me

Herbert Gangl

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

Office: MCS2071, Phone: +44 191 334 3092, Email: herbert.gangl (Please add "@durham.ac.uk".)

Teaching Information

  • Michaelmas term 2024: Single Maths B
  • Epiphany term 2024: Representation Theory IV
  • Michaelmas term 2023: Modular Forms (TAG IV)

    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

  • On the Cohomology of GL2 and SL2 over Imaginary Quadratic Fields (with P. Gunnells, J. Hanke, D. Yasaki), Experimental Mathematics, 2024.

  • On the Goncharov depth conjecture and polylogarithms of depth two (with S. Charlton, D. Radchenko, D. Rudenko), Selecta Mathematica, 2024.

  • "On two conjectures of Sun concerning ApĂ©ry-like series" (with S. Charlton, L. Lai, C. Xu, J. Zhao), Forum Mathematicum 2023, 1533--1547.

  • "Functional equations of polygonal type for multiple polylogarithms in weights 5, 6 and 7" (with S. Charlton, D. Radchenko), Pure and Applied Mathematics Quarterly, 19(1), 2023, 85-93. Preprint arXiv: 2012.09840.

  • "Hands-on Tropical Geometry", (with Y. Ren, Z. Urbancic), Computeralgebra-Rundbrief: Vol 70. (2023).

  • Jewellery from tessellations of hyperbolic space, Snapshots of modern mathematics from Oberwolfach;2022-05.

  • "Clean single-valued polylogarithms" (with S. Charlton, C. Duhr), SIGMA 17 (2021), 107, 34 pages. 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.

  • "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

    Seminars:

  • Arithmetic Study Group

    Upcoming Activities

    Previous activities

    August 2024, Munich Institute for Astro-, Particle and BioPhysics (MIAPbP).

    3-12 June 2024, Regulators V, Pisa.

    22 - 26 Apr 2024, Follow-Up Workshop: "Periods in Physics, Number Theory and Algebraic Geometry", Hausdorff Center for Mathematics, Bonn.

    11 - 15 Sep 2023, Workshop "Polylogarithms, Cluster Algebras, and Scattering Amplitudes", Brin Mathematics Center, Maryland. (Co-organiser)

    20 - 24 Mar 2023, Workshop "Geometries and Special Functions for Physics and Mathematics", Bethe Center, Bonn. (Co-organiser)

    Oct 2022-Sep 2023, Research Stay at MPIM Bonn.

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

    Aug - Sep 2022, Isaac Newton Institute (Cambridge), Special Semester on ``New connections in number theory and physics"

    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