Research Interests

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

Peer-reviewed Articles

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


  1. Christensen-Evans theorem and extensions of GNS-symmetric quantum Markov semigroups, arXiv:2203.00341.
  2. (with L. Dello Schiavo) Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms, arXiv:2109.000615.
  3. A Noncommutative Transport Metric and Symmetric Quantum Markov Semigroups as Gradient Flows of the Entropy, arXiv:1808.05419.
  4. (with D. Lenz, M. Schmidt) Geometric properties of Dirichlet forms under order isomorphisms, arXiv:1801.08326.