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: Fall 2015:

·  Math for Liberal Arts


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 book An Introduction to Rota-Baxter Algebra, International Press and High Education Press. See also A Page on Rota-Baxter Algebra for a list of related references.


Publications: Find my papers posted on the arXiv. Take a look of my ResearchGate profile. See below for a selected list of publications.


Conference organization:

·  Differential Algebra and Related Topics VI, August 10-14, 2015 Beijing, China (with X. Gao and R. Feng).

·  Higher Structures in China IV, August 14 – 16, 2013, Lanzhou (with C. Chen, Y. Sheng and W. Pan).

·  Mathematical Methods in Physics (KITPC), July 22 – September 5, 2013 Beijing, China (with F. Li, Z. Lin et. al).

·  International Workshop on Multiple Zeta Values, Rota-Baxter Algebras and Related Topics, August 1-4, 2012 Lanzhou, China (with Y. Luo and H. Zhang).

·  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).


Selected publications.

1.      Monads and distributive laws for Rota-Baxter and differential algebras (with W. Keigher and S. Zhang), Adv Applied Math, to appear, arXiv:1412.8058.

2.      Rota-Baxter type operators, rewriting systems and Gröbner-Shirshov bases (with X. Gao, W. Sit and S. Zheng), Jour. Symbolic Computation, accepted, arXiv: 1412.8055.

3.      Rota-Baxter operators on polynomial algebra, integration and averaging operators (with M. Rosenkranz and S. Zheng), Pacific Jour. Math. 275 (2015) 481-507, arXiv:1407.5306.

4.      Free integro-differential algebras and Gr¨ obner-Shirshov bases (with X. Gao and M. Rosenkranz), J. Algebra, 442 (2015) 354-396, arXiv:1402.1890.

5.      Averaging algebras, Schroeder numbers and rooted trees (with J. Pei), Jour. Algebraic Combinatorics, 42 (2015) 73-109, arXiv:1401.7386.

6.      Families of weighted sum formulas for multiple zeta values (with P. Lei and J. Zhao), International Jour. Number Theory, 11 (2015) 997-1025, arXiv:1401.6461.

7.      Generating functions from the viewpoint of Rota-Baxter algebras (with N. S. Gu), Discrete Structures, 338 (2015) 536-554, arXiv:1301.3419.

8.      Structure of Hochschild cohomology of path algebras and differential formulation of Euler’s polyhedron formula (with F. Li), Asian Journal of Mathematics, 18 (2014) 545-572, arXiv:1010.1980.

9.      Applications of shuffle product to restricted decomposition formulas for multiple zeta values (with P. Lei and B. Ma), Jour. Number Theory, 144 (2014) 219-233.

10.  Rota-Baxter operators on sl(2,C) and solutions of the classical Yang-Baxter equation (with C. Bai and J. Pei), Jour. Math. Phys. 55 (2014), 021701.

11.  Conical zeta values and their double subdivision relations (with S. Paycha and B. Zhang), Adv. Math. 252 (2014) 343-381.

12.  Localization of Rota-Baxter algebras (with C. Chu), J. Pure Appl. Algebra, 218 (2014), 237-251, arXiv:1210.1799.

13.  On integro-differential algebra (with G. Regensburger and R. M. Rosenkranz), J. Pure Appl. Algebra 218 (2014), 456-471, arXiv:1212.0266.

14.  Rota-Baxter 3-Lie algebras (R. Bai, J. Li and Y. Wu), Jour. Math. Phy. 54 (2013), 063504.

15.  The category and operad of matching dialgebras (with C. Bai and Y. Zhang), Applied Categorical Structures 21 (2013), 851-865.

16.  Structure theorems of mixable shuffle algebr as and free commutative Rota-Baxter algebras (with B. Xie), Comm. Alg. 41 (2013), 2629-2649, arXiv:0807:2267.

17.  Relative Rota-Baxter algebras and tridendriform algebras (with C. Bai and X. Ni), Jour.Alg. Its Appl 12 (2013), 1350027, arXiv:1003.2432.

18.  Explicit shuffle relations of MZVs and a generalization of Euler’s decomposition formula (with B. Xie), J. Algebra 380 (2013), 46-77.

19.  Differential type operators and Gr¨ obner-Shirshov bases (with W. Sit and R. Zhang), J. Symbolic Computation 52 (2013), 97-123.

20.  Splitting of operations, Manin products and = Rota-Baxter operators (with C. Bai, O. Bellier and X. Ni), Int. Math. Res. Not. IMRN. (2013), 485-524.


Editorial Board:

·  Global Journal of Mathematics and Mathematical Sciences (GJMMS) ;

·  International Journal of Pure & Applied Mathematical Sciences (IJPAMS) .

Recent talks and conferences.

1.      Renormalization of conical zeta values and Euler-Maclaurin formula, Resurgence, Physics and Numbers, Pisa, Italy, May 2015.

2.      Construction of free integro-differential algebras by the method of Gröbner-Shirshov bases, Kolchin Seminar, Graduate Center, CUNY, US, April 2014.

3.      Decomposition formulas for multiple zeta values, New York Number Theory Seminar, Graduate Center, CUNY, April 2014.

4.      Free integro-differenital algebras, AMS Reginal Meeting, Texas Tech Unive= rsity, Lubbock, US, April 2014.

5.      Splitting and replicating of operads, Algebra Seminar, Temple University, Philadelphia, US, April 2014.

6.      Splitting and replicating of operads, Workshop on Representation Theory and Combinatorics, University of Science and Technology of Southern China, Guangzhou, China, December 2013.

7.      Conical zeta values and renormalization, Math Colloquium, Pekin University, Beijing, China, October 2013.

8.      Constructions of free i= ntegro-differential algebras, Kolchin Seminar, Graduate Center, CUNY, US, May 2013.

9.      Cone multiple zeta values and their renormalization, Renormalization at the Confluence of Analysis, Algebra and Geometry, Luminy, France, September 2012.

10.  Successors and duplicators of operads, The XXIX International Colloquium on Group Theoretic Methods in Physics, Tianjin, China, August 2012.

11.  Free integro-differential algebras, 18th International Conference on Applications of Computer Algebra, Sophia, Bulgaria, June 2012.  

12.  Differential type operators, rewriting systems and Gröbner-Shirshov bases, Kolchin Seminar, Graduate Center, CUNY, April 2012.

13.  Differential type operators, rewriting systems and Gröbner-Shirshov bases, Colloquium, Northwest Normal University, China, January 2012.

14.  Rota-Baxter operators on associative algebras, Lie algebras and generalizations, Workshop on Lie Theory and Applications, University of Science and Technology of China, Hefei, December 2011.

 


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