Selma Yildirim Yolcu

I am a Visiting Fellow at Case Western Reserve University. Before this, I was a postdoc at Purdue University working with R. Banuelos from 2010 to 2013.

Department of Mathematics
Case Western Reserve University
10900 Euclid Ave, Yost Hall 231
Cleveland, OH 44106

Office: Yost Hall 341

This semester, I am teaching MATH 223: Multivariable Calculus (2 sections). Course website is Blackboard.


My office hours are M 12:00pm-1:20pm, W 11:30am-12:20pm.





MWF 9:30am-10:20am

Wickenden Building 306


MWF 10:30am-11:20am

Wickenden Building 306

PhD in Mathematics, Georgia Institute of Technology, 2009. My adviser is Evans M. Harrell.

Research Interests: Partial Differential Equations, Mathematical Physics and probability(symmetric stable processes).

Research Publications:

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

2. An Improvement to a Berezin-Li-Yau type inequality for the Klein-Gordon Operator, Proceedings of the American Mathematical Society, 138(11) (2010) 4059-4066.

3. Bounds for the eigenvalues of the fractional Laplacian (with T. Yolcu), Reviews in Mathematical Physics, 24(3) (2012) 1250003.

4. Multidimensional lower bounds for the eigenvalues of Stokes and Dirichlet Laplacian operators (with T. Yolcu), Journal of Mathematical Physics, 53(4) (2012) 043508.

5. Estimates for the sums of eigenvalues of the fractional Laplacian on a bounded domain (with T. Yolcu),  Communications in Contemporary Mathematics (2013) (DOI: 10.1142/S0219199712500484)

6.  Heat trace of nonlocal operators (with R. Banuelos), Journal of the London Mathematical Society, 87(1) (2013) 304-318.

7. Estimates on the eigenvalues of the clamped plate problem (with T. Yolcu),  Journal of Mathematical Physics, 54(4), (2013) 43515 .

Articles Submitted to a Journal

8. Eigenvalue bounds for the poly-harmonic operators (with T. Yolcu),  November 2013.

9. Sharper estimates on the eigenvalues of the Dirichlet fractional Laplacian (with T. Yolcu), December 2013.

Work in Progress:

10. Revised Estimates on the eigenvalues of the fractional Laplacian operator on a planar domain  (with T. Yolcu), in progress.

11. Some Estimates for Relativistic Stable Processes (with K. Kaleta and R. Banuelos), in progress.

12. Bounds on the spectra of the Stokes operator, (with T. Yolcu), in preparation.

13. Sharp Bounds for spectral functions of the Klein-Gordon operator (with L. Hermi), (2010), preprint.


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


Previous Teaching Experience at Purdue

Graduate courses:

MA 52000- Boundary Value Problems of Differential Equations: Summer 2013.

MA 52700- Advanced Mathematics for Engineers and Physicists I: Summer 2012.

Undergraduate Courses:

MA 35100- Elementary Linear Algebra: Spring 2011, Fall 2011, Spring 2012.

MA 26200- Linear Algebra and Differential Equations: Fall 2010, Fall 2012, Spring 2013.