Ralph Martin Kaufmann
Purdue University; Department of Mathematics
150 N. University Street; West Lafayette, IN
 Phone: (765) 494-1205; Fax: (765) 494-0548
e-mail: rkaufman@math.purdue.edu  URL:http://www.math.purdue.edu/~rkaufman

Publications 

Publications in Mathematics and Sciences

Published

  1. Kaufmann, Ralph M., Mousa, Mohamad and Wehefritz-Kaufmann, Birgit.
    "Quantum Phase diagrams and transitions for Chern topological insulators".
    Annals of Physics Volume 490, July 2026, 170473
    (pdf)

  2. Kaufmann, Ralph M., Ward, Benjamin C. .
    "Schwarz Modular Operads Revisited: SM=S°M".
    Journal of Pure and Applied Algebra Volume 230, Issue 5, May 2026, 108247
    (pdf)

  3. Mohamad Mousa, Birgit Wehefritz-Kaufmann, Sabre Kais, Shawn Cui, Ralph Kaufmann.
    "A Novel Phase Diagram for a Spin-1 System Exhibiting a Haldane Phase".
    Phys. Rev. B 111, 085303. (pdf)

  4. Kaufmann, Ralph M. and Zuniga, J. Javier.
    A combinatorial model for the moduli of bordered Riemann surfaces and a compactification''.
    Contemp. Math., 802.  American Mathematical Society, [Providence], RI, 2024, 117–137. (pdf)

  5. Kaufmann, Ralph M. and Monaco, Michael
    "Plethysm Products, Element and Plus Constructions"
    C. R. Math. Acad. Sci. Paris 362 (2024), 357-411. (pdf)

  6. Kaufmann, Ralph M., Li, Dan, and Wehefritz-Kaufmann, Birgit.
    "Topological insulators and K-theory".
    J. Math. Phys. 65, 043502 (2024). (pdf)

  7. Nghi Nguyen, Tao Hou, Enrico Amico, Jingyi Zheng, Huajun Huang, Alan D. Kaplan, Giovanni Petri, Joaquín Goñi,
    Ralph Kaufmann, Yize Zhao, Duy Duong-Tran, Li Shen.
    "Volume-optimal persistence homological scaffolds of hemodynamic networks covary with MEG theta-alpha aperiodic dynamics".
    Medical Image Computing and Computer Assisted Intervention MICCAI 2024.
    Lecture Notes in Computer Science, vol 15003. Springer, Cham., 2024 (pdf)

  8. Duong-Tran, Duy; Kaufmann Ralph; et al.
    "Homological Landscape of Human Brain Functional Sub-Circuits''
    Mathematics 2024, 12(3), 455. (pdf)

  9. Kaufmann, Ralph M. and Ward, Benjamin C.
    "Koszul Feynman Categories"
    Proc. Amer. Math. Soc. 151 (2023), no. 8, 3253--3267 (pdf)

  10. Kaufmann, Ralph M. and Medina-Mardones, Anibal M.
    "A combinatorial E∞ algebra structure on cubical cochains"
    Cahiers de topologie et géométrie différentielle catégoriques, 63,4 (2022), 387-424. (pdf)

  11. Kaufmann, Ralph M.
    "A detailed look on actions on Hochschild complexes especially the degree 1 co-product and actions on loop spaces" 
    J. Noncommut. Geom. 16 (2022), no. 2, 677-716. (pdf)

  12. Kaufmann, Ralph M. and Mo, Yang.
    "Pathlike Co/bialgebras and their antipodes with applications to bi- and Hopf algebras appearing in topology, number theory and physics"
    SIGMA 18 (2022), 053, 42 pages (pdf)

  13. Kaufmann, Ralph M. and Medina-Mardones, Anibal M.
    "Cochain level May-Steenrod operations". (pdf)
    Forum Math. 33 (2021), no. 6, 1507–1526

  14. Kaufmann, Ralph M.,
    "Feynman categories and Representation Theory"
    Contemp. Math. 769 (2021), 11-81, (pdf)

  15. Kaufmann, Ralph M., Khlebnikov, Sergei and Wehefritz-Kaufmann, Birgit,
    "Local models and global constraints for degeneracies and band crossings"
    J. of Geometry and Physics 158 (2020) 103892. (pdf)

