Research

Research interests: Functional analysis, harmonic analysis, functional inequalities, noncommutative analysis, quantum information, mathematical aspects of quantum theory and related areas. 

Preprints

• Noncommutative Bohnenblust--Hille Inequality for qudit systems (with Joseph Slote and Alexander Volberg), arXiv:2406.08509 

• Intertwining Curvature Bounds for Graphs and Quantum Markov Semigroups (with Florentin Münch and Melchior Wirth), arXiv:2401.05179. 

• Dimension-free Remez Inequalities and norm designs (with Lars Becker, Ohad Klein, Joseph Slote, and Alexander Volberg), arXiv:2310.07926. 

• A dimension-free Remez-type inequality on the polytorus (with Joseph Slote and Alexander Volberg), arXiv:2305.10828 

• Interpolation of quasi noncommutative L_p-spaces (with Zhi Yin and Juan Gu), arXiv:1905.08491.

Publications

• Bohnenblust--Hille inequality for cyclic groups (with Joseph Slote and Alexander Volberg), to appear in Adv. Math. arXiv:2305.10560 

• Quantum Talagrand, KKL and Friedgut's theorems and the learnability of quantum Boolean functions (with Cambyse Rouzé and Melchior Wirth), Comm. Math. Phys. 2024, arXiv:2209.07279 (QIP2023).

• Quantum and classical low-degree learning via a dimension-free Remez inequality ( with Ohad Klein, Joseph Slote, and Alexander Volberg), ITCS 2024, arXiv:2301.01438 (TQC 2024).

• Approximation of polynomials from Walsh tail spaces, to appear in Studia Math. 2024 (with Alexandros Eskenazis), arXiv:2311.09021.

• Noncommutative Bohnenblust--Hille inequalities (with Alexander Volberg), Math. Ann. 2023 , arXiv:2210.14468 

• Lp-Lq Fourier multipliers on locally compact quantum groups, J Fourier Anal Appl 2023, arXiv:2201.08346.

• Some convexity and monotonicity results of trace functionals, Ann. Henri Poincaré 2023, arXiv:2108.05785.

• Heat-smoothing for holomorphic subalgebras of free group von Neumann algebras, Proc. Amer. Math. Soc. 2023,  arXiv:2205.12833. 

• Norms of certain functions of the Laplace operator on the ax+b groups (with Rauan Akylzhanov, Yulia Kuznetsova and Michael Ruzhansky), Math. Z. 2022, arXiv:2101.00584.

• Monotonicity versions of Epstein's Concavity Theorem and related inequalities (with Eric Carlen), Linear Algebra Appl. 2022, arXiv:2205.02342.

• Curvature-dimension conditions for symmetric quantum Markov semigroups (with Melchior Wirth), Ann. Henri Poincaré 2022, arXiv:2105.08303. 

• Complete gradient estimates of quantum Markov semigroups (with Melchior Wirth), Comm. Math. Phys. 2021, arXiv:2007.13506.

• Equality conditions of Data Processing Inequality for α-z Rényi relative entropies,  J. Math. Phys. 2020, arXiv:2007.06644.

• From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture,  Adv. Math. 2020, arXiv:1811.01205 (QIP 2022).

• Infinitely divisible states on finite quantum groups, Math. Z. 2019, arXiv:1809.04417.

• Idempotent states on Sekine quantum groups, Comm. Algebra 2019, arXiv:1809.02798.

• Hypercontractivity of heat semigroups on free quantum groups (with Uwe Franz, Guixiang Hong, Francois Lemeux and Michael Ulrich), J. Operator Theory 2017, arXiv:1511.02753.