PD Dr. Konstantin Merz Institute of Analysis and Algebra and Institute for Partial Differential Equations Carl-Friedrich-Gauß-Fakultät Technische Universität Carolo-Wilhelmina Universitätsplatz 2 D-38106 Braunschweig Germany Email: k.merz(at)tu-bs.de Tel:   +49 (0)531   391 7433 Office: F 522 From October 2025 on at Institute for Theoretical Physics, Department of Physics, ETH Zürich.

Research interests

• Schrödinger operators with general kinetic energies, in particular
  • eigenvalue estimates
  • heat kernel estimates
  • spectral multiplier theorems
• Functional inequalities
• Many-particle quantum systems

Publications

1. (with R. L. Frank and H. Siedentop) Equivalence of Sobolev norms involving generalized Hardy operators. Int. Math. Res. Not. 2021 (2021), no. 3, 2284-2303 - Article - Preprint
2. (with H. Siedentop) The atomic density on the Thomas-Fermi length scale for the Chandrasekhar Hamiltonian. Rep. Math. Phys. 83 (2019), no. 3, 387-391 - Article - Preprint
3. On scales of Sobolev spaces associated to generalized Hardy operators. Math. Z. 299 (2021), no. 1, 101-121 - Article - Preprint
4. (with R. L. Frank, H. Siedentop, and B. Simon) Proof of the strong Scott conjecture for Chandrasekhar atoms. Pure Appl. Funct. Anal. 5 (2020), no. 6, 1319-1356. (issue dedicated to Yakov Sinai on his 85th Birthday). - Article - Preprint
5. (with J.-C. Cuenin) Weak coupling limit for Schrödinger-type operators with degenerate kinetic energy for a large class of potentials. Lett. Math. Phys. 111 (2021), no. 2, paper number 46 - Article - Preprint
6. (with H. Siedentop) Proof of the Strong Scott Conjecture for Heavy Atoms: the Furry Picture. Ann. H. Lebesgue 5 (2022), 611-642 - Article - Preprint
7. (with R. L. Frank and H. Siedentop) Relativistic strong Scott conjecture: A short proof. In: Density Functionals for Many-Particle Systems. Mathematical Theory and Physical Applications of Effective Equations, B.-G. Englert, H. Siedentop, and M.-I. Trappe (eds.), Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap. 41, 69-79, World Scientific, Singapore, 2023 - Article - Preprint
8. On complex-time heat kernels of fractional Schrödinger operators via Phragmén-Lindelöf principle. J. Evol. Equ. 22 (2022), no. 3, paper number 62 - Article - Preprint
9. (with J.-C. Cuenin) Random Schrödinger operators with complex decaying potentials. Anal. PDE 18 (2025), no. 2, 279-306 - Article - Preprint
10. (with J.-C. Cuenin) On the number and sums of eigenvalues of Schrödinger-type operators with degenerate kinetic energy. In: From Complex Analysis to Operator Theory: A Panorama: In Memory of Sergey Naboko, M. Brown, F. Gesztesy, P. Kurasov, A. Laptev, B. Simon, G. Stolz, and I. Wood, Operator Theory: Advances and Applications 291, 313-340, Birkhäuser, Cham, 2023 - Article - Preprint
11. (with R. L. Frank and H. Siedentop) The Scott conjecture for large Coulomb systems: a review. Lett. Math. Phys. 113 (2023), paper number 11 - Article - Preprint
12. (with R. L. Frank) On Sobolev norms involving Hardy operators in a half-space. J. Funct. Anal. 285 (2023), no. 10, paper number 110104 - Article - Preprint
13. (with K. Bogdan) Ground state representation for the fractional Laplacian with Hardy potential in angular momentum channels. J. Math. Pures Appl. (9) 186 (2024), 176-204 - Article - Preprint
14. (with J.-C. Cuenin) Lieb-Thirring-type inequalities for random Schrödinger operators with complex potentials. To appear in RIMS Kôkyûroku Bessatsu - Preprint
15. (with K. Bogdan) Subordinated Bessel heat kernels. Theory Probab. Math. Statist. 112 (2025), 67-83 - Article - Preprint
16. (with T. A. Bui) Equivalence of Sobolev norms in Lebesgue spaces for Hardy operators in a half-space. Submitted - Preprint
17. (with K. Bogdan and T. Jakubowski) Hardy perturbations of subordinated Bessel heat kernels. Submitted - Preprint
18. (with T. A. Bui and X. T. Duong) Equivalence of Sobolev norms for Kolmogorov operators with scaling-critical drift. Submitted - Preprint
19. (with K. Bogdan) Heat kernel bounds for the fractional Laplacian with Hardy potential in angular momentum channels. Submitted - Preprint

Seminars and conferences

Gauss Mini Workshop on Analysis, PDE, and Mathematical Physics (23 January 2025)

GAuS online seminar (joint with Christoph Kehle and Simone Rademacher)

Minisymposium Mathematical Analysis of Complex Quantum Systems at the DMV Annual Meeting 2022 (joint with Heinz Siedentop)

Teaching / Lehre (in German)

Curriculum Vitae

Links