  16. Galvez-Carillo, Imma, Kaufmann, Ralph M., and Tonks, Andrew,
    "Three Hopf algebras from number theory, physics & topology, and their common background I:
    Operadic & simplicial aspects    ".
    Comm. in Numb. Th. and Physics (CNTP) 14,1 (2020) 1-90.  (pdf)

  17. Galvez-Carillo, Imma, Kaufmann, Ralph M., and Tonks, Andrew,
    "Three Hopf algebras from number theory, physics & topology, and their common background II:
    General categorical formulation    ".
    Comm. in Numb. Th. and Physics (CNTP) 14,1 (2020) 91-169. (pdf)

  18. Kaufmann, Ralph M.,
    "Lectures on Feynman categories"
    2016 MATRIX annals, 375-438.
    MATRIX Book Ser., 1, Springer, Cham, 2018. (pdf)

  19. Kaufmann, Ralph M and Wehefritz-Kaufmann, Birgit,
    "Theoretical Properties of Materials Formed as Wire Network Graphs from Triply Periodic CMC Surfaces, Especially the Gyroid".
    In: "The Role of Topology in Materials",  Eds: Gupta, S. and Saxena, A..
    Springer Series in  Solid State Sciences. Springer, 2018

  20. Kaufmann, Ralph M., Lucas, Jason,
    "Decorated Feynman categories".
    J. of Noncommutative Geometry, 11 (2017), no 4 1437–1464. (pdf)

  21. Berger, Clemens and Kaufmann, Ralph M.,
    "Comprehensive Factorization Systems".
    Special Issue in honor of Professors Peter J. Freyd
    and F.William Lawvere on the occasion of their 80th birthdays,
    Tbilisi Mathematical Journal Volume 10, no. 3, (2017). 255-277. (pdf)

  22. Kaufmann, Ralph M. and Ward, Benjamin C.,
    "Feynman categories".
    Astérisque 387 (2017), x+161 pages. (arXiv pdf).

  23. Kaufmann, Ralph M., Zhang, Yongheng,
    "Permutohedral Structures of E2 Operads".
    Forum Mathematicum, 29 (2017), no. 6, 1371–1411. (pdf)

  24. Kaufmann, Ralph M., Li, Dan, and Wehefritz-Kaufmann, Birgit,
    "Notes on topological insulators".
    Reviews in Math. Physics, Vol. 28, No. 10 (2016) 1630003 (57 pages). (pdf)

  25. Kaufmann, Ralph M., Khlebnikov, Sergei and Wehefritz-Kaufmann, Birgit,
    "Geometry of the momentum space: From wire networks to quivers and monopoles"
    J. of Singularities 15 (2016) 53-79. (pdf)

  26. Kaufmann, Ralph M., Khlebnikov, Sergei and Wehefritz-Kaufmann, Birgit,
    "Re-gauging groupoid, symmetries and degeneracies for Graph Hamiltonians and applications to the Gyroid wire network".
    Ann. H. Poincaré, 17, 6 pp 1383–1414. (pdf)

  27. Kaufmann, Ralph M., Ward, Benjamin C. and Zuniga, J. Javier,
    "The odd origin of Gerstenhaber, BV and the master equation".
    Journal of Math. Physics (2015) 56, 103504. (pdf)

  28. Kaufmann, Ralph M., Khlebnikov, Sergei and Wehefritz-Kaufmann, Birgit,
    "Projective representations from quantum enhanced graph symmetries",
    J. Phys.: Conf. Ser. (2015) 597 012048. (pdf)

  29. Kaufmann, Ralph M.,
    "Arc Geometry and Algebra: Foliations, Moduli Spaces, String Topology and Field Theory".
    Chapter in Handbook of Teichmüller Theory IV.
    Ed: Athanase Papadopoulos. European Mathematical Society 2014. (pdf)

  30. Kaufmann, Ralph M., Khlebnikov, Sergei and Wehefritz-Kaufmann, Birgit,
    "The geometry of the Double Gyroid wire network: Quantum and Classical".
      Journal of Noncommutative Geometry, 6 (2012), 623-664. (pdf)

  31. Kaufmann, Ralph M., Khlebnikov, Sergei and Wehefritz-Kaufmann, Birgit,
    "Singularities, swallowtails and Dirac points. An analysis for families of Hamiltonians
    and applications to wire networks, especially the Gyroid    ". (pdf)
    Annals of Physics, 327 (2012), 2865-2884.

