The main focus of my research is Lle algebra, representation theory, division algebra, and linear algebra. 

• University Research Professor (2014/15).

I have research assistantships opportunities for graduate students interested in algebra. Contact me for more information. I am willing to supervise graduate students in the areas of algebra. 

• V. Mazorchuk, K. Zhao, “Simple Virasoro modules which are locally finite over a positive part”, Selecta Math. (N.S.), 20 (2014), no. 3, 839-854.
• R. Lu, K. Zhao, “Irreducible Virasoro modules from irreducible Weyl modules”, J. Algebra, 414(2014), 271-287.
• B. Cox, X. Guo, R. Lu, K. Zhao, “n-Point Virasoro algebras and their modules of densities”, Commun. Contemp. Math. 16 (2014), no. 3, 1350047.
• R. Lu, V. Mazorchuk, K. Zhao, “On simple modules over conformal Galilei algebras”, J. of Pure and Applied Algebra, 218 (2014) 1885-1899.
• X. Guo, G. Liu, and K. Zhao, “Irreducible Harish-Chandra modules over extended Witt algebras”, Arkiv for matematik, 52(2014), no.1, 99-112.
• H. Chen, X. Guo, K. Zhao, “Tensor product weight modules over the Virasoro algebra”, J. London Math. Soc. (2) 88 (2013) 829-844.
• H. Tan, K. Zhao, “Irreducible Virasoro modules from tensor products (II)”, J. Algebra, 394(2013), 357-373.
• G. Liu, K. Zhao, “Irreducible Harish-Chandra modules over the derivation algebras of rational quantum tori”, Glasgow J. Math., Vol. 55(3), 677-693 (2013).
• V. Mazorchuk, K. Zhao, “Characterization of simple highest weight modules”, Canadian Math. Bull., Vol. 56 (3), 606-614 (2013).
• X. Guo, R. Lu and K. Zhao, “Fraction representations and highest-weight-like representations of the Virasoro algebra”, J. Algebra, 387(2013), 68-86.
• L. Feng, K. Zhao, “Classifying zeros of quaternionic two-sided polynomials and computing zeros of two-sided polynomials with complex coefficients”, Pacific J. Math., 262-2 (2013), 317-337.
• X. Guo, R. Lu, K. Zhao, “Classification of irreducible Harish-Chandra modules over generalized Virasoro algebras”, Proceedings of the Edinburgh Mathematical Society, (2012)55, 697-709.
• J. Morita, K. Zhao, “Automorphisms and derivations of Borel subalgebras and their nilradicals in Kac-Moody algebras”, Communications in Contemporary Mathematics, Vol.14, No.2 (2012), 63-84.
• S. Eswara Rao, K. Zhao, “Integrable Representations of Toriodal Lie Algebras Co-ordinatized by Rational Quantum Tori”, J. Algebra, 361 (2012), 225-247.
• L. Feng, H. Tan, K. Zhao,” A generalized Cayley-Hamilton theorem”, Linear Algebra and its Applications, 436 (2012), 2440-2445.
• X. Guo, R. Lu and K. Zhao, “Irreducible modules over the Virasoro algebra”, Documenta Mathematica, 16 (2011), 709-721.
• X. Guo, R. Lu, K. Zhao, “Irreducible Harish-Chandra modules over the loop-Virasoro algebra”, Math. Forum, 23 (2011), 1029-1052.
• G. Liu, K. Zhao, “Irreducible weight modules over derivation algebras of quantum tori”, J. Algebra, Vol.340, 28-34(2011).
• X. Guo, K. Zhao, “Irreducible modules over Witt algebra”, Proc. Amer. Math. Soc., Volume 139, Number 7, July 2011, 2367-2373.
• V. Mazorchuk and K. Zhao, “Supports of weight modules over Witt algebras”, Proceedings of the Royal Society of Edinburgh, 141A, 155-170(2011).
• X. Guo, X. Liu and K. Zhao, “Harish-Chandra modules over the ${Q}$ Heisenberg-Virasoro Algebra”, J Aust. Math. Soc., Vol.89, 9-15(2010).
• R. Lu, K. Zhao, “Classification of Irreducible Weight Modules Over the Twisted Heisenberg-Virasoro Algebra”, Communications in Contemporary Mathematics, Vol.12, No.2, 183-205(2010).
• D. Z. Djokovic, K. Zhao, “An octonion algebra originating in combinatorics”, Proc. Amer. Math. Soc., 138(2010), 4187-4195.
• R. Lu, K. Zhao, “Verma modules over quantum torus Lie algebras”, Canadian Journal of Mathematics, Vol.62 (2), 382-399(2010).

