Publications 

arXiv, Google Scholar, MathSciNet, zbMATH, ORCID ID

Preprints

1. Lieb-Thirring-type inequalities for random Schrödinger operators with complex potentials, joint with Konstantin Merz, 14 pages.

2. Effective upper bounds on the number of resonance in potential scattering, 32 pages.

Publications

1. Random Schrödinger operators with complex decaying potentials, joint with Konstantin Merz. Accepted for pubilication in Analysis & PDE, 26 pages.

2. From spectral cluster to uniform resolvent estimates on compact manifolds, accepted for publication in J. Funct. Anal.,  Volume 286, Issue 2, https://doi.org/10.1016/j.jfa.2023.110214, 34 pages.   

3. On the number and sums of eigenvalues of Schrödinger-type operators with degenerate kinetic energy, joint with Konstantin Merz. In: Brown, M., et al. From Complex Analysis to Operator Theory: A Panorama. Operator Theory: Advances and Applications, vol 291, 2023, https://doi.org/10.1007/978-3-031-31139-0_13,19 pages.

4. Counterexample to the Laptev--Safronov conjecture, joint with Sabine Bögli, Commun. Math. Phys, 398, (2023), https://doi.org/10.1007/s00220-022-04546-z, 22 pages.

5. Fourier transform of surface--carried measures of two-dimensional generic surfaces and applications, joint with Robert Schippa, Comm. Pure and Appl. Anal., 2022,  doi: 10.3934/cpaa.2022079, 17 pages.

6. Schrödinger Operators with Complex Sparse Potentials. Commun. Math. Phys., 2022. https://doi.org/10.1007/s00220-022-04358-1, 42 pages. Full-text access https://rdcu.be/cKKTy

7. Sharp time decay estimates for the discrete Klein-Gordon equation, joint with Isroil Ikromov, Nonlinearity, 2021, 34, 7938–7962. 

8. Weak coupling limit for Schrödinger-type operators with degenerate kinetic energy for a large class of potentials, joint with Konstantin Merz, Lett. Math. Phys., 2021, 111, Paper No. 46, 29.  

9. Lieb-Thirring inequalities for an effective Hamiltonian of bilayer graphene, joint with Philippe Briet, Stanislas Kupin and Leonid Golinskii, J. Spectral Theory, 2021, 11, 1145-1178 .

10. Sharp spectral bounds for complex perturbations of the indefinite Laplacian, joint with Orif Ibroginov, J. Funct. Anal., 2021, 280, 26 pages.

11. Improved eigenvalue bounds for Schrödinger operators with slowly decaying potentials, Comm. Math. Phys., 2020, 376, 2147-2160. 

12. Embedded eigenvalues of generalized Schrödinger operators, J. Spectr. Theory, 2020, 10, 415-437 

13. Eigenvalue estimates for bilayer graphene, Ann. Henri Poincaré, 2019, 20, 1501-1516. 

14. Eigenvalues of one-dimensional non-self-adjoint Dirac operators and applications , joint with P. Siegl, Lett. Math. Phys., 2018, 108, 1757-1778.

15. Sharp spectral estimates for the perturbed Landau Hamiltonian with L^p potentials, Integral Equations Operator Theory, 2017, 88, 127-141.

16. L^p resolvent estimates for magnetic Schrödinger operators with unbounded background fields, joint with Carlos Kenig, Comm. Partial Differential Equations, 2017, 42, 235-260.

17. Eigenvalue bounds for Dirac and fractional Schrödinger operators with complex potentials, J. Funct. Anal., 2017, 272, 2987-3018.

18. Non-symmetric perturbations of self-adjoint operators, joint with Christiane Tretter, J. Math. Anal. Appl., 2016, 441, 235-258.

19. Dipoles in graphene have infinitely many bound states, joint with Heinz Siedentop, J. Math. Phys., 2014, 55, 10 pages.

20. Estimates on complex eigenvalues for Dirac operators on the half-line, Integral Equations Operator Theory, 2014, 79, 377-388.

21. Eigenvalue estimates for non-selfadjoint Dirac operators on the real line, joint with Ari Laptev and Christiane Tretter, Ann. Henri Poincaré, 2014, 15, 707-736.

22. Block-diagonalization of operators with gaps, with applications to Dirac operators, Rev. Math. Phys., 2012, 24, 31 pages.                

Misc

1. Eigenvalue estimates for Dirac and Schrödinger type operators, Habilitation form LMU Munich, 2018 (link).  

Recent talks

• Heriot-Watt Analysis Seminar (25/09/2023)

• Oberseminar "Calculus of Variations and Applications", LMU Munich (05/07/2023)

• Statistical mechanics seminar, Warwick (29/06/2023)

• Workshop "Interactions of Harmonic and Geometric Analysis", Birmingham (17/05/2023): Spectral cluster bounds for orthonormal functions on compact manifolds with nonsmooth metrics

• Seminar "Spectral problems in mathematical physics", Institut Henri Poincaré (14/11/2022): Effective bounds on scattering resonances

• Cardiff Analysis Seminar (24/10/2022): Effective bounds on scattering resonances

• London-Paris Analysis Seminar, QMUL (21/10/2022): Effective bounds on scattering resonances

• Cork Mathematics Colloquium (22/09/2022): Effective bounds on scattering resonances

• Banff (15/07/2022): Schrödinger operators with complex random or sparse potentials

• Euler Institute (Saint-Petersburg) and Chebyshev Laboratory (Saint Petersburg State University) seminar on spectral theory and related topics (postponed)

• Warsaw math-phys online  seminar (27/01/2022): Random Schrödinger operators with complex decaying potentials 

• Spectral geometry in the clouds (06/12/2021): Schrödinger operators with complex potentials: Beyond the Laptev-Safronov conjecture 

• KIT Functional Analysis Seminar (03/12/2021): Schrödinger operators with complex potentials

• Institute of Mathematics of the Academy of Sciences of Uzbekistan "Modern problems of mathematical physics" (01/12/2021): Sharp time decay estimates for the discrete Klein-Gordon equation 

• Oxford Functional Analysis Seminar (23/11/2021): Schrödinger operators with complex potentials 

• Maxwell Analysis seminar (08/10/21): Harmonic analysis tools in spectral theory (slides)

• DMV-ÖMG Jahrestagung, Minisymposium-M1 (30/09/21): Schrödinger operators with complex sparse potentials

• Seminar of the math department, American University of Beirut (21/09/21): Beyond stationary phase: Oscillatory integrals and applications (slides)

• Iwota Lancaster, special session on spectral theory and differential operators (17/08/21): Schrödinger operators with complex sparse potentials (slides)