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

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

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

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

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

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

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

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

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

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

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

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

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

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

  15. 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)

  16. 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.

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

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

  19. 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.

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

  21. 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.

  22.  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.

  23. 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.

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

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

Accepted for Publication  

  1. Kaufmann, Ralph M.
    "Graphs, strings and actions"
      in Manin Festschrift., 51p, to appear.
      Final version , MPIM 2007-95

  2. Kaufmann, Ralph M. and Schwell, Rachel
    "Associahedra, Cyclohedra and a Topological solution to the A∞&ndash Deligne conjecture"
    Advances in Math. to appear.
    Preprint version arXiv:0710.3967, 36p.

Submitted Preprints  

  1. Kaufmann, Ralph M.
    "A Note on the Two Approaches to Stringy Functors for Orbifolds".
    Preprint,  math.AG/0703209, MPIM 2007-96 , 16p.

  2. Kaufmann, Ralph M.
    "Open/Closed String Topology and Moduli Space Actions via Open/Closed Hochschild Actions".
    Preprint arXiv:0910.5929, 37p.