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 

Journal Articles

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

  2. 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, 10, no. 3,. 255-277 (pdf)

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

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

  5. 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).

  6. 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).

  7. 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  7, 6 (),  1383-1414. (pdf)

  8. Kaufmann, Ralph M., Ward, Benjamin C. and Zuniga, J. Javier
    "The odd origin of Gerstenhaber brackets, Batalin-Vilkovisky operators and the master equations".
    Journal of Math. Phys. 56 (2015), 103504. (pdf)

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

  10. 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)

  11. 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)

  12. 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".
    Annals of Physics, 327 (2012), 2865-2884. (pdf)

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

  14. 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)

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

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

  17. 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)

  18. 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)

  19. 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)

  20. 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)

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

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

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

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

  25. Jarvis, T.; Kaufmann, R. and Kimura, T.
    "Stringy K-theory and the Chern character''.
    Inventiones Math. 168, 1 (2007), 23-81. (pdf)

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

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

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

  29. Jarvis, T.; Kaufmann, R. and Kimura, T.
    "Pointed admissible G-covers and G-cohomological Field  theories''.
    Compositio Mathematica 141 (2005), 926-978.  (pdf)

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

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

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

  33. 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)

  34. 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)

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

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

  37. 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)

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

  39. 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)

  40.  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)

  41. Kaufmann, R.; Manin, Yu.; and Zagier, D.
    "Higher Weil-Petersson Volumes of Moduli Spaces of Stable n-pointed Curves''.
    Comm. Math. Phys. 181 (1996), 763-787. (pdf)

  42. Kontsevich, M. and Manin, Yu. with appendix by R. Kaufmann.
    "Quantum cohomology of a product''.
    Invent. Math. 124 (1996), 313-339. (pdf)

  43. 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)


Book Chapters

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

  2. 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

Reports in Proceedings 

  1. 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.

  2. 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.
    "Topological insulators and K-theory".
     arXiv:1510.08001

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

  3. Kaufmann, Ralph M., Li, Dan, and Wehefritz-Kaufmann, Birgit.
    "Noncommutative topological Z2 invariant ".
     arXiv:1604.02792

  4. Galvez-Carillo, Imma, Kaufmann, Ralph M., and Tonks, Andrew.
    "Three Hopf algebras and their common simplicial and categorical background ".
    arXiv:1607.00196

  5. Kaufmann, Ralph M., Khlebnikov, Sergei and Wehefritz-Kaufmann, Birgit.
    "Local models and global constraints for degeneracies and band crossings ".
    arXiv:1807.05751

  6. Kaufmann, Ralph M.
    "A detailed look on actions on Hochschild complexes especially the degree 1 co-product and actions on loop spaces"
    arXiv:1807.10534



Miscellaneous Publications    

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

  2. 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.

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

  4. Kaufmann, Ralph.
    "Anmerkungen zu dem Hölderlin Text von Oswald Egger''
    in Paradigmenwechsel: Wandel in Den Künsten und Wissenschaften,
     Eds: A. Sakoparnig, A. Wolfsteine and, J. Bohm. De Gruyter 2014.

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

  6. 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.