Li Guo's Home Page


Address: Department of Mathematics and Computer Science, Rutgers University at Newark, Newark, NJ 07102
E-mail: liguo@rutgers.edu; Phone: (973)353-3917; Fax: (973) 353-5270.
Teaching: Spring 2012:
  • Calculus I. .
    Research: I am interested in algebra, especially Rota-Baxter algebra, and its applications to number theory, mathematical physics, operads and combinatorics. For a brief discussion of Rota-Baxter algebra, see WHAT IS a Rota-Baxter Algebra, Notice of Amer. Math. Soc. 56 (2009), 1436-1437. For a more detailed introduction, see the forthcoming book An Introduction to Rota-Baxter Algebra. See also A Page on Rota-Baxter Algebra for a list of related references.
    Conferences:
  • Differential Algebra and Related Topics IV, October 27 - 30, 2010 Beijing, China (with X. Gao, J. Hartmann, E. Hubert, Z. Li, F. Ollivier, M. Singer and W. Sit).
  • Operads and Universal Algebra, June 28 - July 9, 2010 at Chern Institute of Mathematics, Nankai University, Tianjin, China (with C. Bai, J-L. Loday et. al).
  • Third International Workshop on Differential Algebra and Related Topics III, November 13-16, 2008 at Rutgers University at Newark (with M. Marcolli, M. Singer, W. Sit and J. Stasheff).
  • AMS Special Session on Noncommutative Geometry and Arithmetic Geometry, October 6-7, 2007 at New Brunswick (with C. Consani).
  • Second International Workshop on Differential Algebra and Related Topics II, April 12-13, 2007 at Rutgers University at Newark, (with P. J. Cassidy, R. Churchill, W. Keigher, J. Kovacic and W. Sit).
  • AMS Special Session on Differential Algebra and Related Topics, April 14-15, 2007 at Stevens Institute of Technology, Hoboken, NJ, (with P. J. Cassidy, R. Churchill, W. Keigher, J. Kovacic and W. Sit).
    Recent papers (see here for older papers).
  • Splitting of operations, Manin products and Rota-Baxter operators, (with C. Bai, O. Bellier and X. Ni), to appear in Int. Math. Res. Not. IMRN. arXiv:1106.6080.
  • Structure of Hochschild cohomology of path algebras and differential formulation of Euler's polyhedron formula (with F. Li), submitted.
  • PostLie algebra structures on the Lie algebra sl(2,C) (with C. Bai, Y. Pan and Q. Liu), to appear in Electron. J. Linear Algebra arXiv:1111.6128.
  • Relative Rota-Baxter operators on associative algebras and dendriform algebras (with C. Bai and X. Ni), submitted.
  • O-operators on associative algebras and associative Yang-Baxter equations, (with C. Bai and X. Ni), to appear in Pacific J. Math. arXiv:0910.3261.
  • Generalizations of the classical Yang-Baxter equation and O-operators (with C. Bai and X. Ni), to appear in J. Math. Phys.
  • On Rota's problem for linear operators in associative algebras (with W. Sit and R. Zhang), to appear in Proc. of ISSAC'11.
  • O-operators on associative algebras, associative Yang-Baxter equations and dendriform algebras, a survey, (with C. Bai and X. Ni), to appear in Quantized Algebra and Physics.
  • Enumeration and generating functions of differential Rota-Baxter words (with W. Sit), Math. in Comp. Sci. 4 (2010), 339-358.
  • Shuffle relation of fractions from multiple zeta values and their product formula (with B. Xie), Ramanujan Jour. 25 (2011) 307-317.
  • Enumeration and generating functions of Rota-Baxter words (with W. Sit), to appear in Math. in Comp. Sci. 4 (2010), 313-337.
  • Polylogarithms and multiple zeta values from free Rota-Baxter algebras (with B. Zhang), Science in China. 53 (2010) 2239-2258.
  • Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras, (with C. Bai and X. Ni), Comm. Math. Phys. 297 (2010) 553-596.
  • WHAT IS a Rota-Baxter algebra, Notice of Amer. Math. Soc. 56 (2009), 1436-1437.
  • Double shuffle relations and renormalization of multiple zeta values (with S. Paycha, B. Xie and B. Zhang), to appear in Proceedings of the Conference on Algebraic Cycles, 2008.
  • Weighted sum formula for multiple zeta values, (with Bingyong Xie) J. Number Theory 129 (2009), 2747-2765, arXiv:0809.5110v1 [math.NT].
  • Explicit double shuffle relations and a generalization of Euler's decomposition formula, (with Bingyong Xie) arXiv:0808.2618v1 [math.NT].
