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.
-
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.
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- 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.