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

Since October 2022 at
Department of Mathematics, Graduate School of Science, Osaka University
Toyonaka, Osaka 560-0043, Japan


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. To appear in Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap. - 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. Submitted - Preprint
  10. (with J.-C. Cuenin) On the number and sums of eigenvalues of Schrödinger-type operators with degenerate kinetic energy. To appear in Operator Theory: Advances and Applications - Preprint
  11. (with R. L. Frank and H. Siedentop) The Scott conjecture for large Coulomb systems: a review. Submitted - Preprint



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)

Analysis 3 (WS 2016/17)
Übungen zur Vorlesung Partielle Differentialgleichungen 2 (WS 2019/20)
Seminar: Spurideale und Matrixungleichungen (WS 2019/20)
Harmonic Analysis (SS 2020))
Seminar: Streutheorie (WS 2020/21)
Topics in PDE (WS 2020/21)
Seminar: Hochdimensionale Wahrscheinlichkeitstheorie (SS 2021)
Fourier Restriction and Applications (SS 2021)
Übungen zur Vorlesung Lineare Algebra 1 (WS 2021/22)
Übungen zur Vorlesung Lineare Algebra 2 (SS 2022)
Seminar: Themen der Vielteilchenquantenmechanik (SS 2022)



Curriculum Vitae




Links

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

Last modified: October 03, 2022