karen Yeats
4. Hierarchies in relative Picard-Lefschetz theory, December 2022
   with Marko Berghoff
5. 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
6. Hepp's bound for Feynman graphs and matroids (arXiv), Ann. Inst. Henri Poincaré Comb. Phys. Interact. 10 (2023), no. 1, pp. 31–119
7. Manifestly dual-conformal loop integration (arXiv), Nuclear Physics B, 942 (May, 2019) pp. 251-302,
   with Jacob Bourjaily and Falko Dulat
8. 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
9. 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
10. Feynman integral relations from parametric annihilators (arXiv), Letters in Mathematical Physics, August 2018
    with Thomas Bitoun, Christian Bogner and René Pascal Klausen
11. Minimally subtracted six loop renormalization of O(n)-symmetric φ⁴ theory and critical exponents (arXiv), Phys. Rev. D 96:036016 (2017)
    with Mikhail Kompaniets
12. The Galois coaction on ϕ⁴ periods (arXiv), Communications in Number Theory and Physics, Vol. 11, 3:657-705 (2017)
    with Oliver Schnetz
13. The parity theorem for multiple polylogarithms (arXiv), Journal of Number Theory, March 2017, 172:93-113
14. 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
15. 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
16. Renormalization, Hopf algebras and Mellin transforms (arXiv), pages 169-202 in Feynman Amplitudes, Periods and Motives, Contemporary Mathematics 648 (AMS, 2015)
17. 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
18. 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™)
19. 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
20. Hopf algebraic Renormalization of Kreimer's toy model, Master's thesis, June 2011

Selected talks

1. Cosmic Galois group and φ⁴ theory
   (Straßbourg, July 2022)
2. Multiple Zeta Values in Deformation Quantization
3. Tropical field theory
   (Vienna, November 2021)
4. Modular graph functions as iterated Eisenstein integrals
   (Durham, November 2019)
5. Feynman integral relations from parametric annihilators
   (Loops & Legs in Quantum Field Theory, May 3rd, 2018, St Goar)
6. 6-loop φ⁴ theory in 4-2ε dimensions
   (Worksop on multi-loop calculations: Methods and applications, June 7th, 2017, Paris)
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. Symbolic integration of multiple polylogarithms
   (ACA 2015, Kalamata, July 22nd, 2015)
10. Multiple polylogarithms and Feynman integrals
    (Amplitudes 2015, Zürich, July 7th, 2015)
11. Master integrals without subdivergences
    (HOCTOOLS NNLO meeting, Athens, January 18th, 2015)
12. Renormalization by kinematic subtraction and Hopf algebras
    (Renormalisation from Quantum Field Theory to Random and Dynamical Systems, November 07-09, 2013, Potsdam)
13. Relations among multiple zeta values
    (Multiple Zeta Values in Mathematics and Physics, October 1-5, 2013, Berlin)