  32. Borisov, Lev and Kaufmann, Ralph M.,
    "On CY-LG correspondence for (0,2) toric models".
    Advances in Math. 230 (2012), 531-551. (pdf)

  33. Kaufmann, Ralph M., Khlebnikov, Sergei and Wehefritz-Kaufmann, Birgit,
    "The noncommutative geometry of wire networks from triply periodic surfaces".
    Journal of Physics: Conf. Ser. 343 (2012), 012054. (pdf)

  34. Kaufmann, Ralph M.,
    "Global Stringy Orbifold Cohomology, K-Theory and de Rham Theory".
    Letters in Mathematical Physics 94, 2 (2010) 165-195.  (pdf)

  35. Kaufmann, Ralph M.,
    "Open/Closed String Topology and Moduli Space Actions via Open/Closed Hochschild Actions".
    SIGMA 6 (2010) 036, 33 pages. (pdf)

  36. Kaufmann, Ralph M.,
    "Graphs, strings and actions".
    In: Algebra, Arithmetic and Geometry Volume II: In Honor of Yu. I. Manin.
    Progress in Mathematics 270, 127-178. Birhauser, Boston (2010). (pdf)

  37. Kaufmann, Ralph M. and Schwell, Rachel,
    "Associahedra, Cyclohedra and a Topological solution to the A∞-Deligne conjecture."
    Advances in Math. 223, 6 (2010), 2166-2199. (pdf)

  38. Kaufmann, Ralph M. and Pham, David,
    "The Drinfel'd Double and Twisting in Stringy Orbifold Theory".
    International Journal of Mathematics, 20, 5 (2009) 623-657. (pdf)

  39. Kaufmann, Ralph M.,
    "Dimension vs. Genus: A surface realization of the little k-cubes and an E∞-operad".
    In: Algebraic Topology - Old and New. M. M. Postnikov Memorial Conference, 241-274,
    Banach Center Publ., 85, Polish Acad. Sci., Warsaw, 2009. (pdf)

  40. Kaufmann, Ralph M.,
    "A proof of a cyclic version of Deligne's conjecture via Cacti"
    Math. Res. Letters, 15, 5(2008), 901-921. (pdf)

  41. Kaufmann, Ralph M.,
    "Moduli space actions on the Hochschild cochain complex II: correlators".
    Journal of Noncommutative Geometry 2, 3 (2008), 283-332. (pdf)

  42. Kaufmann, Ralph M.,
    "Noncommutative aspects of open/closed strings via foliations"
      Reports on Math. Phys., 61, 2 (2008), 281-293. (pdf)

  43. Kaufmann, Ralph M.
    "Moduli space actions on the Hochschild cochain complex I: cell models".
    Journal of Noncommutative Geometry 1, 3 (2007) 333-384. (pdf)

  44. Jarvis, Tyler; Kaufmann, Ralph M. and Kimura, Takashi,
    Stringy K-theory and the Chern character''.
    Inventiones Math., 168, 1 (2007), 23-81. (pdf)

  45. Kaufmann, Ralph M,
    "On Spineless Cacti, Deligne's Conjecture and Connes-Kreimer's Hopf Algebra.''
    Topology, 46, 1 (2007), 39-88. (pdf)

  46. Kaufmann, Ralph M. and  R.C. Penner,
    "Closed/open string diagrammatics".
    Nucl. Phys. B748 (2006), 3, 335-379. (pdf)

  47. Kaufmann, Ralph M.
    "Singularities with Symmetries, Orbifold Frobenius algebras and Mirror Symmetry"
    Contemp. Math., 403 (2006), 67-116. (pdf)

