Dr. Konstantin Merz

Institute of Analysis and Algebra
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


Profile Picture



Research interests

Analysis and mathematical physics, in particular


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. To appear in Anal. PDE - 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. Submitted - Preprint
  16. (with T. A. Bui) Equivalence of Sobolev norms in Lebesgue spaces for Hardy operators in a half-space. Submitted - Preprint



Seminars and conferences

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)

Diskrete Mathematik (SS 2024)
Ramp-up course for data scientists: Analysis (SS 2024)
Harmonic Analysis (WS 2023/24)
Ramp-up course for data scientists: Analysis (WS 2023/24)
Seminar: Themen der Quantenelektrodynamik (WS 2023/24)
Übungen zur Vorlesung Lineare Algebra 2 (SS 2022)
Seminar: Themen der Vielteilchenquantenmechanik (SS 2022)
Übungen zur Vorlesung Lineare Algebra 1 (WS 2021/22)
Seminar: Hochdimensionale Wahrscheinlichkeitstheorie (SS 2021)
Fourier Restriction and Applications (SS 2021)
Seminar: Streutheorie (WS 2020/21)
Topics in PDE (WS 2020/21)
Harmonic Analysis (SS 2020)
Übungen zur Vorlesung Partielle Differentialgleichungen 2 (WS 2019/20)
Seminar: Spurideale und Matrixungleichungen (WS 2019/20)
Analysis 3 (WS 2016/17)


Curriculum Vitae




Links

Mathematics Institute, University of Munich
International Max Planck Research School for Quantum Science and Technology (IMPRS-QST)
diversity@TU

Last modified: May 23, 2024