Li Guo's Home Page

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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.

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Teaching: Spring 2013:

· Calculus I. Syllabus. , Review1,Review 2，Final Review.

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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.

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Conference organization:

· 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).

· 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).

· 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).

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Recent papers (see here for older papers).

· Generating functions from the view point of Rota-Baxter algebras (with N. S. Gu), arXiv:1301.3419, submitted.

· Conical zeta values and their double subdivision relations (with S. Paycha and B. Zhang), arXiv:1301.3370, submitted.

· Replicating of binary operads, Koszul duality, Main products and averaging operators (with J. Pei, C. Bai and X. Ni), arXiv:1212.0177.

· On integro-differential algebra (with G. Regensburger and R. M. Rosenkranz), arXiv:1212.0266, submitted.

· Structure of Hochschild cohomology of path algebras and differential formulation of Euler's polyhedron formula (with F. Li), to appear in Asian J. Math., arXiv:1010.1980.

· Localization of Rota-Baxter algebras, (with Chenghao Chu),to appear in J.Pure Appl. Algerba.

· Explicit double shuffle relations and a generalization of Euler's decomposition formula, (with Bingyong Xie), J. Algebra, 380 (2013), 46-77.

· 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].

· Differential type operators and Grobner-Shirshov bases (with W. Sit and R. Zhang), J. Symbolic Computation, 52 (2013), 97-123.

· The category and operad of matching dialgebras (with C. Bai and Y. Zhang), Applied Categorial Structures, 2012, DOI:10.1007/s10485-012-9290-7.

· Nijenhuis algebras, NS algebras and N-dendriform algebras (with P. Lei), Frontiers Math. 7 (2012) 827-846.

· Splitting of operations, Manin products and Rota-Baxter operators, (with C. Bai, O. Bellier and X. Ni), Int. Math. Res. Not. IMRN. (2012); doi:10.1093/imrn/rnr266, arXiv:1106.6080.

· PostLie algebra structures on the Lie algebra sl(2,C) (with C. Bai, Y. Pan and Q. Liu), Electron. J. Linear Algebra 23 (2012) 180-197, arXiv:1111.6128.

· Relative Rota-Baxter operators on associative algebras and dendriform algebras (with C. Bai and X. Ni), to appear in J. Algebra and Its Applications.

· O-operators on associative algebras and associative Yang-Baxter equations, (with C. Bai and X. Ni), Pacific J. Math. 256 (2012) 257-289, arXiv:0910.3261.

· Generalizations of the classical Yang-Baxter equation and O-operators (with C. Bai and X. Ni), J. Math. Phys. 52 (2011) 063515.

· On Rota's problem for linear operators in associative algebras (with W. Sit and R. Zhang), Proc. ISSAC'11, 147-154.

· O-operators on associative algebras, associative Yang-Baxter equations and dendriform algebras, a survey, (with C. Bai and X. Ni), Quantized Algebra and Physics (2012) 10-51.

· Enumeration and generating functions of differential Rota-Baxter words (with W. Sit), Math. 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), Math. 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.

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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.

· Oberseminar, Max Planck Institute in Mathematics, Germany, August 2008.

· Number Theory Seminar, Max Planck Institute in Mathematics, Germany, August 2008.

· Applied and Computational Algebra 08, Linz University, Austria, July 2008

· Noncommutative geometry and geometry over the field with one element, Vanderbilt University, May 2008.

· Conference on Algebraic Cycles, Ohio State University, March 2008.

· Kolchin Seminar, Graduate Center, CUNY, February 2008.

· Colloquium, Iowa State University, November 2007.

· Colloquium, Kansas State University, October 2007.

· International Conference on Noncommutative Geometry, Tianjing, China, August 2007.

· Second International Congress in Algebra and Combinatorics (ICAC 07), Xi'an, China, July 2007.

· Formal Power Series and Algebraic Combinatorics (FPSAC 2007), Tianjing, China, July 2007.

· Langlands and Geometric Langlands Program, Guangzhou, China, June 2007.

· Combinatorial and Additive Number Theory (CANT 2007), Multiple zeta values at negative integers, New York, May 2007.

· AMS Special Session Algebraic structures on rooted trees, Hoboken, NJ, April 2007. \vspace{-.5cm}

· Colloquium, Quasi-shuffle and renormalization of multiple zeta values, Wesleyan University, CT, April 2007.

