Seminars

The Algebraic and Enumerative combinatorics seminar at its now hopefully permanent, non-organizer-dependent location. Past website, website previous to that, older website and even older website.

Our most recent learning seminar with links to past learning seminars.

Papers and preprints

  1. Asymptotic Density in Combined Number Systems. New York J. Math. 8 (2002), 63-83.
  2. A Multiplicative Analogue of Schur's Tauberian Theorem. Canad. Math. Bull. 46 no.3 (2003), 473-480. Errata.
  3. The Saga of the High School Identities (with Stanley Burris). Algebra Universalis, 52 nos.2-3 (2005), 325-342. Available in postscript or pdf format.
  4. Admissible Dirichlet Series (with Stanley Burris). arXiv:math.CA/0507487
  5. The size of characters of exceptional Lie groups (with Kathryn E. Hare). J. Austral. Math. Soc. 77 (2004), 233-248.
  6. Counting Rooted Trees: The Universal Law t(n) ∼ Cρ−nn−3/2 (with Jason Bell and Stanley Burris). Elec. J. Combin. 13 (2006), #R63. (Also arXiv:math.CO/0512432.)
  7. An Étude in non-linear Dyson-Schwinger Equations (with Dirk Kreimer). Nucl. Phys. B Proc. Suppl., 160, (2006), 116-121. (Also arXiv:hep-th/0605096.)
  8. Sufficient Conditions for Labelled 0-1 Laws (with Stanley Burris). Discrete Math. Theor. Comput. Sci. 10 no.1, (2008), 147-156. (Also arXiv:math.CO/0608735.)
  9. Recursion and growth estimates in renormalizable quantum field theory (with Dirk Kreimer). Commun. Math. Phys. 279, no.2, (2008), 401-427. (Also arXiv:hep-th/0612179.)
  10. Unbounded regions of Infinitely Logconcave Sequences (with David Uminsky). Elec. J. Combin. 14 (2007), #R72. (Also arXiv:math.CO/0703770.)
  11. My PhD thesis: Growth estimates for Dyson-Schwinger equations, or no longer in BU thesis format at arXiv:0810.2249.
  12. The QED beta-function from global solutions to Dyson-Schwinger equations (with Guillaume van Baalen, Dirk Kreimer, and David Uminsky). Ann. Phys. 234, 1, (2009), 205-219. (Also arXiv:0805.0826.)
  13. Characteristic points of recursive systems (with Jason Bell and Stanley Burris). Elec. J. Combin. 17 (2010), #R121. (Also arXiv:0905.2585.)
  14. The QCD beta-function from global solutions to Dyson-Schwinger equations (with Guillaume van Baalen, Dirk Kreimer, and David Uminsky). Ann. Phys. 325, 2, (2010), 300-324. (Also arxiv:0906.1754.)
  15. Spanning forest polynomials and the transcendental weight of Feynman graphs (with Francis Brown). Commun.Math.Phys. 301 no. 2, (2011) 357-382. (Also arxiv:0910.5429.)
  16. Spectra and Systems of Equations (with Jason Bell and Stanley Burris), in "Model Theoretic Methods in Finite Combinatorics", Martin Grohe and Johann A. Makowsky eds., Contemporary Mathematics, 558, (2011), 43-96. Also arXiv:0911.2494.
  17. Monadic second-order classes of forests with a monadic second-order 0-1 law (with Jason Bell and Stanley Burris). Discrete Math. Theor. Comput. Sci. 14, 1, (2012), 87-108. Also arXiv:1004.1128.
  18. Tensor structure from scalar Feynman matroids (with Dirk Kreimer). Phys. Lett. B 698, 5, (2011) 443-450 (Also arxiv:1010.5084.)
  19. On the set of zero coefficients of a function satisfying a linear differential equation(with Jason Bell and Stanley Burris). Math. Proc. Camb. Phil. Soc. 153, (2012), 235-247. Also arXiv:1105.6078.
  20. A four-vertex, quadratic, spanning forest polynomial identity (with Aleksandar Vlasev). Electron. J. Linear Alg., 23 (2012) 923-941. Also arXiv:1106.2869.
  21. Properties of c2 invariants of Feynman graphs (with Francis Brown and Oliver Schnetz). Advances in Theoretical and Mathematical Physics, 18, 2, (2014), 323-362. Also arXiv:1203.0188.
  22. Properties of the Corolla Polynomial of a 3-regular Graph (with Dirk Kreimer). Elec. J. Combin., 20, 1 (2013), P41. Also arXiv:1207.5460.
  23. Resummed small-x and first-moment evolution of fragmentation functions in perturbative QCD (with Chun-Kay Kom and Andreas Vogt). J. High Energ. Phys. 2012, no 10, (2012), 33-55. Also arXiv:1207.5631. As a conference proceedings paper (along with other results by other contributors): A. Vogt, C. H. Kom, N. A. Lo Presti, G. Soar, A. A. Almasy, S. Moch, J. A. M. Vermaseren, K. Yeats Progress on double-logarithmic large-x and small-x resummations for (semi-)inclusive hard processes.
