Information Algebras and Their Applications

  • Matilde MarcolliEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9389)


In this lecture we will present joint work with Ryan Thorngren on thermodynamic semirings and entropy operads, with Nicolas Tedeschi on Birkhoff factorization in thermodynamic semirings, ongoing work with Marcus Bintz on tropicalization of Feynman graph hypersurfaces and Potts model hypersurfaces, and their thermodynamic deformations, and ongoing work by the author on applications of thermodynamic semirings to models of morphology and syntax in Computational Linguistics.


Hopf Algebra Shannon Entropy Feynman Graph Tsallis Entropy Tropical Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Abe, S., Okamoto, Y.: Nonextensive Statistical Mechanics and Its Applications. Lecture Notes in Physics, vol. 560, 1st edn. Springer, Heidelberg (2001)CrossRefzbMATHGoogle Scholar
  2. 2.
    Aluffi, P., Marcolli, M.: A motivic approach to phase transitions in Potts models. J. Geom. Phys. 63, 6–31 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Beck, C., Schlögl, F.: Thermodynamics of Chaotic Systems: An Introduction. Cambridge University Press, Cambridge (1993)CrossRefzbMATHGoogle Scholar
  4. 4.
    Bintz, M., Marcolli, M.: Thermodynamic tropicalization of Feynman graph and Potts model hypersurfaces (in preparation)Google Scholar
  5. 5.
    Connes, A., Consani, C.: From Monoids to Hyperstructures: in Search of an Absolute Arithmetic, “Casimir Force, Casimir Operators and the Riemann Hypothesis”. Walter de Gruyter, Berlin (2010). pp. 147–198zbMATHGoogle Scholar
  6. 6.
    Connes, A., Kreimer, D.: Renormalization in quantum field theory and the Riemann-Hilbert problem. I. The Hopf algebra structure of graphs and the main theorem. Commun. Math. Phys. 210(1), 249–273 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Connes, A., Marcolli, M.: Noncommutative Geometry, Quantum Fields and Motives, vol. 55, p. 785, Colloquium Publications, American Mathematical Society (2008)Google Scholar
  8. 8.
    Ebrahimi-Fard, K., Guo, L.: Rota-Baxter algebras in renormalization of perturbative quantum field theory in “universality and renormalization". Fields Inst. Commun. 50, 47–105 (2007). American Mathematical SocietyMathSciNetzbMATHGoogle Scholar
  9. 9.
    Ebrahimi-Fard, K., Guo, L., Kreimer, D.: Integrable renormalization II the general case. Ann. Henri Poincaré 6(2), 369–395 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Gell-Mann, M., Tsallis, C. (eds.): Nonextensive Entropy. Oxford University Press, New York (2004)zbMATHGoogle Scholar
  11. 11.
    Itenberg, I., Mikhalkin, G.: Geometry in tropical limit. Math. Semesterber. 59(1), 57–73 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Itenberg, I., Mikhalkin, G., Shustin, E.: Tropical algebraic geometry, Oberwolfach Seminars, vol. 35. Birkhäuser Verlag, Basel (2007)zbMATHGoogle Scholar
  13. 13.
    Kuich, W., Salomaa, A.: Semirings, Automata, Languages. Springer, Heidelberg (1986)CrossRefzbMATHGoogle Scholar
  14. 14.
    Manin, Y.I.: Renormalization and computation, I: motivation and background, in “OPERADS 2009". Sémin Congr. Soc. Math. France 26, 181–222 (2013)MathSciNetGoogle Scholar
  15. 15.
    Manin, Y.I.: Renormalization and computation II: time cut-off and the halting problem. Math. Struct. Comput. Sci. 22(5), 729–751 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Manin, Y.I.: Infinities in quantum field theory and in classical computing: renormalization program. In: Ferreira, F., Löwe, B., Mayordomo, E., Mendes Gomes, L. (eds.) CiE 2010. LNCS, vol. 6158, pp. 307–316. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  17. 17.
    Marcolli, M.: Feynman Motives. World Scientific, Singapore (2010) zbMATHGoogle Scholar
  18. 18.
    Marcolli, M.: Thermodynamics Semirings in Computational Linguistics (in preparation)Google Scholar
  19. 19.
    Marcolli, M., Tedeschi, N.: Entropy algebras and Birkhoff factorization. J. Geom. Phys. 97, 243–265 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Marcolli, M., Thorngren, R.: Thermodynamic semirings. J. Noncommut. Geom. 8(2), 337–392 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Pachter, L., Sturmfels, B.: Tropical geometry of statistical models. Proc. Nat. Ac. Sci. USA 101(46), 16132–16137 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Quadrat, J.P., Max-Plus Working Group: Min-Plus linearity and statistical mechanics. Markov Process. Relat. Fields 3(4), 565–597 (1997)Google Scholar
  23. 23.
    Roark, B., Sproat, R.: Computational Approaches to Morphology and Syntax. Oxford University Press, Oxford (2007)Google Scholar
  24. 24.
    Viro, O.: Dequantization of real algebraic geometry on logarithmic paper. In: European Congress of Mathematics, Vol. I (Barcelona, 2000), Progr. Math., 201, pp. 135–146. Birkhäuser (2001)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.California Institute of TechnologyPasadenaUSA

Personalised recommendations