· Kolchin Seminar, Birkhoff decomposition of differential algebras and multiple zeta values, CUNY Hunter College, December 2006.

· Algebraic Geometry Seminar, Renormalization of multiple zeta values, Ohio State University, Columbus, OH, November 2006

· Algebra Seminar, Rota-Baxter algebras and their constructions, Fudan University, Shanghai, China, August 2006

· Algebra Seminar, Zhejiang University, Hangzhou, China, August 2006.

· Mathematical Physics Seminar, Algebraic approach of renormalization of quantum field theory, Chern Institute of Mathematics, Tianjin, China, July 2006.

· Number Theory Seminar, Algebraic Birkhoff decomposition and renormalization of multiple zeta values, Capital Normal University, Beijing, June 2006.

· Two lectures on multiple zeta values, Morningside Center, Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing, June 2006.

· Conference on Motives and Periods, Algebraic Birkhoff decomposition and renormalization of multiple zeta values, University of British Columbia, Vancouver, June 5-12, 2006.

· Mini Course The fourth annual spring institute on NCGOA: Noncommutative Geometry, Quantum Field Theory and Motives, Constructions and applications of Rota-Baxter algebras, Nashville, May 2006.

· Renormalization and Galois theory, Regularization renormalization of multiple zeta values, Luminy, France, March 2006.

· Oberseminar, Rota-Baxter algebras: their constructions and applications, Max Planck Institute for Mathematics, Bonn, December 2005.

· Number Theory Seminar, Renormalization and multiple zeta values at non-positive integers, Max Planck Institute at Bonn, December 2005.

· Algebra and Topology Seminar, On Birkhoff type decompositions, Nice University, Nice, France, December 2005.

· Algebra Seminar, Rota-Baxter algebra of rooted trees and operads, Buhr-University, Bochum, Germany, November 2005.

· Mathematical Physics Seminar, Rota-Baxter algebras and shuffle products, rooted trees and operads, Max-Planck Institute, Leipzig, Germany, November 2005.

· Renormalization and universality in mathematical physics workshop, Rota-Baxter algebra method in the Hopf algebra approach of pQFT renormalization, Fields Institute, Toronto, October 2005, Toronto.

· Algebra and Combinatorics Seminar, Free Rota-Baxter algebras, shuffle products, rooted trees and operads, Texas A&M University, Texas, September 2005.

· Colloquium, Rota-Baxter algebra and its applications, City University of New York, CUNY, New York, September 2005

· Open Questions and Recent Developments in Iwasawa Theory, In honor of Ralph Greenberg's 60th Birthday, Boston University, June 13-17, 2005, Boston.

· Combinatorical and Additive Number Theory (CANT 2005), Rota-Baxter operators and multiple zeta values, New York, May 2005.

· Operads 2005, Coherent unit actions and Hopf algebras, Luminy, France, April 2005.

· Mathematical Physics Seminar, Rota-Baxter algebras, operators and operads, University of Lyon, France, April 2005.

· Mathematics Seminar, Free Rota-Baxter algebras and shuffle products, IHES, Paris, March 2005.

· Seminar of pure mathematics,Aspects of Rota-Baxter operators, University of Clermont-Ferrand, France, March 2005.

· Number Theory Seminar,Special values of zeta functions and multiple zeta functions, University of Nancy, France, March 2005.

· Algebra and Toplogy Seminar,Multiple zeta values and Rota-Baxter operators, University of Strasbourg, France, March 2005.

· Algebra Seminar, Birkhoff decomposition in QFT and CBH formula, Rutgers University, New Brunswick, February 2005.

· Kolchin Seminar, From quantum field theory renormalization to differential Galois groups, CUNY Hunter College, December 2004.

· Mathematical Physics Seminar, Rota-Baxter type operators, shuffle type products and congruences , Boston University, Boston, November 2004.

· Colloquium, Rota-Baxter algebras in the renormalization of QFT, West Ontario University, June 2004.

· Canadian Number Theory Association VIII, Baxter algebras and multiple zeta values, Fields Institute, Toronto, June 2004.

· Algebra Seminar, Dendriform algebras and linear operators, Rutgers University, New Brunswick, April 2004.

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

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

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