Winter 2017:

• MATH 685, "Advanced Linear Algebra and Lie Algebra"

Fall 2016:

• MATH 222, "Linear Algebra"
• MATH 323, "Introduction to Groups and Rings"
• MATH 422, "Advanced Linear Algebra"

Winter 2016:

• sabbatical leave

Fall 2015:

• MATH 215, "Set Theory"
• MATH 422, "Advanced Linear Algebra"

Fall 2014:

• MATH 222, "Linear Algebra"
• MATH 323, "Introduction to Groups and Rings"

Winter 2014:

• MATH 222, "Linear Algebra"
• MATH 475, "Ring and Field Theory"

Fall 2013:

• MATH 525, "Graduate Algebra for Applications" (graduate course)
• MATH 489, "Honours Seminar" (supervising project)

Winter 2013:

• MATH 222, "Linear Algebra"
• MATH 525, "Graduate Algebra for Applications" (graduate course)

Fall 2012:

• MATH 323, "Introduction to Groups and Rings"
• MATH 425, "Group Theory"

Winter 2012:

• MATH 222, "Linear Algebra"
• MATH 489, "Honours Seminar"

Fall 2011:

• MATH 323, "Introduction to Groups and Rings"
• MATH 475, "Ring and Field Theory"
• MATH 489, "Honours Seminar"

Winter 2011:

• MATH 425, "Group Theory"

Fall 2010:

• MATH 323, "Introduction to Groups and Rings"
• MATH 121, "Mathematical Proofs"

Winter 2010:

• MATH 222, "Linear Algebra"
• MATH 525, "Graduate Algebra for Applications" (graduate course)

Fall 2009:

• MATH 215, "Set theory"
• MATH 103, "Calculus I"
• MATH 489, "Honours Seminar: Number Theory"

Winter 2009:

• MATH 685, "Graduate Lie Algebra"

Summer 2008 (May 5 to July 15):

• MATH 525, "Graduate Algebra for Applications"

Fall 2007:

• MATH 215, "Set Theory"
• MATH 122A, "Introductory Linear Algebra" (course coordinator)
• MATH 122B, "Introductory Linear Algebra"
• MATH 489, "Honours Seminar: Number Theory"

Winter 2007:

• MATH 122D, "Introductory Linear Algebra" (course coordinator)
• MATH 317, "Number Theory"
• MATH 489, "Honours Seminar: Advanced Linear Algebra"

Fall 2006:

• MATH 122A, "Introductory Linear Algebra" (course coordinator)
• MATH 215, "Set Theory"

Winter 2006:

• MATH 222, "Linear Algebra"
• MATH 659, "Harmonic Analysis" (graduate course)

Fall 2005:

• MATH 122, "Introductory Linear Algebra" (course coordinator)
• MATH 422, "Advanced Linear Algebra"

Winter 2005:

• MATH 122-D, "Introductory Linear Algebra" (course coordinator)
• MATH 122-F, "Introductory Linear Algebra"
• MATH 222, "Linear Algebra"
• MATH 489, "Honours Seminar: Lie Groups"

• Editor, International Journal of Mathematics and Mathematical Science, 2011–present.
• Editor, Chinese Advances in Mathematics, 2000–2010.
• Reviewer, American Mathematical Review, 1992–present.
• Reviewer, Zentralblatt Math, 2010–present.
• Editor, Science in China, 2000–2003.
• Editor, Bulletin of Chinese Sciences, 2000–2003.

