Li Guo's Home Page

Address: Department of Mathematics and Computer Science, Rutgers University at Newark, Newark, NJ 07102
E-mail: liguo@newark.rutgers.edu; Phone: (973)353-5156 ext. 30; Fax: (973) 353-5270.

Teaching:

Spring 2009: Differential Equations. Syllabus , Review 2.

Topics in Algebra.

Research interests: Algebra and applications in number theory, mathematical physics and combinatorics.

Editorial Board:

Global Journal of Mathematics and Mathematical Sciences (GJMMS) ;

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

Conference Organizers:

Third International Workshop on Differential Algebra and Related Topics on 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 on October 6-7, 2007 at New Brunswick, (with Caterina Consani).

Second International Workshop on Differential Algebra and Related Topics on 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 on 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).

Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras, (with C. Bai and X. Ni), to appear in Comm. Math. Phys..
WHAT IS a Rota-Baxter algebra, to appear in Notice of AMS.
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.
Shuffle relation of fractions from multiple zeta values and their product formula (with B. Xie), submitted.
O-operators on associative algebras and associative Yang-Baxter equations, (with C. Bai and X. Ni), submitted.
Shuffle relation of fractions from multiple zeta values and their product formula (with B. Xie), submitted.
Weighted sum formula for multiple zeta values, (with Bingyong Xie) to appear in J. Number Theory, 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) arXiv:0807.2267v2 [math.RA].
Rota-Baxter operators on generalized power series rings, (with Zhongkui Liu), to appear in J. Algebra Its Applications 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.

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
AMS Special Session, Renormalization of multiple zeta values, Storrs, CT, October 2006.
Algebra Seminar, Rota-Baxter algebras and their constructions, Fudan University, Shanghai, China, August 2006
Algebra Seminar, Zhejiang University, Hangzhou, China, August 2006.
Three lectures on semigroups with operators and combinatorics, Kunming University, Kunming, China, August, 2006.
Two lectures on Rota-Baxter algebras, Northwest Normal University, Lanzhou, China, August 2006.
Six lectures on Rota-Baxter algebras, Lanzhou University, Lanzhou, China, July 2006.
Mathematical Physics Seminar, Algebraic approach of renormalization of quantum field theory, Chern Institute of Mathematics, Tianjin, China, July 2006.
Two lectures on combinatorial and operads, Combinatorial Center, 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.
AMS Regional Meeting, Combinatorics of Rota-Baxter algebras, Bard College, NY, October 2005.
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.
AMS Regional Meeting, Commutative Baxter algebras and commutative dendriform algebras, Lawrenceville, NJ, April 2004.
New York Number Theory Seminar, Baxter algebras and generating functions, CUNY Graduate Center, March 2004.
Kolchin Seminar, Differential algebras and dendriform algebras, CUNY Hunter College, March 2004.

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.