# about me

I am a mathematical physicist and interested in the mathematical structures of *quantum field theories*. Currently, I am a postdoc at the theory group of Nikhef, Amsterdam.

Download my CV.

### Contact

michael.borinsky@nikhef.nl

### Publications

#### Preprints

Tropical Monte Carlo quadrature for Feynman integrals, preprint August 2020

a proof-of-concept implementation of the algorithm for Feynman integral estimation is available on this page

The Euler characteristic of Out(F

_{n}), preprint July 2019with Karen Vogtmann - accepted for publication in Commentarii Mathematici Helvetici

#### Journal articles

The Hopf algebra structure of the R

^{∗}-operation,*Journal of High Energy Physics*, Article 61, July 2020 (arXiv)with Robert Beekveldt and Franz Herzog

Non-Perturbative Completion of Hopf-Algebraic Dyson-Schwinger Equations,

*Nuclear Physics B*, Volume 957, August 2020, 115096 (arXiv)with Gerald V. Dunne

Renormalized asymptotic enumeration of Feynman diagrams,

*Annals of Physics*, Volume 385, October 2017, Pages 95-135 (arXiv)

Generating asymptotics for factorially divergent sequences,

*Electronic Journal of Combinatorics*, Volume 25, Issue 4, October 2018, P4.1 (arXiv)The results of this article are summarized in this colorful poster for FPSAC 2017.

Algebraic lattices in QFT renormalization,

*Letters in Mathematical Physics*, Volume 106, Issue 7, July 2016, Pages 879-911 (arXiv).Feynman graph generation and calculations in the Hopf algebra of Feynman graphs,

*Computer Physics Communications*, Volume 185, Issue 12, December 2014, Pages 3317-3330 (arXiv):Information and downloads to the two programs

*feyngen*and*feyncop*is available on this page.

#### Proceedings

Generating Asymptotics for factorially divergent sequences,

*Séminaire Lotharingien de Combinatoire*, 78B.28 (2017), 12 pp.Proceedings contribution for FPSAC 2017.

Feynman diagrams and their algebraic lattices,

*Resurgence, Physics and Numbers*CRM Series - Edizioni della Normale, Volume 20, 2017, Pages 91-107 (arXiv)with Dirk Kreimer: Proceedings contribution for Resurgence, Physics and Numbers.

Computations and generation of elements on the Hopf algebra of Feynman graphs,

*Proceedings of 16th International workshop on Advanced Computing and Analysis Techniques in physics research (ACAT)*, J. Phys.: Conf. Ser. 608, 2015 (arXiv)Proceedings contribution for ACAT 2014.

#### Other

Graphs in perturbation theory: Algebraic structure and asymptotics, May 2018 (arXiv):

My PhD thesis - available as hardcover in the Springer Theses series (amazon)

Algorithmization of the Hopf algebra of Feynman graphs, August 2013:

My master's thesis

### Science outreach

Winter 2018, Berlin:

Appearance on the podcast Neues Berlin, where I was interviewed about the implications of quantum mechanics

### Teaching

Summer term 2019

Field Theory in Particle Physics at the Universiteit van Amsterdam: I assisted Eric Laenen, Wouter Waalewijn, Bernard de Wit teaching their course on particle physics

Winter and Summer terms 2016/2017

Interdiscplinary research seminar on Eynard-Oratin Topological recursion at the Humboldt-Universität Berlin Campus Nord

Winter and Summer terms 2015/2016

Interdiscplinary research seminar on Infrared and collinear divergences in perturbative QFT at the Humboldt-Universität Berlin Campus Nord

### Research stays

University of Waterloo - Combinatorics and Optimization Department, Waterloo - Canada, May 2018

Visitor in Karen Yeat's group, which works on combinatorics in quantum field theory.

Erwin Schrödinger International Institute for Mathematics and Physics, Vienna - Austria, October 2017

Participant in the Programme Algorithmic and Enumerative Combinatorics.

