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  

  1. 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)

  2. 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.

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

  4. 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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  23. 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. (ps-file)

  24. 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)

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

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

  27. 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.

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

  29. 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''. (pdf)
    Bonner Mathematische Schriften 312, 95 p., Bonn 1997.

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

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

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

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

Reports in Proceedings   

  1. 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

Accepted Papers   

  1. Kaufmann, Ralph M.
    "Arc Geometry and Algebra: Foliations, Moduli Spaces, String Topology and Field Theory".
    Article for the Handbook of Teichmueller Theory. (pdf)

Preprints   

  1. 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".
    arXiv:1208.3266. DESY 12-133.

  2. Kaufmann, Ralph M., Ward, Benjamin C. and Zuniga, J. Javier
    "The odd origin of Gerstenhaber, BV and the master equation".
    arXiv:1208.5543 .

  3. Kaufmann, Ralph M., Khlebnikov, Sergei and Wehefritz-Kaufmann, Birgit. 
    "Geometry of the momentum space: From wire networks to quivers and monopoles"
    arXiv:1302.1260 .