  48. Jarvis, Tyler; Kaufmann, Ralph M. and Kimura, Takashi,
    "Pointed admissible G-covers and G-cohomological Field  theories''.
    Compositio Mathematica 141 (2005), 926-978.  (pdf)

  49. Kaufmann, Ralph M.,
    " On several varieties of cacti  and their relations''.
    Algebraic & Geometric Topology 5 (2005), 237-300. (pdf)

  50. Kaufmann, Ralph M.,
    "The algebra of discrete torsion''.
    J. of Algebra 282 (2004), 232-259. (pdf)

  51. Kaufmann, Ralph M.,
    "Second quantized Frobenius algebras''. 
    Commun. Math. Phys. 248 (2004),  33-83. (pdf)

  52. Kaufmann, Ralph M., 
    "Operads, Moduli of Surfaces and Quantum Algebras'',
    in: N. Tongring and R. C. Penner "Woods Hole Mathematics. Perspectives in Mathematics and Physics",
    Series on Knots and Everything - Vol. 34, World Scientific 2004. (pdf)

  53. Kaufmann, Ralph M.,
    "Discrete torsion, symmetric products and the Hilbert scheme", 
    in:  C. Hertling and M. Marcolli (eds.) "Frobenius Manifolds, Quantum Cohomology and Singularities",
    Aspects of Mathematics E 36, Vieweg 2004. (arXiv version)

  54. Kaufmann, Ralph M.; Livernet, Muriel and Penner, Robert C., 
    " Arc Operads and Arc Algebras''.
    Geometry and Topology 7 (2003), 511-568. (pdf)

  55. Kaufmann, Ralph M.,
    "Orbifolding Frobenius Algebras''. 
    Internat. J. of Math. 14 (2003), 573-619. (pdf)

  56. Kaufmann, Ralph M.,
    "Orbifold Frobenius Algebras, Cobordisms and Monodromies''.
    In: "Orbifolds in Mathematics and Physics'', 135-161.
    Contemp. Math. (310) . Amer. Math. Soc.,  Providence, RI, 2002. (pdf)

  57. Kaufmann, Ralph M.,
    "The tensor product in the theory of Frobenius manifolds''. 
    Internat. J. of Math. 10 (1999), 159-206. (pdf)

  58. Kaufmann, Ralph M.,
    "The geometry of the moduli space of pointed curves, the tensor product
    in the theory of Frobenius manifolds and the explicit Künneth formula
    in quantum cohomology''.
    Bonner Mathematische Schriften 312, 95 p., Bonn 1997. (pdf)

  59.  Kaufmann, Ralph M.,
    " The intersection form in H*(M0,n) and the explicit Künneth formula in quantum cohomology''.
    Internat. Math. Res. Notices 19 (1996), 929-954. (pdf)

  60. Kaufmann, Ralph M.; Manin, Yuri I. and Zagier, Don,
    "Higher Weil-Petersson Volumes of Moduli Spaces of Stable n-pointed Curves''.
    Comm. Math. Phys. 181 (1996), 763-787. (pdf)

  61. Kontsevich, Maxim and Manin, Yuri I. with appendix by Kaufmann, Ralph,
    "Quantum cohomology of a product''.
    Invent. Math. 124 (1996), 313-339. (pdf)

  62. Kaufmann, Ralph M,
    "Path Space Decompositions for the Virasoro Algebra and its Verma Modules''.
    Internat. J. of Modern Phys. A 10 (1995), 943-961. (pdf)

Accepted

  1. Kaufmann, Ralph M. and Monaco, Michael.
    "Plus constructions, plethysm, and unique factorization categories with applications to graphs and operad-like theories"
    .arXiv:2209.06121

Memorial Article

  1. Bogomolov, Fedor; Tschinkel, Yuri; Beilinson, Alexander; Berkovich, Vladimir; Colliot-Thélène,
    Jean-Lois; Drinfeld, Vladimir; Goncharov, Alexander; Michael Harris, Michael; Katz, Nicholas
    M.; Kaufmann, Ralph; Marcolli, Matilde; Penkov, Ivan; Schechtman, Vadim; Skorobogatov,
    Alexei; Shokurov, Vyacheslav V.; Tsfasman, Michael; Voronov, Alexander; Zagier, Don; and
    Zarhin, Yuri G.
    “Memorial Article for Yuri Manin”. Notices of the AMS, 70 (11), 2023. (pdf)

    2. Reports  

    1. Kaufmann, Ralph M. "New Developments in Feynman Categories: Bar and Koszul''.
      Oberwolfach Reports, 2024/39 Report No. 46/2021.
      ``Derived Decorated Feynman categories''.
      Organized by: Batanin, M., Lazarev, A., Livernet, M., Markl, M.
      25-29.

