Publications
Publications in Mathematics and Sciences
Published
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)
Kaufmann, Ralph M. and Monaco, Michael
"Plethysm Products, Element and Plus Constructions"
C. R. Math. Acad.
Sci. Paris 362 (2024), 357-411. (pdf)
Kaufmann, Ralph M., Li, Dan, and Wehefritz-Kaufmann,
Birgit.
"Topological insulators and K-theory".
J. Math. Phys. 65, 043502 (2024). (pdf)
Duong-Tran, Duy; Kaufmann Ralph; et al.
"Homological Landscape of Human Brain Functional
Sub-Circuits''
Mathematics 2024, 12(3), 455. (pdf)
Kaufmann, Ralph M. and Ward, Benjamin C.
"Koszul Feynman Categories"
Proc. Amer. Math. Soc. 151 (2023), no. 8, 3253--3267 (pdf)
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)
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)
Kaufmann, Ralph M. and Yang Mo.
"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)
Kaufmann, Ralph M.
"Feynman categories and Representation Theory"
Contemp. Math. 769 (2021), 11-81, (pdf)
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)
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)
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)
Kaufmann, Ralph M.
"Lectures on Feynman categories"
2016 MATRIX annals, 375-438.
MATRIX Book Ser., 1, Springer, Cham, 2018. (pdf)
Kaufmann, Ralph M., Lucas, Jason.
"Decorated Feynman categories".
J. of Noncommutative Geometry, 11 (2017), no 4 1437–1464.
(pdf)
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, (2017). 255-277.
(pdf)
Kaufmann, Ralph M. and Ward, Benjamin C.
"Feynman categories".
Astérisque 387 (2017), x+161 pages. (arXiv pdf).
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).
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).
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)
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)
Kaufmann, Ralph M., Khlebnikov, Sergei and
Wehefritz-Kaufmann, Birgit.
"Projective representations from quantum enhanced graph
symmetries",
J. Phys.: Conf. Ser. (2015) 597 012048 (pdf)
Kaufmann, Ralph M.
"Arc Geometry and Algebra: Foliations, Moduli Spaces,
String Topology and Field Theory".
In: "Handbook of Teichmüller Theory IV". Athanase
Papadopoulos (Ed).
European Mathematical Society 2014. (pdf)
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)
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)
Borisov, Lev and Kaufmann, Ralph M.
"On CY-LG correspondence for (0,2) toric models".
Advances in Math. 230 (2012), 531-551 (pdf)
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)
Kaufmann, Ralph M.
"Global Stringy Orbifold Cohomology, K-Theory and de Rham
Theory".
Letters in Mathematical Physics, 94, 2 (2010) 165-195. (pdf)
Kaufmann, Ralph M.
"Open/Closed String Topology and Moduli Space Actions via
Open/Closed Hochschild Actions".
SIGMA 6 (2010) 036, 33 pages. (pdf)
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)
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)
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)
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)
Kaufmann, Ralph M.
"A proof of a cyclic version of Deligne's conjecture via
Cacti"
Math. Res. Letters 15, 5 (2008), 901--921. (pdf)
Kaufmann, Ralph M.
"Moduli space actions on the Hochschild cochain complex
II: correlators".
Journal of Noncommutative Geometry 2, 3 (2008), 283-332. (pdf)
Kaufmann, Ralph M.
"Noncommutative aspects of open/closed strings via
foliations"
Reports on Math. Phys., 61, 2 (2008), 281-293. (pdf)
Kaufmann, Ralph M.
"Moduli space actions on the Hochschild cochain complex I:
cell models''.
Journal of Noncommutative Geometry 1, 3 (2007) 333-384. (pdf)
Jarvis, T.; Kaufmann, R. and Kimura, T.
"Stringy K-theory and the Chern character''.
Inventiones Math. 168, 1 (2007), 23-81. (pdf)
Kaufmann, Ralph M.
"On Spineless Cacti, Deligne's Conjecture and
Connes-Kreimer's Hopf Algebra.''
Topology 46, 1 (2007), 39-88. (pdf)
Kaufmann, Ralph M. and R.C. Penner.
