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: 0000000298975812
CV
Research interests
Feynman graphs and Feynman integrals,
hyperlogarithms,
(elliptic) polylogarithms,
(elliptic) multiple zeta values,
motivic periods,
combinatorial Hopf algebras,
renormalization,
resummation
Research grant description: Quantum perturbation theory at large orders
Coorganized events

Tropical and Convex Geometry and Feynman integrals, 0509 September 2022 at ETHITS, Zurich

Special Values of Lfunctions, Periods, and Fundamental Groups,
2728 June 2022 at All Souls College, Oxford

Algebraic Structures in Perturbative Quantum Field Theory,
A conference in honor of Dirk Kreimer's 60th birthday,
1620 November 2020, online via IHES, BuressurYvette
Links: videos, proceedings

Arithmetic and Geometric Aspects of Modular Forms,
2223 July 2019 at All Souls College, Oxford

The Mathematics of Linear Relations between Feynman Integrals,
1822 March 2019, Mainz

Modular forms, periods and scattering amplitudes,
11 February  12 April 2019, ETH Institute for Theoretical Studies
Selected Publications
(full list in CV)
 Feynman symmetries of the Martin and c_{2} invariants of regular graphs, April 2023
with Karen Yeats

Hierarchies in relative PicardLefschetz theory, December 2022
with Marko Berghoff
 Cusp and collinear anomalous dimensions in fourloop QCD from form factors (arXiv), Physics Review Letters, Vol. 124, 162001  24 April 2020
with Andreas von Manteuffel and Robert M. Schabinger
 Hepp's bound for Feynman graphs and matroids (arXiv), Ann. Inst. Henri Poincaré Comb. Phys. Interact. 10 (2023), no. 1, pp. 31–119
 Manifestly dualconformal loop integration (arXiv), Nuclear Physics B, 942 (May, 2019) pp. 251302,
with Jacob Bourjaily and Falko Dulat
 Multiple zeta values in deformation quantization (arXiv), Inventiones Mathematicae 222 (2020), pp. 79159.
with Peter Banks and Brent Pym
Introduction: Research case study
Software: kontsevint and starproducts
 LambertW solves the noncommutative φ^{4}model (arXiv), Communications in Mathematical Physics (October 2019)
with Raimar Wulkenhaar
The story: Mathematician discusses solving a seemingly unsolvable equation
 Feynman integral relations from parametric annihilators (arXiv), Letters in Mathematical Physics, August 2018
with Thomas Bitoun, Christian Bogner and René Pascal Klausen
 Minimally subtracted six loop renormalization of O(n)symmetric φ^{4} theory and critical exponents (arXiv), Phys. Rev. D 96:036016 (2017)
with Mikhail Kompaniets
 The Galois coaction on ϕ^{4} periods (arXiv), Communications in Number Theory and Physics, Vol. 11, 3:657705 (2017)
with Oliver Schnetz
 The parity theorem for multiple polylogarithms (arXiv), Journal of Number Theory, March 2017, 172:93113
 A quasifinite basis for multiloop Feynman integrals (arXiv), Journal of High Energy Physics, February 2015, 2015:120
with Andreas von Manteuffel and Robert M. Schabinger
 Feynman integrals and hyperlogarithms (also on arXiv), PhD thesis (HumboldtUniversität zu Berlin, supervisor Dirk Kreimer)
submitted 26th August 2014, defended 5th February 2015, last updated 24th June 2015
 Renormalization, Hopf algebras and Mellin transforms (arXiv), pages 169202 in Feynman Amplitudes, Periods and Motives, Contemporary Mathematics 648 (AMS, 2015)
 Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals (arXiv), Computer Physics Communications 188 (2015), pages 148166
Latest version of the program: HyperInt
 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™)
 On the analytic computation of massless propagators in dimensional regularization (arXiv), Nuclear Physics, Section B 874 (2013), pp. 567593
Maple™ files with epsilonexpansions of three and some fourloop massless propagators:
raw data,
utilities,
illustrative Maple worksheet
 Hopf algebraic Renormalization of Kreimer's toy model, Master's thesis, June 2011
Selected talks

Cosmic Galois group and φ^{4} theory
(Straßbourg, July 2022)

Multiple Zeta Values in Deformation Quantization

Tropical field theory
(Vienna, November 2021)

Modular graph functions as iterated Eisenstein integrals
(Durham, November 2019)

Feynman integral relations from parametric annihilators
(Loops & Legs in Quantum Field Theory, May 3rd, 2018, St Goar)

6loop φ^{4} theory in 42ε dimensions
(Worksop on multiloop calculations: Methods and applications, June 7th, 2017, Paris)

Feynman integrals, graph polynomials and zeta values
(North meets South Colloquium, May 26th, 2017, Oxford)

Conical sums and multiple polylogarithms
(The 5th International Congress on Mathematical Software, July 14th, 2016, Berlin)

Feynman integrals and hyperlogarithms
(5th Itzykson Colloquium, IHES, April 07th, 2016)

Parametric Feynman integrals with hyperlogarithms
(Trinity College Dublin, February 15th, 2016)

Symbolic integration of multiple polylogarithms
(ACA 2015, Kalamata, July 22nd, 2015)

Multiple polylogarithms and Feynman integrals
(Amplitudes 2015, Zürich, July 7th, 2015)

Master integrals without subdivergences
(HOCTOOLS NNLO meeting, Athens, January 18th, 2015)

Renormalization by kinematic subtraction and Hopf algebras
(
Renormalisation from Quantum Field Theory to Random and Dynamical Systems, November 0709, 2013, Potsdam)

Relations among multiple zeta values
(Multiple Zeta Values in Mathematics and Physics, October 15, 2013, Berlin)

Parametric Feynman integrals and hyperlogarithms
(Feynman Graphs and Motives, March 1822, 2013, Bingen)