University of Waterloo - Combinatorics and Optimization Department, Waterloo - Canada, March 2017

Visitor in Karen Yeat's group, which works on combinatorics in quantum field theory.

Radboud University Nijmegen - IMAPP, Nijmegen - Netherlands, November 2013 - January 2014

Visitor in Walter van Suijlekom's group, where we studied BRST symmetries and associated cohomologies in matrix models.

CERN, Geneva - Switzerland, June - September 2012

In the scope of the CERN Summer Student Programme, I programmed tools to facilitate high energy physics data analysis under the supervision of Lorenzo Moneta.

### Invited talks

#### 2020/2021

ACPMS, Intereuropean virtual seminar, 18 September 2020

Talk on 'The Euler characteristic of Out(F_n) and the Hopf algebra of graphs' (online talk: video/slides)

~~Graph Complexes and Quantum Field Theory, Berlin - Germany, 21-25 September 2020~~~~Talk on 'Out(F_n), M_gn and renormalized topological field theory'~~*(postponed due to SARS-CoV-2)*

#### 2019/2020

Topology Seminar, Karlsruhe - Germany, 02 July 2020

Talk on 'The Euler characteristic of Out(Fn) and renormalized topological field theory'

*(online talk)*Structure of Local Quantum Field Theories, Berlin - Germany, 04 May 2020

Talk on 'Fast Feynman parametric integral evaluation via tropical sampling'

*(online talk)*~~Resurgence in string and gauge theory, AIM - San Jose - US, 05 Mai 2020~~~~Talk on 'The ring of factorially divergent power series and its applications'~~*(canceled due to SARS-CoV-2)*~~Algebraic Structures in Perturbative Quantum Field Theory, IHES - Paris - France, 30 March 2020~~~~Talk on 'The Hopf algebra structure of the R* operation'~~*(postponed due to SARS-CoV-2)*Theoretical Physics Seminar, Liverpool - UK, 26 February 2020

Talk on 'Graphical functions applied to phi^3 in D = 6' (slides)

Emmy-Noether-Seminar, Erlangen - Germany, 7 February 2020

Talk on 'The Euler characteristic of Out(F_n)' (slides)

Geometry Seminar, Nijmegen - Netherlands, 28 January 2020

Talk on 'Renormalized topological field theory and the Euler characteristic of Out(F_n)' (slides)

Algebraic Combinatorics Seminar, Waterloo - Canada, 12 December 2019

Talk on 'Out(F_n), M_gn and renormalized topological field theory'

Canadian Mathematical Society Winter Meeting, Toronto - Canada, 9 December 2019

Talk on 'Constrained Graph Counting' (slides)

Theory Seminar of the Max-Planck-Institute, Munich - Germany, 4 December 2019

Talk on 'Efficient Monte-Carlo on Feynman parametric integrals'

Combinatorics Seminar, Vienna - Austria, 21 November 2019

Talk on 'Renormalized topological field theory'

Mathematical Physics Seminar, Vienna - Austria, 19 November 2019

Talk on 'The graphical function method applied to phi^3 in D=6' (slides)

Topology Seminar, Oxford - UK, 4 November 2019

Talk on 'The Euler characteristic of Out(Fn) and renormalized topological field theory'

Emmy-Noether-Seminar, Erlangen - Germany, 18 September 2019

Talk on 'The graphical function method in 2n-dimensions' (slides)

RADCOR 2019, Avignon - France, 12 September 2019

Talk on 'Systematic integration of higher loop gauge theory amplitudes in position space' (slides)

#### 2018/2019

Structure of Local Quantum Field Theories, Berlin - Germany, 28 Januar 2019

Talk on 'The Euler characteristic of OutFn'

Emmy-Noether-Seminar, Erlangen - Germany, 16 November 2018

Talk on 'Deriving asymptotics for factorially divergent power series'

Higgs as Probe and Portal Meeting, Amsterdam - Netherlands, 21 September 2018

Talk on 'Asymptotics and algebraic structure in perturbation theory'

#### 2017/2018

Summer school on structures in local quantum field theory, Les Houches - France, 4 - 15 June 2018