    2. Duong-Tran*, Duy; Kaufmann*, Ralph; Wang Xuan; Enrico; Amico, Enrico; Kaplan, Alan; Petri, Giovanni; Zhao, Yize; Goñi, Joaquìn ; Chung,Moo; Shen, Li.
      "On topological landscapes of human brain functional networks"
      Extended Abstract/Poster, 2023 Organization for Human Brain Mapping (OHBM), Montreal, CA.

    3. Kaufmann, Ralph M. "Derived Decorated Feynman categories''.
      Oberwolfach Reports, Report No. 46/2021.
      "Homotopical Algebra and Higher Structures".
      Organized by: Batanin, M., Lazarev, A., Livernet, M., Markl, M.
      2216-2219.

    4. Kaufmann, Ralph M.
      "BV and Feynman categories''.
      Oberwolfach Reports Volume 11, Issue 1, 2014, 
      Batalin-Vilkovisky Algebras, Operads, and Hopf Algebroids,
      organized by: V. Dotsenko and U. Krähmer pp. 624-626.

    5. Kaufmann, Ralph M.
      "Moduli Spaces, Foliations and Algebraic Structures".
      Oberwolfach Reports  Issue 4, 2010, Report 53/2010 Teichmüller Theory
      Organized by: Shigeyuki Morita, Athanase Papadopoulos and Robert C. Penner
      pp. 3124-3128

    Preprints   

    1. Kaufmann, Ralph M., Li, Dan, and Wehefritz-Kaufmann, Birgit,
      "The Stiefel-Whitney theory of topological insulators".
      arXiv:1604.02792

    2. Kaufmann, Ralph M., Li, Dan, and Wehefritz-Kaufmann, Birgit.
      "Noncommutative topological Z2 invariant".
      arXiv:1605.09470

    3. Berger, Clemens and Kaufmann, Ralph M.
      "Trees, graphs and aggregates: a categorical perspective on combinatorial surface topology, geometry, and algebra.
      arXiv:2201.10537

    4. Kumar, Mohit, Kaufmann, Ralph M., and Semperlotti, Fabio
      "Nonabelian elastic metamaterials using holonomies acquired by crossing degeneracies."
      arXiv:2603.13979

    5. Bairnsfather, Christopher A., Kaufmann, Ralph M., Loring, Terry A. and Cerjan, Alexander .
      "Band Unfolding via the Quadratic Pseudospectrum."
      arXiv:2605.05423

    Volume edited    

    1. Kaufmann, Ralph M., Markl, Martin and Voronov, Alexander A. [Edts.]
      "Higher Structures in Topology, Geometry and Physics''. Contemp. Math. 802. American Mathematical Society, [Providence], RI 2024.


    Publications in Philosophy and Liberal Arts    

    1. Ralph M. Kaufmann.
      "Hegel’s Mechanics as a System of Steps from Space and Time to Celestial Motion".
      In: Hegel's Philosophy of Nature. A Critical Guide. Marina F. Bykova (Ed).
      Cambridge University Press 2024

    2. Kaufmann, Ralph M. and Yeomans, Christopher L.
      "Hegel's Theory of Space-Time". In " Life, Organisms, and Human Nature: New Perspectives on Classical German Philosophy"
      Corti, Luca and Schuelein, Johannes-Georg (Eds.),
      Studies in German Idealism, Springer Cham 2023.