"Closed/open string diagrammatics".
Nucl. Phys. B748 (2006), 3, 335-379. (pdf)
Kaufmann, Ralph M.
"Singularities with Symmetries, Orbifold Frobenius
algebras and Mirror Symmetry"
Contemp. Math., 403 (2006), 67-116. (pdf)
Jarvis, T.; Kaufmann, R. and Kimura, T.
"Pointed admissible G-covers and G-cohomological
Field theories''.
Compositio Mathematica 141 (2005), 926-978. (pdf)
Kaufmann, Ralph M.
"On several varieties of cacti and their
relations''.
Algebraic & Geometric Topology 5 (2005), 237?300. (pdf)
Kaufmann, Ralph M.
"The algebra of discrete torsion''.
J. of Algebra 282 (2004), 232-259. (pdf)
Kaufmann, Ralph M.
"Second quantized Frobenius algebras''.
Commun. Math. Phys. 248 (2004), 33-83. (pdf)
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)
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)
Kaufmann, Ralph M.; Livernet, Muriel and Penner, Robert
C.
"Arc Operads and Arc Algebras''.
Geometry and Topology 7 (2003), 511-568. (pdf)
Kaufmann, Ralph M.
"Orbifolding Frobenius Algebras''.
Internat. J. of Math. 14 (2003), 573-619. (pdf)
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)
Kaufmann, Ralph M.
"The tensor product in the theory of Frobenius
manifolds''.
Internat. J. of Math. 10 (1999), 159-206. (pdf)
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)
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)
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)
Kontsevich, M. and Manin, Yu. with appendix by R.
Kaufmann.
"Quantum cohomology of a product''.
Invent. Math. 124 (1996), 313-339. (pdf)
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)
Reports
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.
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
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.
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.
Preprints
Kaufmann, Ralph M., Li, Dan, and Wehefritz-Kaufmann,
Birgit.
"The Stiefel-Whitney theory of topological insulators".
arXiv:1604.02792
Kaufmann, Ralph M., Li, Dan, and Wehefritz-Kaufmann,
Birgit.
"Noncommutative topological Z2 invariant ".
arXiv:1604.02792
Berger, Clemens and Kaufmann, Ralph M.
"Trees, graphs and aggregates: a categorical perspective
on combinatorial surface topology, geometry, and algebra.
arXiv:2201.10537
Kaufmann, Ralph M. and Monaco, Michael
"Plus constructions, plethysm, and unique factorization
categories with applications to graphs and operad-like
theories"
arXiv:2209.06121
Ralph M. Kaufmann, Benjamin C. Ward.
"Schwarz Modular Operads Revisited: SM=S°M".
arXiv:2404.17540
Mohamad Mousa, Birgit Wehefritz-Kaufmann, Sabre Kais, Shawn Cui, Ralph Kaufmann.
"A Novel Phase Diagram for a Spin-1 System Exhibiting a Haldane Phase".
arXiv:2406.19372
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".
arXiv:2407.05060
Volume edited
Publications in Philosohpy and Liberal Arts
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
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.
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
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.
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)
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).
Kaufmann, Ralph M. and Yeomans, Christopher L.
"Hegel on Calculus''.
History of Philosophy Quarterly 34,4 (2017): 371-390 (pdf)
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)
Kaufmann, Ralph M.
Der
Dichter spricht: Eine Rezeption Hölderlins
'Verfahrensweise des Poetischen Geistes'",
Zeitschrift
für Kulturphilosophie, 2017/1 "Sprache und
Gestalt'', Meiner Verlag, Hamburg.
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.
Kaufmann, Ralph M.
"Truth
or Beauty: what can mathematical language do for you?"
Institute
for Advanced Studies Newsletter Spring 2014.
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
Kaufmann, Ralph M.,
"Moduli spaces and Deformations"
Habilitation in Mathematics Universität Bonn, Germany 2003
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.
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.
Kaufmann, Ralph M.,
"Path space decompositions for the Virasoro algebra and
its Verma modules.''
Diploma (Master) thesis in Physics (German) Universität
Bonn, Germany 1994.