Talk on 'Graphs in Perturbation Theory' (slides)

Combinatorial structures in perturbative QFT, Waterloo - Canada, 25 May 2018

Talk on 'Counting graphs without given edge-induced subgraphs' (slides)

University of Waterloo: Algebraic Combinatorics Seminar, Waterloo - Canada, 10 May 2018

Talk on 'Hopf algebra of graphs for restricted graphical enumeration'

Workshop on Enumerative Combinatorics, Vienna - Austria, 16 - 20 October, 2017

Talk on 'Hopf algebras and factorial divergent power series: Algebraic tools for graphical enumeration' (slides)

ALEA in Europe, Vienna - Austria, 9 - 13 October, 2017

Talk on 'Generating Asymptotics for factorially divergent sequences' (slides)

#### 2016/2017

Formal Power Series and Algebraic Combinatorics (FPSAC), London - United Kingdom, 9 - 13 July, 2017

Poster about 'Generating Asymptotics for factorially divergent sequences'

Proceedings contribution: Generating Asymptotics for factorially divergent sequences,

*Séminaire Lotharingien de Combinatoire*, 78B.28 (2017), 12 pp.Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA), Luminy - France, 26 - 30 June, 2017

Talk on 'Flag decompositions of graphs and their Hopf algebraic structure'

International school of subnuclear physics, Erice - Italy, 14 - 23 June 2017

Talk on 'Bounds and estimates for Feynman-perturbative expansions' (slides)

University of Waterloo: Algebraic Combinatorics Seminar, Waterloo - Canada, 30 March 2017

Talk on 'Zero-dimensional quantum field theory or counting classes of graphs using Gaussian integrals and Hopf algebras'

#### 2015/2016

Resurgence in Gauge and String Theories, Lisbon - Portugal, 18 - 22 July 2016

Talk on 'Asymptotic Calculus for Combinatorial Dyson-Schwinger Equations' (slides)

Kolleg Mathematik Physik Berlin (KMPB-Day), Berlin - Germany, 20 June 2016

Talk on 'Factorially divergent expansions from a QFT perspective'

Combinatorial Structures in Perturbative Quantum Field Theory, Vancouver - Canada, 21 March 2016

Talk on 'Generating functions' asymptotics' generating functions' (slides)

Paths to, from and in renormalisation, Potsdam - Germany, 8 - 12 February 2016

Talk on 'Asymptotic expansions and combinatorial Dyson-Schwinger equations' (slides)

#### 2014/2015

Resurgence, Physics and Numbers, Pisa - Italy, 18 - 22 May 2015

Talk on 'Combinatorics of Feynman diagrams and the algebraic lattice structure in QFT' (slides)

Proceedings contribution with Dirk Kreimer: Feynman diagrams and their algebraic lattices,

*Resurgence, Physics and Numbers*CRM Series - Edizioni della Normale, Volume 20, 2017, Pages 91-107 (arXiv)

Dyson-Schwinger Equations in Modern Mathematics & Physics, Trento - Italy, 22 - 26 September 2014

Talk on 'The Hopf-Algebra of Feynman graphs as the foundation of Dyson-Schwinger equations'

Parallel session - Track 3, 16th International workshop on Advanced Computing and Analysis Techniques in physics research (ACAT), Prague - Czech Republic, 1 - 5 September 2014

Talk on 'Computations and generation of elements on the Hopf algebra of Feynman graphs'

Proceedings contribution: Computations and generation of elements on the Hopf algebra of Feynman graphs,

*Proceedings of 16th International workshop on Advanced Computing and Analysis Techniques in physics research (ACAT)*, J. Phys.: Conf. Ser. 608, 2015 (arXiv).

#### 2013/2014

Summer school on structures in local quantum field theory, Les Houches - France, 9 - 20 June 2014

Talk on 'The Hopf algebra of Feynman graphs as foundation for Dyson Schwinger equations'

#### 2012/2013

CERN Summer Student Lecture Programme, CERN - Switzerland, Summer 2012