Herbert Gangl

Department of Mathematical Sciences
South Road
Durham, DH1 3LE
United Kingdom

Office: CM220

Phone: +44 191 334 3092

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

Teaching Information

  • Michaelmas term 2010: an undergraduate colloquium in 2010 on finite polylogarithms
  • Epiphany term 2014: Algebra II
  • Epiphany term 2014: Modular Forms (MAGIC course)
  • Easter term 2014: A mini-workshop on 3D printing
  • Summer Projects 2014, based on an undergraduate colloquium in 2013 on hyperbolic tessellations:
    3D models for hyperbolic tessellation (Josh Inoue)
    an app game to train your 3D visualization, alas only for iOS <7 Polyshadow (App Store link) (Josh Yaxley)
  • Michaelmas term 2015: Linear Algebra I
  • Epiphany term 2016: Algebra II
  • Easter 2016: Post-exam activity on 3D printing
  • Michaelmas term 2016: Linear Algebra I
  • Epiphany term 2017: Number Theory III/IV
  • Easter 2017: Workshop on 3D printing (guest speakers H.~Segerman, S.~Schleimer, E.~Matsumoto), co-organised with Prof Norbert Peyerimhoff
  • Epiphany term 2019: Topics in Algebra and Geometry IV
  • Easter 2019: Post-exam activity on 3D printing

  • Previous teaching

  • 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

  • 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).

  • "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.

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

  • "Multiple polylogarithms in weight 4", Preprint.

  • "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

    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".

    Previous activities