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Research Interests

Matrices, Lie Algebras, Lie Groups, Symmetric Spaces, etc.


Publications

8.

Xuhua Liu, Tin-Yau Tam
Extensions of three matrix inequalities to semisimple Lie groups
Submitted.

7.

Xuhua Liu, Ronald L. Smith
The copositive-plus matrix completion problem
Submitted.

6.

Ming Liao, Xuhua Liu, Tin-Yau Tam
A geometric mean for symmetric spaces of noncompact type
Journal of Lie Theory, Vol.24 (2014) No.3, 725-736.

5.

Xuhua Liu, Tin-Yau Tam
Connectedness, Hessians and generalized numerical ranges
Textos de Matematica, The Natalia Bebiano Anniversary Volume, Vol.44 (2013), 107-119.

4.

Xuhua Liu, Brice M. Nguelifack, Tin-Yau Tam 
Unitary similarity to a complex symmetric matrix and its extension to orthogonal symmetric Lie algebras
Linear Algebra and Its Applications, Vol.438 (2013), No.10, 3789-3796.

3.

Xuhua Liu, Tin-Yau Tam 
Gradient flows for the minimum distance to the sum of adjoint orbits
Linear and Multilinear Algebra, Vol.61 (2013), No.5, 678-696.

2.

Xuhua Liu, Dawit G. Tadesse, Tin-Yau Tam 
A range associated with skew symmetric matrix
Linear and Multilinear Algebra, Vol.59 (2011), No.10, 1105-1120.

1.

Wai-Shun Cheung, Xuhua Liu, Tin-Yau Tam 
Multiplicities, boundary points, and joint numerical ranges
Operators and Matrices, Vol.5 (2011), No.1, 41-52.

0. Xuhua Liu 
Gradient Flows, Convexity, and Adjoint Orbits
PhD Dissertation, Auburn University, 2012. 

Conferences and Presentations

18 

Southern Regional Algebra Conference, Auburn University Montgomery, April 25-27, 2014. 
Talk: Inequalities on Elements of Lie Groups

17

Southeast Geometry Seminar XXIII, Emory University, November 10, 2013.

16

Mathematics Colloquium, The University of Tennessee at Chattanooga, October 25, 2013. 
Talk: Geometric Mean for Symmetric Spaces of Noncompact Type

15.

The 18th Conference of the International Linear Algebra Society, Providence, Rhode Island, USA, June 3-7, 2013.
Talk: Connectedness, Hessian, and Generalized Numerical Ranges

14.

The Sixth Annual Southeastern Lie Theory Conference on Noncommutative Algebraic Geometry and Representation Theory, Louisiana State University, May 10-12, 2013.

13.

Southern Regional Algebra Conference, Southeastern Louisiana University, March 15-17, 2013. 
Talk: On Copositive-Plus Matrices

12.

Mathematics Colloquium, The University of Tennessee at Chattanooga, October 5, 2012. 
Talk: Connectedness, Hessian, and Generalized Numerical Range

11.

Southern Regional Algebra Conference, Clayton State University, March 30 - April 1, 2012. 
Talk: Unitary Similarity to a Complex Symmetric Matrix and its Extension to Orthogonal Symmetric Lie Algebras

10.

Math Club Talk, Auburn University Montgomery, March 23, 2012. 
Talk: An Invitation to Numerical Range

9.

Joint Mathematics Meetings, Boston, January 4-7, 2012. 
Talk: Gradient Flows for the Minimum Distance to the Sum of Adjoint Orbits

8.

Graduate Student Seminar, Department of Mathematics and Statistics, Auburn University, September 28, 2011. 
Talk: Unitary Similarity to a Complex Symmetric Matrix

7.

Graduate Student Seminar, Department of Mathematics and Statistics, Auburn University, March 23, 2011. 
Talk: An Invitation to Lie Theory

6.

Joint Mathematics Meetings, New Orleans, January 6-9, 2011. 
Talk: Multiplicities and Generalized Numerical Ranges

5.

The Second Annual Southeastern Lie Theory Conference on Homological Methods in Representation Theory, University of Georgia, May 22-24, 2010.

4.

Southern Regional Algebra Conference, Auburn University Montgomery, March 26-28, 2010. 
Talk: Multiplicities and Joint Numerical Ranges

3.

Graduate Student Seminar, Department of Mathematics and Statistics, Auburn University, March 24, 2010. 
Talk: Numerical Range

2.

The First Annual Southeastern Lie Theory Conference on Combinatorial Lie Theory and Applications, North Carolina State University, October 9-11, 2009.

1.

IMA PI Summer Program for Graduate Students: Linear Algebra and Applications, Iowa State University, June 30 - July 25, 2008.


Professional Memberships

  • International Linear Algebra Society (ILAS)
  • American Mathematical Society (AMS)

Journal Referee

  • Linear Algebra and its Applications (LAA)
  • Linear and Multilinear Algebra (LAMA)
  • The Electronic Journal of Linear Algebra (ELA)
  • Mathematical Communications
  • Alabama Journal of Mathematics
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