  24. A chord diagram expansion coming from some Dyson-Schwinger equations (with Nicolas Marie). Communications in Number Theory and Physics, 7, no 2 (2013), 251-291. Also arXiv:1210.5457
  25. Some combinatorial interpretations in perturbative quantum field theory. in "Feynman Amplitudes, Periods and Motives", Proceedings of the 2012 ICMAT workshop "Periods and Motives", Contemporary Mathematics, 648 (2015), 261-289. Also arXiv:1302.0080.
  26. Towards a Combinatorial Understanding of Lattice Path Asymptotics (with Samuel Johnson and Marni Mishna). Advances in Applied Mathematics 92 (2018) 144-163. Also arXiv:1305.7418
  27. Forbidden minors for graphs with no first obstruction to parametric Feynman integration (with Samson Black, Iain Crump and Matt DeVos). Discrete Mathematics 338 (2015), 9-35. Also arXiv:1310.5788.
  28. A bijection between certain quarter plane walks and Motzkin paths.
  29. Tree hook length formulae, Feynman rules and B-series (with Bradley R. Jones). Ann. Inst. Henri Poincaré Comb. Phys. Interact. 2, no 4 (2015), 413-430. Also arXiv:1412.6053.
  30. Period Preserving Properties of an Invariant from the Permanent of Signed Incidence Matrices (with Iain Crump and Matt DeVos). Ann. Inst. Henri Poincaré Comb. Phys. Interact. 3, no 4 (2016) 429-454. Also arXiv:1505.06987.
  31. A few c2 invariants of circulant graphs. Commun. Number Theory Phys., 10, no 1 (2016), 63-86. Also arXiv:1507.06974
  32. A Hopf algebraic approach to Schur function identities. Elec. J. Combin. 24(3) (2017), #P3.10. Also arXiv:1511.06337. Thanks to Steph van Willigenburg for contributing to this paper's existence.
  33. Some results on an algebro-geometric condition on graphs (with Avi Kulkarni and Gregory Maxedon). J. Austral. Math. Soc. 104 no 2 (2018) 218-254. Also arXiv:1602.00356.
  34. Generalized chord diagram expansions of Dyson-Schwinger equations (with Markus Hihn). Ann. Inst. Henri Poincaré Comb. Phys. Interact. 6 no 4 (2019) 573-605. Also arXiv:1602.02550.
  35. Terminal chords in connected chord diagrams (with Julien Courtiel). Ann. Inst. Henri Poincaré Comb. Phys. Interact. 4 no 4 (2017) 417-452. Also arXiv:1603.08596.
  36. Diffeomorphisms of quantum fields (with Dirk Kreimer). Math. Phys. Anal. Geom. (2017) 20: 16. Also arXiv:1610.01837.
  37. Connected chord diagrams and bridgeless maps (with Julien Courtiel and Noam Zeilberger), Electronic Journal of Combinatorics, 26 no 4 (2019) P4.37. Also arXiv:1611.04611.
  38. c2 Invariants of Recursive Families of Graphs (with Wesley Chorney). Ann. Inst. Henri Poincaré Comb. Phys. Interact. 6 no 2 (2019) 289-311. Also arXiv:1701:01208.
  39. A special case of completion invariance for the c2 invariant of a graph. Canad. J. Math., 70, 6 (2018) 1416-1435. Also arXiv:1706.08857.
  40. Graph minors and the linear reducibility of Feynman diagrams (with Benjamin Moore). Advances in Theoretical and Mathematical Physics. 23, no 6 (2019) 1657--1685. Also arXiv:1708.01691.
  41. A study on prefixes of c2 invariants. Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA), IRMA Lectures in Mathematics and Theoretical Physics 32 (2020). Also arXiv:1805.11735.
  42. Bijections between Łukasiewicz walks and generalized tandem walks (with Frédéric Chyzak). Electronic Journal of Combinatorics, 27, no 2 (2020), P2.3. Also arXiv:1810.04117.
  43. Limbs and cospectral vertices in trees (with Xiaojing Wang). 17, no 1 (2026), 35-65. Also arXiv:1811.12344.
  44. Further investigations into the graph theory of φ4-periods and the c2 invariant (with Simone Hu, Oliver Schnetz, and Jim Shaw). Ann. Inst. Henri Poincaré Comb. Phys. Interact. 9, no 3 (2022), 473–524. Also arXig:1812.08751.
  45. Some results on double triangle descendants of K5 (with Mohamed Laradji and Marni Mishna). Ann. Inst. Henri Poincaré Comb. Phys. Interact., 8, no. 4 (2021) 537-581. Also arXiv/1904.06923.
  46. Next-tok leading log expansions by chord diagrams (with Julien Courtiel). Commun. Math. Phys. 377, 469–501 (2020). Also arXiv:1906.05139.
  47. Compatible Cycles and CHY Integrals (with Freddy Cachazo and Sam Yusim). J. High Energ. Phys. 2019, 105 (2019). Also arXiv:1907.12661.
