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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

20.

Southeast Geometry Seminar XXV, University of Tennessee, Knoxville, October 26, 2014.

19.

Mathematics Colloquium, The University of Tennessee at Chattanooga, September 10, 2014. 
Talk: Extensions of three matrix inequalities to semisimple Lie groups

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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