Herbert Gangl

Department of Mathematical Sciences
Mathematical Sciences & Computer Science Building
Durham, DH1 3LE
United Kingdom

Office: MCS2071

Phone: +44 191 334 3092

Email: herbert.gangl (Please add "".)

Teaching Information

  • Epiphany term 2022: Algebra II
  • Michaelmas term 2021: Algebra II
  • Epiphany term 2021: Algebra II
  • Michaelmas term 2020: Algebra II
  • Epiphany term 2020: Number Theory III
  • Michaelmas term 2019: Number Theory III
  • Easter term 2019: Post-exam activity on 3D printing
  • Epiphany term 2019: Topics in Algebra and Geometry IV
  • Epiphany term 2017: Number Theory III/IV
  • Michaelmas term 2016: Linear Algebra I
  • Epiphany term 2016: Algebra II

    Previous teaching

  • Student summer projects and 3D printing activities

  • Epiphany term 2021: an (2min announcement of an) undergraduate colloquium in 2021 on finite polylogarithms,
  • Easter 2017: Workshop on 3D printing (guest speakers H.~Segerman, S.~Schleimer, E.~Matsumoto et al.), co-organised with Prof Norbert Peyerimhoff (Maths) and Dr Ioannis Ivrissimtzis (CS)
  • Easter 2016: Post-exam activity on 3D printing
  • Summer Projects 2014, based on an undergraduate colloquium in 2013 on hyperbolic tessellations:
    Report on 3D models for hyperbolic tessellation (Josh Inoue) and an app game to train your 3D visualization, alas only for iOS <7 Polyshadow (Josh Yaxley)
  • Easter term 2014: A mini-workshop on 3D printing

    Research Information

    My work is concentrated around polylogarithms and variants thereof, in connection with algebraic K-theory, algebraic number theory and arithmetic algebraic geometry. The questions that I am interested in lead to a variety of rather disparate topics, comprising for instance the homology of the general linear group, configuration and moduli spaces, combinatorial Hopf algebras, multiple zeta values or (quasi-)modular forms and in recent years particle physics. A good chunk of my research has a computer-experimental flavour, using mostly the GP/PARI scripting language to try to detect patterns in piles of data, to find hitherto unknown objects or to formulate conjectures.

    Recent Publications and Preprints

  • "Functional equations of polygonal type for multiple polylogarithms in weights 5, 6 and 7" (with S. Charlton, D. Radchenko), Preprint arXiv: 2012.09840.

  • "Clean single-valued polylogarithms" (with S. Charlton, C. Duhr), Preprint arXiv: 2104.04344.

  • " Explicit formulas for Grassmannian polylogarithms" (with S. Charlton, D. Radchenko), Preprint arXiv: 1909.13869v1.

  • "Hyperbolic tessellations and generators of K_3 for imaginary quadratic fields" (with D. Burns, R. de Jeu, A. Rahm, D. Yasaki), Forum of Mathematics, Sigma, volume 9 (2021), arXiv: 1909.13869v1.

  • "On functional equations for Nielsen polylogarithms" (with S. Charlton, D. Radchenko), Communications in Number Theory and Physics, Vol.15, no.2 (2021), arXiv: 1908.04770v1.

  • "On the topological computation of K_4 of the Gaussian and Eisenstein integers" (with M. Dutour Sikiric, P. Gunnells, J. Hanke, A. Schuermann, D. Yasaki), J of Homotopy and Related Structures, 14 (2019), 281-291.

  • "Homophonic Quotients of Linguistic Free Groups: German, Korean, and Turkish" (with G. Kiraali, W. Lee), Involve 12:3 (2019), 463-474.

  • "Jewellery from hyperbolic space", Article for Snapshots of Modern Mathematics, Oberwolfach Journal aiming to provide insights into current topics of the mathematical community for everyone who is interested in modern mathematics (accepted for publication).

  • "The Grassmannian complex and Goncharov's motivic complex in weight 4", Preprint arXiv:1801.07816v2.

  • "Multiple polylogarithms in weight 4", Preprint arXiv:1609.05557v1.

  • "On the cohomology of linear groups over imaginary quadratic fields" (with M. Dutour Sikiric, P. Gunnells, J. Hanke, A. Schuermann, D. Yasaki), J Pure Appl Alg, 220 (2016), 2564--2589.

  • "Finite polylogarithms, their multiple analogues and the Shannon entropy", (with Ph. Elbaz-Vincent) GSI 2015 (F. Nielsen and F. Barbaresco eds.), LNCS 9389 (2015) 1--9.

  • "On the Broadhurst-Kreimer generating series for multiple zeta values" (with S. Carr, L. Schneps), in ``Feynman Amplitudes, Periods and Motives'', (L. Alvarez-Consul, J.I. Burgos-Gil, K. Ebrahimi-Fard), Contemp. Math. 648, AMS (2015), 57--78.

  • "Functional equations and ladders for polylogarithms", Communications in Number Theory and Physics, 7, no.3 (2013), 397--410.

  • "Perfect forms, K-theory and the cohomology of modular groups" (with Ph. Elbaz-Vincent and C. Soulé), Adv. in Math. 245 (2013), 587-624.

  • "Tame kernels and second regulators of number fields and their subfields" (with J. Browkin), Journal of K-Theory 12 (2013), 137-165.

  • "From polygons and symbols to polylogarithmic functions" (with C. Duhr and J. Rhodes), JHEP 10 (2012), 075.

  • "On special elements in higher algebraic K-theory and the Lichtenbaum-Gross Conjecture" (with D. Burns and R. de Jeu), Adv. in Math. 23 (2012), 1502-1529.

    Further publications


  • Arithmetic Study Group

    Upcoming Activities

    May - Jul 2022, Isaac Newton Institute (Cambridge), Special Semester on ``K-theory, algebraic cycles and motivic homotopy theory''

    Previous activities

    10-15 Oct 2021: Banff International Research Station: Conference on "Cohomology of Arithmetic Groups: Duality, Stability, and Computations" (Web page)

    3-8 Oct 2021: Banff International Research Station: Conference on "Lattices and Cohomology of Arithmetic Groups: Geometric and Computational Viewpoints (Online)"> (Web page)

    20 Nov 2019, University Open Day on Postgraduate opportunities (Information meeting 14:15, CM 107)

    9 Nov 2019, 10:30am Saturday Morning Science Talk, "Jewellery from hyperbolic tessellations" (Wolfendale Lecture Theatre, CLC)

    Sept 2019: Programme ``Illustrating Mathematics'' at ICERM, Brown University, Providence, RI

    Aug 2019: Research stay at MPIM, Bonn

    Workshop on "Interactions between Hyperbolic Geometry and Number Theory", Luxembourg, 4-5 Jul 2019.

    21-25 Jan 2019 "Arithmetic and Algebraic Geometry", in honour of Tomohide Terasoma's 60th birthday,

    May --Dec 2018: Research stay at MPIM, Bonn

    Jan -- Apr 2018: Co-organiser of a Special programme on "Periods in Number Theory, Algebraic Geometry and Physics".

    More previous activities