  48. Combinatorics of the geometry of Wilson loop diagrams I: equivalence classes via matroids and polytopes (with Susama Agarwala and Siân Fryer). Canadian J. Math., 74 no 4 (2022) 1177-1208. Also arXiv:1908.10919.
  49. Combinatorics of the geometry of Wilson loop diagrams II: Grassmann necklaces, dimensions, and denominators (with Susama Agarwala and Siân Fryer). Canadian J. Math., 74 no 6 (2022) 1625-1672. Also arXiv:1910.12158.
  50. Diffeomorphisms of Scalar Quantum Fields via Generating Functions (with Ali Assem Mahmoud). Ann. Inst. Henri Poincaré Comb. Phys. Interact. 10 (2023) 611-633. Also arXiv:2007.12341.
  51. Connected Chord Diagrams and the Combinatorics of Asymptotic Expansions (with Ali Assem Mahmoud). Journal of Integer Sequences, 25 (2022), Article 22.7.5. Also arXiv:2010.06550.
  52. c2 invariants of hourglass chains via quadratic denominator reduction (with Oliver Schnetz). SIGMA 17 (2021), 100, 26 pages. Also arXiv:2102.12383.
  53. Algebraic Interplay between Renormalization and Monodromy (with Dirk Kreimer). Advances in Theoretical and Mathematical Physics, 27, no 1 (2023), 87-191. Also arXiv:2105.05948.
  54. Subdivergence-free gluings of trees (with Xinle Dai and Jordan Long). Australasian Journal of Combinatorics. 91 no 2 (2025). Also arXiv:2106.07494.
  55. Column expansion identities and quadratic spanning forest identities (with Melanie Fraser). Australasian Journal of Combinatorics. 86 no 2 (2023) 271-307. Also arXiv:2109.13401
  56. A degree preserving delta wye transformation with applications to 6-regular graphs and Feynman periods (with Shannon Jeffries). Ann. Inst. Henri Poincaré Comb. Phys. Interact. 11 (2024), no. 4, 641-682. Also arXiv:2110.07764.
  57. A result on the c2 invariant for powers of primes (with Maria S. Esipova). Canadian Mathematical Bulletin, 66 no. 4, 1164-1178. Also arXiv:2206.06835
  58. Completing the c2 completion conjecture for p=2 (with Simone Hu). Communications in Number Theory and Physics. 17 no 2 (2023) 343-384. Also arXiv:2206.07223
  59. Sequences of Trees and Higher-Order Renormalization Group Equations (with William Dugan and Loïc Foissy). Journal of Mathematical Physics, 64, no 7 (2023), 072302. arXiv:2209.06576.
  60. Combinatorial and Algebraic Enumeration: a survey of the work of Ian P. Goulden and David M. Jackson (with Angèle M. Foley, Alejandro H. Morales, and Amarpreet Rattan). ALCO special issue in honour of Ian Goulden and David Jackson. ALCO. 5 no 6 (2022) 1205-1226. Also arXiv:2209.10075
  61. Some results on Landau poles and Feynman diagram cut structure by Hopf algebra (with William Dallaway).
  62. Tubings, chord diagrams, and Dyson--Schwinger equations (with Paul-Hermann Balduf, Amelia Cantwell, Kurusch Ebrahimi-Fard, Lukas Nabergall, and Nicholas Olson-Harris), J. London Math. Soc., 110: e70006. Also arXiv:2302.02019.
  63. Feynman symmetries of the Martin and c2 invariants of regular graphs (with Erik Panzer). Combinatorial Theory, 2025. Also arXiv:2304.05299.
  64. Reconstructing a bijection on the level of Le diagrams (with Simone Hu).
  65. Hopf algebras from poset growth models (with Stav Zalel). Electron. J Combin. 31 no.3 (2024), #P3.9. Also arXiv:2310.17547
  66. Rado matroids and a graphical calculus for boundaries of Wilson loop diagrams (with Susama Agarwala and Colleen Delaney). J. Math. Phys. 66, (2025), 083508. Also arXiv:2401.05592.
  67. Φp Amplitudes from the Positive Tropical Grassmannian: Triangulations of Extended Diagrams (with Bruno Giménez Umbert). Phys. Rev. D 110 (2024), 125018. Also arXiv:2403.17051.
  68. Tree-tubings and the combinatorics of resurgent Dyson-Schwinger equations (with Michael Borinsky and Gerald V. Dunne). Ann. Inst. Henri Poincaré Comb. Phys. Interact, (2025). Also arXiv:2408.15883.
  69. Combinatorial interpretation of the coefficients of the causal set d'Alembertian Class. Quantum Grav. (2025), 145003. Also arXiv:2412.14036.
  70. The algebraic structure of Dyson--Schwinger equations with multiple insertion places (with Nicholas Olson-Harris), Canadian Mathematical Communications, 2025. Also arXiv:2501.12350
  71. The Generalized Interval Polynomial of a Poset (with Ian George).
  72. Sizes of witnesses in Covtree (with Jette Gutzeit, Kimia Shaban, and Stav Zalel).

