Research Interests: Spectral theory, partial differential equations, stable processes.    

In particular: Eigenvalue inequalities for Klein-Gordon operators,Dirichlet Laplacian, Fractional Laplacian and symmetric stable processes.

Teaching:

Summer 2012: MA 527: Advanced Mathematics for Engineers and Physicists I

Spring 2012  : MA 351- Elementary Linear Algebra

Fall 2011  : MA 351- Elementary Linear Algebra

Spring 2011: MA 351- Elementary Linear Algebra

Fall 2010  : MA 262- Linear Algebra and Differential Equations

Work in Progress:

1. On the eigenvalues of Stokes operator, (with T. Yolcu) in preparation.

2. On the sums of eigenvalues of poly-Laplacian operator, (with T. Yolcu) in preparation.

Papers and Preprints:

8. Estimates on the eigenvalues of the clamped plate problem (with T. Yolcu), 2012, submitted.

7.  Heat trace of nonlocal operators (with R. Banuelos), 2012, submitted.

6. Estimates for the sums of eigenvalues of the fractional Laplacian on a bounded domain (with T. Yolcu), 2011, submitted.

5. Multidimensional lower bounds for the eigenvalues of Stokes and Dirichlet Laplacian operators (with T. Yolcu), 2012, to appear in the Journal of Mathematical Physics, April 2012.

4. Bounds for the eigenvalues of the fractional Laplacian (with T. Yolcu), 2012, Reviews in Mathematical Physics, Vol.24, No.3, (2012) 1250003 (18 pages).

3. An Improvement to a Berezin-Li-Yau type inequality for the Klein-Gordon Operator, Proc. Amer. Math. Soc. 138, Number 11 (2010) 4059-4066.

2. Eigenvalue inequalities for Klein-Gordon Operators, (with  E. Harrell), Journal of Functional Analysis 256, Issue 12 (2009) 3977-3995.

1. Eigenvalue Inequalities for Relativistic Hamiltonians and Fractional Laplacian, PhD Thesis (December 2009).

Awards:

1. 2009 CETL/BP Outstanding Graduate Student Instructor (GSI) Award, Georgia Tech.

2. 2008 Outstanding Teaching Assistant Award, School of Math, Georgia Tech.