    3. Kaufmann, Ralph M.,
      "Beseelte Natur. Alexander von Humboldt and Data Driven Paradigm Segues”.
      In: "Alexander von Humboldt: Perceiving the World",
      Allert, Beate; Clason, Christopher; Peach, Niall A. and Quintana, Ricardo (Eds).
      Purdue Univ. Press 2023

    4. Kaufmann, Ralph M. ``Zeitlicher Gedankenraum/räumliche Gedankenzeit (Darstellung einer verdichteten Ideenreihung)''
      (Time--like Mental--space/space--like Mental--time, A Presentation of a Condensed String of Ideas).
      In: ``Das Buch vom Drehen und Wenden der Blätter'' (The book on the Twisting and Turning of Leaves.) Egger, Oswald; Schestag, Thomas and Eckert, Jennifer (Eds).
      Das böhmische Dorf, 2022.

    5. Kaufmann, Ralph M.
      "Wörtlich. Ummantelndes und Fügendes in Oswald Eggers 'Harlekinsmäntel & andere Bewandtnisse. A-Z'".
      In: "›Wort für Wort‹ – Lektüren zum Werk von Oswald Egger", Endres, Martin and Simon, Ralf (Eds).
      Theorie der Prosa, De Gruyter (2021). (pdf)

    6. Kaufmann, Ralph M., Lyssy, Ansgar and Yeomans, Christopher L.,
      "Hegel's Philosophy of Nature: The Expansion of Particularity as the Filling of Space and Time''.
      In: " Hegel's Encyclopedia of the Philosophical Sciences, A Critical Guide", Stein, Sebastian and Wretzel, Joshua (Eds).
      Cambridge Univ. Press (2021).

    7. Kaufmann, Ralph M. and Yeomans, Christopher L.
      "Hegel on Calculus''.
      History of Philosophy Quarterly 34,4 (2017): 371-390. (pdf)

    8. Kaufmann, Ralph M. and Yeomans, Christopher L.
      "Math by Pure Thinking: R First and the Divergence Of Measures in Hegel's Philosophy of Mathematics''.
      European Journal of Philosophy 25 (2017), 985-1020. (pdf)

    9. Kaufmann, Ralph M.,
      Der Dichter spricht: Eine Rezeption Hölderlins 'Verfahrensweise des Poetischen Geistes'",
      Zeitschrift für Kulturphilosophie, 2017/1  "Sprache und Gestalt'',
      Meiner Verlag, Hamburg.

    10. Egger, Oswald, "Nach dem Muster Vom innigen Band der Begriffe symplektischer Wortgeflechte
      mit Anmerkungen von Ralph M. Kaufmann zu Oswald Eggers  Hölderlin-Schnitten"
      in Paradigmenwechsel: Wandel in den Künsten und Wissenschaften,
       Eds: A. Sakoparnig, A. Wolfsteine and, J. Bohm.
      De Gruyter 2014.

    11. Kaufmann, Ralph M.
      "Truth or Beauty: what can mathematical language do for you?"
      Institute for Advanced Studies Newsletter Spring 2014.

    12. Kaufmann, Ralph M.,
      "Anmerkungen zu Oskar Pastiors Algorismus'' (Remarks on Oskar Pastior's Algorism)
       in Oskar Pastior,  "Gewichtete Gedichte: Chronologie der Materialien".
       Mit Beiträgen von Ralph Kaufmann und Oswald Egger.
       Edition: Das böhmische Dorf (2006). ISBN 3-901024-08-9.



    Theses    

    1. Kaufmann, Ralph M.,
      "Moduli spaces and Deformations".
      Habilitation in Mathematics Universität Bonn, Germany 2003

    2. Kaufmann, Ralph M.,
      "The geometry of the moduli space of pointed curves,  the tensor product in the theory of Frobenius
      manifolds and the explicit Künneth formula in quantum cohomology".
      Dissertation in Mathematics, Universität Bonn, Germany 1997.

    3. Kaufmann, Ralph M.,
      "Socrates' enigma of false identity-judgements in Plato's `Theaetetus' and Gottlob Frege's theory of sense and reference as a possible answer".
      Master thesis in Philosophy (German) Universität Bonn, Germany 1996.

    4. Kaufmann, Ralph M.,
      "Path space decompositions for the Virasoro algebra and its Verma modules".
      Diploma (Master) thesis in Physics (German) Universität Bonn, Germany 1994.