Publications

Databases

Preprints

Equidistribution in 2-nilpotent Polish groups and triple restricted sumsets (with Ethan Ackelsberg), 48pp.
Quadratic maps between non-abelian groups (with Andreas Thom), 29pp.
Carleson Operators on Doubling Metric Measure Spaces (with Lars Becker, Floris van Doorn, Rajula Srivastava, and Christoph Thiele), 130pp. [lean]
A Peter-Weyl theorem for compact group bundles and the geometric representation of relatively ergodic compact extensions (with Nikolai Edeko and Henrik Kreidler), 81pp. [video]
A Host-Kra F₂^ω-system of order 5 that is not Abramov of order 5, and non-measurability of the inverse theorem for the U⁶(F₂ⁿ) norm (with Or Shalom and Terence Tao), 70pp. [blog], [video]
The structure of totally disconnected Host-Kra-Ziegler factors, and the inverse theorem for the U^k Gowers uniformity norms on finite abelian groups of bounded torsion (with Or Shalom and Terence Tao), 96pp. [blog]

On compact extensions of tracial W*-dynamical systems (with Pieter Spaas) Groups, Geometry, and Dynamics, to appear. [journal]
Uniform syndeticity in multiple recurrence (with Minghao Pan), Ergodic Theory and Dynamical Systems, 45(2): 504-525, 2025. [journal]
The structure of arbitrary Conze-Lesigne systems (with Or Shalom and Terence Tao), Communications of the American Mathematical Society, 4:182–229,2024. [blog], [journal]
The inverse theorem for the U^3 Gowers uniformity norm on arbitrary finite abelian groups: Fourier-analytic and ergodic approaches (with Terence Tao), Discrete Analysis, Paper No. 11, 48 pp., 2023. [blog], [journal]
An uncountable Furstenberg-Zimmer structure theory, Ergodic Theory and Dynamical Systems, 43(7): 2404-2436, 2023. [journal]
An uncountable Moore-Schmidt theorem, Ergodic Theory and Dynamical Systems, 43(7): 2376-2403, 2023. [blog], [journal], [video]
Foundational aspects of uncountable measure theory: Gelfand duality, Riesz representation, canonical models, and canonical disintegration (with Terence Tao), Fundamenta Mathematicae, 261, 1-98, 2023. [blog], [journal]
An uncountable ergodic Roth theorem and applications (with Polona Durcik, Rachel Greenfeld, Annina Iseli, and José Madrid), Discrete and Continuous Dynamical Systems, 42(11): 5509-5540, 2022. [journal]
Decoupling for fractal subsets of the parabola (with Alan Chang, Jaume de Dios Pont, Rachel Greenfeld, Zane Kun Li, and José Madrid), Mathematische Zeitschrift, 301(2): 1851-1879, 2022. [journal], [video]
An uncountable Mackey-Zimmer theorem (with Terence Tao), Studia Mathematica, 266, 241-289, 2022. [blog], [journal]
Wasserstein Distance to Independence Models (with Türkü Özlüm Çelik, Guido Montúfar, Bernd Sturmfels, and Lorenzo Venturello), Journal of Symbolic Computation, 104: 855-873, 2021. [journal], [video]
Optimal Transport to a Variety (with Türkü Özlüm Çelik, Guido Montúfar, Bernd Sturmfels, and Lorenzo Venturello), Optimal Transport to a Variety Mathematical Aspects of Computer and Information Sciences, MACIS 2019, Springer Lecture Notes in Computer Science 11989: 364-381, 2020. [journal]
Parameter-dependent Stochastic Optimal Control in Finite Discrete Time (with Michael Kupper and José M. Zapata) Journal Optimizaton Theory and Applications, 186(2): 644–666, 2020. [journal]
A Fenchel-Moreau theorem for L⁰-valued functions (with Samuel Drapeau and Michael Kupper), Journal of Convex Analysis, 26(2): 593–603, 2019. [journal]
A transfer principle for second-order arithmetic, and applications (with Merlin Carl), Journal of Logic and Analysis, 10, Paper No. 8, 32 pp, 2018. [journal]
Measures and integrals in conditional set theory (with Michael Kupper and Martin Streckfuß) Set-Valued and Variational Analysis, 26(4): 947–973, 2018. [journal]
Multidimensional quadratic BSDEs with separated generators (with Michael Kupper and Peng Luo) Electronic Communications in Probability, 22, Paper No. 58, 10 pp, 2017. [journal]
Conditional Preference Orders and their Numerical Representations (with Samuel Drapeau) Journal of Mathematical Economics, 63: 106–118, 2016. [journal]
The algebra of conditional sets and the concepts of conditional topology and compactness (with Samuel Drapeau, Martin Karliczek, and Michael Kupper) Journal of Mathematical Analysis and Applications, 437(1): 561–589, 2016. [journal]
A Theory of Conditional Sets, PhD Thesis, Humboldt University Berlin, 2014.
Iterative operator splitting with time overlapping algorithms (with Jürgen Geiser) in Wave Propagation in Materials for Modern Applications, ed. A. Petrin, INTECH Open Access Publisher, 2010.