Publications

Connes' trace theorem and the log-polyhomogeneous calculus for Carnot manifolds arXiv (2026)
Fujita Exponents on Quantum Euclidean Spaces with M. Ruzhansky, S. Shaimardan and K. Tulenov arXiv (2026)
Schur bounded patterns and submajorisation with F. Sukochev and D. Zanin arXiv (2026)
Weyl asymptotic formulas in the nilpotent Lie group setting with S. Liu, F. Sukochev and D. Zanin arXiv (2026)
Weyl's laws and Connes' Trace Theorem for operator-valued pseudo-differential operators with X. Xiong and X. Zhang arXiv (2026)
Uniformity of Maximal Hypoellipticity on Graded Lie Groups: From Pointwise to Global with S. Liu, F. Sukochev and D. Zanin (2025)

arXiv

Multiple operator integrals, pseudodifferential calculus, and asymptotic expansions , with E. Hekkelman and T. van Nuland (2024) arXiv
L_p estimates in the Androulidakis-Mohsen-Yuncken calculus (2024) arXiv

A noncommutative integral on spectrally truncated spectral triples, and a link with quantum ergodicity with E. Hekkelman to appear in J. Funct. Anal. (2025)
Calderòn's commutator on Stratified Lie groups , with Y. Chen, Z. Gong and D. Zanin, to appear in J. Operator Theory (2024). (DOI not yet assigned, available on the arXiv)
Nonlinear partial differential equations on noncommutative Euclidean spaces. J. Evol. Equ. 24 (2024), no. 1, Paper No. 16, 58 pp. doi
A general Dixmier trace formula for the density of states on open manifolds. with E. Hekkelman, SIGMA Symmetry Integrability Geom. Methods Appl. 20 (2024), Paper No. 007, 34 pp. doi
Endpoint weak Schatten class estimates and trace formula for commutators of Riesz transforms with multipliers on Heisenberg groups with Z. Fan, Zhijie, J. Li, F. Sukochev and D. Zanin. J. Funct. Anal. 286 (2024), no. 1, Paper No. 110188, 72 pp. doi
Spectral estimates and asymptotics for stratified Lie groups with F. Sukochev, and D. Zanin, Funct. Anal. 285 (2023), no. 10, Paper No. 110105, 64 pp. doi
Krein's theorem revisited with F. Sukochev and D. Zanin. Pure Appl. Funct. Anal. 9 (2024), no. 5, 1281-1317. (DOI not yet assigned, available from publisher here).
Quantum differentiability—the analytical perspective with F. Sukochev and X. Xiong. Proc. Sympos. Pure Math., 105. doi
Dixmier trace formulas and negative eigenvalues of Schrödinger operators on curved noncommutative tori with R. Ponge. Adv. Math. 412 (2023), Paper No. 108815, 57 pp. doi
The density of states depends on the domain with N. Azamov, F. Sukochev and D. Zanin. Oper. Matrices 16 (2022), no. 4, 1185–1189. doi
A noncommutative Tauberian theorem and Weyl asymptotics in noncommutative geometry. with F. Sukochev and D. Zanin, Lett. Math. Phys. 112 (2022), 45 pp. doi
Necessary and sufficient conditions for n-times Fréchet differentiability on S^p, 1<p<infty., with C. Le Merdy, Proc. Amer. Math. Soc. 149 (2021), no. 9, 3881–3887. doi
Estimates for Schur multipliers and double operator integrals—a wavelet approach. with T. Scheckter and F. Sukochev, Anal. i Prilozhen. 55 (2021), no. 2, 5–20. doi
Cwikel estimates and negative eigenvalues of Schrödinger operators on noncommutative tori., with R. Ponge, J. Math. Phys. 63 (2022), no. 4, 37 pp. doi
Quantum Euclidean spaces with noncommutative derivatives., with L. Gao and M. Junge, J. Noncommut. Geom. 16 (2022), no. 1, 153--213. doi
Lipschitz estimates in quasi-Banach Schatten ideals. with F. Sukochev, Math. Ann. 383 (2022), no. 1-2, 571--619. doi
An application of singular traces to crystals and percolation., with N. Azamov, E. Hekkelman, F. Sukochev and D. Zanin, J. Geom. Phys. 179 (2022), 22 pp. doi
Ando's inequality for uniform submajorization. with A. Bikchentaev and F. Sukochev, Linear Algebra Appl. 605 (2020), 206--226. doi
A Dixmier trace formula for the density of states. wit N. Azamov, F. Sukochev and D. Zanin, Comm. Math. Phys. 377 (2020), no. 3, 2597--2628. doi
Quantum Differentiability on Noncommutative Euclidean Spaces, with F. Sukochev and X. Xiong., Commun. Math. Phys. 379 (2019), no. 2, 491--542. doi
A C^*-algebraic approach to the principal symbol II., with F. Sukochev and D. Zanin. Math. Ann. 374 (2019), no. 1-2, 273--322. doi
Quantum Differentiability on Quantum Tori., with F. Sukochev and X. Xiong, Commun. Math. Phys. 371 (2019), no. 3, 1231--1260. doi
Noncommutative Geometry for Symmetric non-self-adjoint operators., with A. Connes, G. Levitina, F. Sukochev and D. Zanin, J. Funct. Anal. 277 (2019), no. 3, 889--936. doi
Conformal trace theorem for Julia sets of quadratic polynomials., with A. Connes, F. Sukochev and D. Zanin, 1-26. Ergodic Theory Dynam. Systems 39 (2019), no. 9, 2481--2506. doi
Quantum differentiability of Essentially bounded functions on Euclidean space., with S. Lord, F. Sukochev and D. Zanin, J. Funct. Anal. 273 (2017), no. 7, 2353--2387. doi