  • Structure theorems of mixable shuffle algebras and free commutative Rota-Baxter algebras, (with Bingyong Xie) to appear in Comm. Algebra, arXiv:0807.2267v2 [math.RA].
  • Rota-Baxter operators on generalized power series rings, (with Zhongkui Liu), J. Algebra & Its Applications 8 (2009), 557-564, arXiv:0710.0433v1 [math.RA].
  • Algebraic Birkhoff decomposition and its applications, Automorphic Forms and the Langlands Program, International Press, 2008, 283-323.
  • Operated semigroups, Motzkin paths and rooted trees, J. Algebraic Combinatorics 29 (2009), 35-62.
  • Renormalization of multiple zeta values, (with Bin Zhang), J. Algebra 319 (2008), 3770-3809.
  • Free Rota-Baxter algebras and rooted trees, (with K. Ebrahimi-Fard), J. Algebra and Its Applications, 7 (2008), 167-194.
  • On matrix representation of renormalization in perturbative quantum field theory, (with K. Ebrahimi-Fard), ArXiv: hep-th/0508155.
  • Differential Birkhoff decomposition and renormalization of multiple zeta values, (with Bin Zhang) J. Number Theory 128, 2318-2339.
  • On differential Rota-Baxter algebras, (with William Keigher), J. Pure Appl. Algebra 212 (2008) 522-540, arXiv:math.RA/0703780.
  • Rota-Baxter algebras and dendriform algebras, (with K. Ebrahimi-Fard), Jour. Pure Appl. Algebra 212 (2008), 320-339, arXiv:math/0503647.
  • Rota-Baxter algebras and multiple zeta values, (with K. Ebrahimi-Fard), Integers 8 (2008) A4.
  • Unit actions on operads and Hopf algebras, (with K. Ebrahimi-Fard), Theory and Applications of Categories 18 (2007), 348-371, arXiv:math.RA/0503342.
  • Rota-Baxter algebras in renormalization of perturbative quantum field theory, (with K. Ebrahimi-Fard) in Universality and Renormalization, I. Binder and D. Kreimer, editors, Fields Institute Communicatins, v. 50, AMS 2007, 47-105, arXiv:hep-th/0604116.
  • Enumeration of Rota-Baxter words, (with William Y. Sit), in Proceedings ISSAC 2006, Genoa, Italy, ACM Press, 124-131, 2006, arXiv: math.RA/0602449.
  • Birkhoff type decompositions and the Baker-Campbell-Hausdorff recursion, (with K. Ebrahimi-Fard and D. Manchon), Comm. Math. Physics 267 (2006) 821-845, arXiv:math-ph/0602004.
  • Quasi-shuffles, mixable shuffles and Hopf algebras, (with K. Ebrahimi-Fard) J. Algebraic Combinatorics 24, no 1, (2006), 83-101, arXiv:math.RA/0506418.
  • Combinatorics of renormalization as matrix calculus, (with K. Ebrahimi-Fard, J. M. Gracia-Bondia and J. C. Varilly), Physics Letters B, 19 (2006), 552-558, arXiv:hep-th/0508154.
  • On products and duality of binary, quadratic, regular operads, (with K. Ebrahimi-Fard), J. Pure Applied Algebra, 200 (2005), 293-317, ArXiv: math.RA/0407162.
  • Integrable renormalization II: the general case, (with K. Ebrahimi-Fard and D. Kreimer) Annales Henri Poincare 6 (2005) 369-395, arXiv:hep-th/0403118.
  • Baxter algebras, Stirling numbers and partitions, J. Alg. Appl. 4 (2005), 153-164, arXiv:math.AC/0402348.
  • Spitzer's Identity and the Algebraic Birkhoff Decomposition in pQFT, (with K. Ebrahimi-Fard, D. Kreimer), J. Phys. A: Math. Gen. 37 (2004) 11037-11052, ArXiv:hep-th/0407082.
  • Adjoint motives of modular forms and the Tamagawa number conjecture, (with F. Diamond and M. Flach), Ann Sci ENS. 37 (2004), no. 5, 663-727.
  • Integrable renormalization I: the ladder case, (with K. Ebrahimi-Fard and D. Kreimer) J. Math. Phys. 45 (2004), 3758-3769, arXiv:hep-th/0402095.
  • Baxter algebras and Hopf algebras, (with G. E. Andrews, W. Keigher and K. Ono), Trans. Amer. Math. Soc. 355 (2003), no.11, 4639-4656.

  • Editorial Board:
  • Global Journal of Mathematics and Mathematical Sciences (GJMMS) ;
  • International Journal of Pure & Applied Mathematical Sciences (IJPAMS) .

    Recent and future talks, conferences and visits.

    Check here for the Workshop on Differential Algebra and Related Topics that Phyllis Cassidy, William Keigher, William Sit and I organized.

    Check here for seminars at Rutgers-Newark, Columbia, New Brunswich, Princeton University, CUNY Graduate Center and the Institute for Advanced Study.

    Check here for the MathSciNet, the arXiv, the number theory web