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.
   https://doi.org/10.1093/imrn/rnae092, arXiv:2307.04502
2. Christensen-Evans theorem and extensions of GNS-symmetric quantum Markov semigroups,
   Journal of Functional Analysis, 2024.
   https://doi.org/10.1016/j.jfa.2024.110475, 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.
   https://doi.org/10.1007/s00220-024-04981-0, arXiv:2209.07279
4. (with M. Vernooij) Derivations and KMS-Symmetric Quantum Markov Semigroups
   Communications in Mathematical Physics, 2023.
   https://doi.org/10.1007/s00220-023-04795-6, 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.
   https://doi.org/10.1090/proc/14361, arXiv:1804.08353
6. (with L. Dello Schiavo) Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms
   Journal of Evolution Equations, 2023.
   https://doi.org/10.1007/s00028-022-00859-7, arXiv:2109.00615
7. (with H. Zhang) Curvature-dimension conditions for symmetric quantum Markov semigroups
   Annales Henri Poincaré, 2022.
   https://doi.org/10.1007/s00023-022-01220-x, arXiv:2105.08303
8. Stability of Kac regularity under domination of quadratic forms
   Advances in Operator Theory, 2022.
   https://doi.org/10.1007/s43036-022-00199-w, arXiv:1709.04164
9. A Dual Formula for the Noncommutative Transport Distance
   Journal of Statistical Physics, 2022.
   https://doi.org/10.1007/s10955-022-02911-9, arXiv:2104.11923
10. (with H. Zhang) Complete Gradient Estimates of Quantum Markov Semigroups
    Communications in Mathematical Physics, 2021.
    https://doi.org/10.1007/s00220-021-04199-4, arXiv:2007.13506
11. (with D. Lenz, T.Weinmann) Self-Adjoint Extensions of Bipartite Hamiltonians
    Proceedings of the Edinburgh Mathematical Society, 2021.
    https://doi.org/10.1017/S0013091521000080, arXiv:1912.03670
12. (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, 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.
    https://doi.org/10.1007/s00454-019-00061-6, arXiv:1711.08903
14. (with D. Lenz, M. Schmidt) Domination of quadratic forms
    Mathematische Zeitschrift, 2020.
    https://doi.org/10.1007/s00209-019-02440-4, 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.
    https://doi.org/10.1007/s00526-018-1456-1, arXiv:1805.06040
16. (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, arXiv:1405.3256

Preprints

1. (with R. Kumar R) Operator-Valued Twisted Araki-Woods Algebras, arXiv:2406.06179
2. (with F. Münch, H. Zhang) Intertwining Curvature Bounds for Graphs and Quantum Markov Semigroups, arXiv:2401.05179
3. (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.
4. The Differential Structure of Generators of GNS-symmetric Quantum Markov Semigroups, arXiv:2207.09247 .
5. A Noncommutative Transport Metric and Symmetric Quantum Markov Semigroups as Gradient Flows of the Entropy, arXiv:1808.05419.
6. (with D. Lenz, M. Schmidt) Geometric properties of Dirichlet forms under order isomorphisms, arXiv:1801.08326.