Research Interests

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

Peer-reviewed Articles

  1. Modular Completely Dirichlet forms as Squares of Derivations
    International Mathematics Research Notices. IMRN, 2024., arXiv:2307.04502
  2. Christensen-Evans theorem and extensions of GNS-symmetric quantum Markov semigroups,
    Journal of Functional Analysis, 2024., arXiv:2203.00341
  3. (with C. Rouzé, H. Zhang) Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum Boolean functions
    Communications in Mathematical Physics, 2024., arXiv:2209.07279
  4. (with M. Vernooij) Derivations and KMS-Symmetric Quantum Markov Semigroups
    Communications in Mathematical Physics, 2023., arXiv:2303.15949
  5. (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., arXiv:1804.08353
  6. (with L. Dello Schiavo) Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms
    Journal of Evolution Equations, 2023., arXiv:2109.00615
  7. (with H. Zhang) Curvature-dimension conditions for symmetric quantum Markov semigroups
    Annales Henri Poincaré, 2022., arXiv:2105.08303
  8. Stability of Kac regularity under domination of quadratic forms
    Advances in Operator Theory, 2022., arXiv:1709.04164
  9. A Dual Formula for the Noncommutative Transport Distance
    Journal of Statistical Physics, 2022., arXiv:2104.11923
  10. (with H. Zhang) Complete Gradient Estimates of Quantum Markov Semigroups
    Communications in Mathematical Physics, 2021., arXiv:2007.13506
  11. (with D. Lenz, T.Weinmann) Self-Adjoint Extensions of Bipartite Hamiltonians
    Proceedings of the Edinburgh Mathematical Society, 2021., arXiv:1912.03670
  12. (with D. Lenz, M. Schmidt) Uniqueness of form extensions and domination of semigroups
    Journal of Functional Analysis, 2021., arXiv:1608.06798
  13. (with C. Richter) Tilings of convex sets by mutually incongruent equilateral triangles contain arbitrarily small tiles
    Discrete and Computational Geometry, 2020., arXiv:1711.08903
  14. (with D. Lenz, M. Schmidt) Domination of quadratic forms
    Mathematische Zeitschrift, 2020., arXiv:1711.07225
  15. (with M. Erbar, J. Maas) On the geometry of geodesics in discrete optimal transport
    Calculus of Variations and Partial Differential Equations, 2019., arXiv:1805.06040
  16. (with M. Keller, D. Lenz, M. Schmidt) Diffusion determines the recurrent graph
    Advances in Mathematics, 2015., arXiv:1405.3256


  1. (with F. Münch, H. Zhang) Intertwining Curvature Bounds for Graphs and Quantum Markov Semigroups, arXiv:2401.05179
  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. The Differential Structure of Generators of GNS-symmetric Quantum Markov Semigroups, arXiv:2207.09247 .
  4. A Noncommutative Transport Metric and Symmetric Quantum Markov Semigroups as Gradient Flows of the Entropy, arXiv:1808.05419.
  5. (with D. Lenz, M. Schmidt) Geometric properties of Dirichlet forms under order isomorphisms, arXiv:1801.08326.