Visiting scholars of 2016/17:

• Xiufu Zhang, Jiangsu Normal University, China, July 15 – Sept. 10, 2016.
• Xuewen Liu, Zhengzhou University, Sept. 1, 2016 – Aug. 31, 2018.

Visiting scholars of 2015/16:

• Yufeng Pei, Shanghai Normal University, China, Jan. 20 – Feb. 19, 2016.
• Yanan Cai, University of Science and Technology of China, Sept. 1, 2013 – Aug. 30, 2015.
• Genqiang Liu, Henan University, China, Aug. 3–30, 2015.

Visiting scholars of 2014/15:

• Yanan Cai, University of Science and Technology of China, Sept. 1, 2013 – Aug. 30, 2015.
• Haijun Tan, Changchun University of Science and Technology, Changchun, Jilin, 130022, P.R. China, Dec. 1, 2014 – Jan. 31, 2015.
• Qiufan Chen, Tongji University, Shanghai 200092, P.R. China, Dec. 10, 2014 – March 10, 2015.

Visiting scholars of 2013/14:

• Drazen Adamovic, University of Zagreb, Zagreb, Croatia, April 6–18, 2014.
• Volodymyr Mazorchuk, Uppsala University, Uppsala, Sweden, Sept. 19–27, 2013.
• Husheng Qiao, Northwest Normal University, China, Nov. 15, 2012 – Nov. 15, 2013.
• Hongjia Chen, University of Alberta, Feb. 1, 2012 – May 20, 2013.
• Xiufu Zhang, Jiangsu Normal University, March 25, 2013 – March 30, 2014.
• Yongsheng Chen, Henan University, China, May 1, 2013 – Dec. 31, 2013.
• Jian-gang Zhang, Shanghai Normal University, Sept. 3, 2013 – Aug. 30, 2014.
• Ran Shen, Shanghai Normal University, Sept. 3, 2013 – Aug. 30, 2014.
• Rencai Lu, Suzhou University, China, Sept. 5, 2013 – Aug. 30, 2014 (at UW).
• Yanan Cai, University of Science and Technology of China, Sept. 1, 2013 – Aug. 30, 2015.

Visiting scholars of 2012/13:

• Xianqian Guo, Zhengzhou Univeristy, China. Feb. 4, 2012 – Jan. 30, 2013.
• Hongjia Chen, University of Alberta, Feb. 1, 2012 – July 31, 2013.
• Vyacheslav Futorny, University of São Paulo, Brazil, Feb. 20 – March 4, 2012.
• Husheng Qiao, Northwest Normal University, China, Nov. 15, 2012 – Nov. 15, 2013.

Visiting scholars of 2011/12:

• Feng Lianggui, National University of Defense Technology, Feb. 20, 11 – Feb. 21, 2012.
• Ben Cox, College of Charleston, USA, June 5 – June 18, 2011
• Yin Chen, Northeast Normal University, April 1 – Aug. 31, 2011.
• Xiangqian Guo, Zhengzhou University, Feb. 4, 2012 – Jan. 30, 2013.
• Volodymyr Mazorchuk, Uppsala University, Sweden, April 17, 2012 – April 29, 2012.

Visiting scholars of 2010/11:

• Feng Lianggui, National University of Defense Technology, Feb. 20, 2011 – Feb. 21, 2012.
• Yin Chen, Northeast Normal University, April 1 – Aug. 31, 2011.
• Ben Cox, College of Charleston, USA, June 27 – July 9, 2010
• Xiangqian Guo, Zhengzhou University, Feb. 4, 2012 – Jan. 30, 2013.
• Fernando Szechtman, Univeristy of Regina, Canada, January, 2011

Visiting scholars of 2008/09:

• Volodymyr Mazorchuk, Uppsala University, Sweden, April 19, 2009 – May 9, 2009.
• Senapati Eswara Rao, Tata Institute, India, Aug. 2 – Aug. 29, 2008.