## Areas of Expertise

Spectral theory of differential operators on manifolds and infinite graphs

## Education

Ph.D. in Mathematics

Northeastern University

## Biography

## Affiliations

American Mathematical Society

## Publications & Presentations

**Publications**

- The m-accretivity of covariant Schroedinger operators with unbounded drift.
*Annals of Global Analysis and Geometry*55 (2019), no. 4, 657–679.

- Inequalities and separation for covariant Schroedinger operators.
**(in collaboration with Hemanth Saratchandran).***Journal of Geometry and Physics*138 (2019), 215--222.

- Self-adjointness, m-accretivity, and separability for perturbations of Laplacian and bi-Laplacian on Riemannian manifolds,
*Integral Equations and Operator Theory*(2018) 90:22.

- Self-adjointness of perturbed biharmonic operators on Riemannian manifolds,
*Mathematische Nachrichten 290 (2017), no. 17-18, 2948--2960.*

- Self-adjoint extensions of differential operators on Riemannian manifolds.
**(in collaboration with Françoise****Truc)***. Annals of Global Analysis and Geometry*49 (2016), no.1, 87--103.

- On a positivity preservation property for Schroedinger operators on Riemannian manifolds.
*Proceedings of the American Mathematical Society*144 (2016), no. 1, 301--313.

- Self-adjointness of the Gaffney Laplacian on vector bundles.
**(in collaboration with Lashi Bandara).***Mathematical Physics, Analysis and Geometry*18 (2015), no.1, Art. 17, 14pp.

- Maximal accretive extensions of Schroedinger operators on vector bundles over infinite graphs
**(in collaboration with Françoise Truc).***Integral Equations and Operator Theory 81*(2015), 35--52.

- Generalized Schroedinger semigroups on infinite graphs
**(in collaboration with Batu Güneysu and Françoise Truc).***Potential Analysis 41*(2014), 517--541.

- Self-adjoint extensions of discrete magnetic Schroedinger operators
**(in collaboration with Françoise Truc).***Annales Henri Poincare*15 (2014), 917--936.

- Separation property for operators in L^p spaces on non-compact manifolds.
*Complex Variables and Elliptic Equations*58 (2013), 853--864.

- A spectral property of discrete Schroedinger operators with non-negative potentials.
*Integral Equations and Operator Theory 76*(2013), 285--300.

- A Sears-type self-adjointness result for discrete magnetic Schroedinger operators.
*Journal of Mathematical Analysis and Applications*396 (2012), 801--809.

- Self-adjoint realizations of Schroedinger operators on vector bundles over Riemannian manifolds. In: Recent Advances in Harmonic Analysis and Partial Differential Equations,
*Contemporary Mathematics*, vol. 581, pp. 175--197, American Mathematical Society, Providence, RI, 2012.

- Essential self-adjointness of magnetic Schroedinger operators on locally finite graphs.
*Integral Equations and Operator Theory*71 (2011), 13--27.

- A separation property for magnetic Schroedinger operators on Riemannian manifolds.
*Journal of Geometry and Physics*61 (2011), 1--7.

- On m-accretivity of perturbed Bochner Laplacian in L^p spaces on Riemannian manifolds.
*Integral Equations and Operator Theory*68 (2010), 243--254.

- Two realizations of Schroedinger operators on Riemannian manifolds.
*Journal of Mathematical Analysis and Applications*354 (2009), 125--133.

- On m-accretive Schroedinger operators with singular potentials on Riemannian manifolds.
*Journal of Geometry and Physics*58 (2008), 368--376.

- On m-accretive Schroedinger operators L^1 spaces on manifolds of bounded geometry.
*Proceedings of the Edinburgh Mathematical Society (2)*51 (2008), 215-227.

- On m-accretive Schroedinger operators in L^p spaces on manifolds of bounded geometry.
*Journal of Mathematical Analysis and Applications*324 (2006), 762--772.

- Separation property for Schroedinger operators on Riemannian manifolds.
*Journal of Geometry and Physics*56 (2006), 1283--1293.

- A property of Sobolev spaces on Riemannian manifolds.
*Electronic Journal of Differential Equations*Vol. 2005, No. 77, (2005), 10 pp.

- Positive perturbations of self-adjoint Schroedinger operators on Riemannian manifolds.
*International Journal of Geometric Methods in Modern Physics*2 (2005), 543--552.

- On holomorphic families of Schroedinger-type operators with singular potentials on manifolds of bounded geometry.
*Differential Geometry and its Applications*21 (2004), 361-377.

- Self-adjointness of Schroedinger-type operators with locally integrable potentials on manifolds of bounded geometry.
*Journal of Mathematical Analysis and Applications*295 (2004), 513-526.

- The form sum and the Friedrichs extension of Schroedinger-type operators on Riemannian manifolds.
*Proceedings of the American Mathematical Society*132 (2004), 147-156.

- Self-adjointness of Schroedinger-type operators with singular potentials on manifolds of bounded geometry.
*Electronic Journal of Differential Equations*, Vol. 2003 (2003), No. 64, 8pp.

- On m-accretive Schroedinger-type operators with singular potentials on manifolds of bounded geometry.
*International Journal of Mathematics and Mathematical Sciences*38 (2003), 2415-2423.

- Localized self-adjointness of Schroedinger-type operators on Riemannian manifolds.
*Journal of Mathematical Analysis and Applications*283 (2003), 304-318.

- Essential self-adjointness of Schroedinger-type operators on manifolds
**(in collaboration with****Maxim Braverman and Mikhail Shubin).***Russian Mathematical Surveys*57 (4) (2002), 641-692.

Contact Information

(904) 620-1745