Research Interests

classical and quantum Markov semigroups and Dirichlet forms, optimal transport, analysis on graphs

Peer-reviewed Articles

  1. (with M. Vernooij) Derivations and KMS-Symmetric Quantum Markov Semigroups
    Communications in Mathematical Physics, 2023.
  2. (with B. Hua, M. Keller, M. Schwarz) Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite Measure
    Proceedings of the American Mathematical Society, 2023.
  3. (with L. Dello Schiavo) Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms
    Journal of Evolution Equations, 2023.
  4. (with H. Zhang) Curvature-dimension conditions for symmetric quantum Markov semigroups
    Annales Henri Poincaré, 2022.
  5. Stability of Kac regularity under domination of quadratic forms
    Advances in Operator Theory, 2022.
  6. A Dual Formula for the Noncommutative Transport Distance
    Journal of Statistical Physics, 2022.
  7. (with H. Zhang) Complete Gradient Estimates of Quantum Markov Semigroups
    Communications in Mathematical Physics, 2021.
  8. (with D. Lenz, T.Weinmann) Self-Adjoint Extensions of Bipartite Hamiltonians
    Proceedings of the Edinburgh Mathematical Society, 2021.
  9. (with D. Lenz, M. Schmidt) Uniqueness of form extensions and domination of semigroups
    Journal of Functional Analysis, 2021.
  10. (with C. Richter) Tilings of convex sets by mutually incongruent equilateral triangles contain arbitrarily small tiles
    Discrete and Computational Geometry, 2020.
  11. (with D. Lenz, M. Schmidt) Domination of quadratic forms
    Mathematische Zeitschrift, 2020.
  12. (with M. Erbar, J. Maas) On the geometry of geodesics in discrete optimal transport
    Calculus of Variations and Partial Differential Equations, 2019.
  13. (with M. Keller, D. Lenz, M. Schmidt) Diffusion determines the recurrent graph
    Advances in Mathematics, 2015.


  1. Modular Completely Dirichlet forms as Squares of Derivations, arXiv:2307.04502.
  2. (with M. Keller, D. Lenz, M. Schmidt and M. Schwarz) Boundary representations of intermediate forms between a regular Dirichlet form and its active main part, arXiv:2301.01035.
  3. (with C. RouzĂ©, H. Zhang) Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum Boolean functions, arXiv:2209.07279.
  4. The Differential Structure of Generators of GNS-symmetric Quantum Markov Semigroups, arXiv:2207.09247 .
  5. Christensen-Evans theorem and extensions of GNS-symmetric quantum Markov semigroups, arXiv:2203.00341.
  6. A Noncommutative Transport Metric and Symmetric Quantum Markov Semigroups as Gradient Flows of the Entropy, arXiv:1808.05419.
  7. (with D. Lenz, M. Schmidt) Geometric properties of Dirichlet forms under order isomorphisms, arXiv:1801.08326.