Talks

I haven't been putting most of my talks here lately. When I can I like to do board talks, and more and more places put up videos themselves, which are better than just the slides anyway, but here is a selection of slides from some talks I've given.

Counting trees with applications to counting Feynman diagrams March 14, 2006; CIRM conference on Renormalization and Galois theories. Available in postscript or pdf format.

Recursion and growth estimates in quantum field theory April 9, 2007; Johns Hopkins University. Available in postscript or pdf format.

Dyson-Schwinger equations and Renormalization Hopf algebras April 10, 2007; Johns Hopkins University. Available in postscript or pdf format.

Feynman graphs to motives, June 28, 2007; Mathematische Arbeitstagung 2007. MPIM2007-75o.

Two different versions of a picture talk. Visualizing solutions to Dyson-Schwinger equations, October 4, 2007, Boston University; available in postscript or pdf format; and Rearranging Dyson-Schwinger equations, October 7, 2007, Special Session on Noncommutative Geometry and Arithmetic Geometry, AMS Fall Eastern Section Meeting; available in postscript or pdf format.

Two different versions of my job talk, A combinatorial perspective on Dyson-Schwinger equations. Simon Fraser University version, January 11, 2008; available in postscript or pdf format. McGill University version, February 14, 2008; available in postscript or pdf format.

Combinatorial and physical content of Kirchhoff polynomials and Weight drop in &phi4 transcendentals, May 19 and 20, 2009, Tulane University.

Some scribbly talks from les Houches: Dyson-Schwinger equations I, II, III, and the animations from talk 3. June 17, 18, and 21, 2010. I also gave a fourth talk on the blackboard which was about spanning forest polynomials.

CMS Winter meeting 2010 talk. I had more material than time, so the later part of it isn't filled in.

Joint Mathematics Meeting 2011 talk in Victor Moll's session. The audience voted to see the knots and matroids instead of the picture proof of double triangle, so the latter is blank.

CMS Summer meeting 2012 talk about the chord diagram expansion.

This was supposed to be a bit of an overview for a physics audience along with a presentation of the QED Landau pole result, but it wasn't well timed nor well tailored to the audience. Perhaps it is more useful as slides.

My CanaDAM 2015 talk about the renormalization group equation.

Coast Combinatorics talk about leading log expansions.

CMS winter meeting talk about skew Schur function identities by Hopf algebras.

Two different versions of a 2018 c2 talk for geometers and related mathematicians.

Les Houches workshop on structures in local quantum field theory talk about the c2 invariant.

An algebraic combinatorics talk on hourglass chains and my usual picture, very similar to an SFU discrete math talk the previous day.

An algebraic combinatorics talk on the Wilson Loop Diagram stuff with Susama Agarwala and Zee Fryer.

A Kolleg Mathematik Physik Berlin day talk on cut structures in Feynman diagrams.