Research

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. https://doi.org/10.1090/proc/14361
  2. (with H. Zhang) Curvature-dimension conditions for symmetric quantum Markov semigroups, Annales Henri Poincaré, 2022. https://doi.org/10.1007/s00023-022-01220-x
  3. Stability of Kac regularity under domination of quadratic forms, Advances in Operator Theory, 2022. https://doi.org/10.1007/s43036-022-00199-w
  4. A Dual Formula for the Noncommutative Transport Distance. Journal of Statistical Physics, 2022. https://doi.org/10.1007/s10955-022-02911-9
  5. (with H. Zhang) Complete Gradient Estimates of Quantum Markov Semigroups. Communications in Mathematical Physics, 2021. https://doi.org/10.1007/s00220-021-04199-4
  6. (with D. Lenz, T.Weinmann) Self-Adjoint Extensions of Bipartite Hamiltonians. Proceedings of the Edinburgh Mathematical Society, 2021. https://doi.org/10.1017/S0013091521000080
  7. (with D. Lenz, M. Schmidt) Uniqueness of form extensions and domination of semigroups. Journal of Functional Analysis, 2021. https://doi.org/10.1016/j.jfa.2020.108848
  8. (with C. Richter) Tilings of convex sets by mutually incongruent equilateral triangles contain arbitrarily small tiles. Discrete and Computational Geometry, 2020. https://doi.org/10.1007/s00454-019-00061-6
  9. (with D. Lenz, M. Schmidt) Domination of quadratic forms. Mathematische Zeitschrift, 2020. https://doi.org/10.1007/s00209-019-02440-4
  10. (with M. Erbar, J. Maas) On the geometry of geodesics in discrete optimal transport. Calculus of Variations and Partial Differential Equations, 2019. https://doi.org/10.1007/s00526-018-1456-1
  11. (with M. Keller, D. Lenz, M. Schmidt) Diffusion determines the recurrent graph. Advances in Mathematics, 2015. https://doi.org/10.1016/j.aim.2014.10.003

Preprints

  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.