top of page
Papers and preprints ​

  • (with O. Shalom and T. Tao)  A Host-Kra F_2^\omega-system of order 5 that is not Abramov of order 5, and non-measurability of the inverse theorem for the U^6(F_2^n) norm 

       submitted.

       [arXiv] - [video] - [blog]

  • (with O. Shalom and T. Tao)  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 

       submitted.

       [arXiv] - [blog]

  • (with N. Edeko and H. Kreidler)  A Peter-Weyl theorem for compact group bundles and the geometric representation of relatively ergodic compact extensions

       submitted.

       [arXiv] - [video]

  • (with P. Spaas)  On compact extensions of tracial W*-dynamical systems 

       Groups, Geometry, and Dynamics, to appear.

         [arXiv]

  • (with M. Pan)  Uniform syndeticity in multiple recurrence

       submitted.

       [arXiv] 

  • (with T. Tao)  The inverse theorem for the U^3 Gowers uniformity norm on arbitrary finite abelian groups: Fourier-analytic and ergodic approaches

       Discrete Anal., Paper No. 11, 48 pp., 2023. 

       [arXiv] - [blog] - [journal]

  • (with O. Shalom and T. Tao)  The structure of arbitrary Conze-Lesigne systems

       Comm. Amer. Math. Soc.,  4: 182-229, 2024. 

       [arXiv] - [blog] - [journal]

  • An uncountable Furstenberg-Zimmer structure theory

       Ergodic Theory Dynam. Systems, 43(7): 2404-2436, 2023.   

       [arXiv] - [journal]

       Discrete Contin. Dyn. Syst., 42(11): 5509-5540, 2022.   

       [arXiv] - [journal] - [video]

       Math. Z., 301(2): 1851-1879, 2022. 

       [arXiv] - [journal] - [video]

  • (with T. Tao)  Foundational aspects of uncountable measure theory: Gelfand duality, Riesz representation, canonical models, and canonical disintegration

       Fund. Math., 261, 1-98, 2023. 

       [arXiv] - [blog]  - [journal]

  • (with T. Tao)  An uncountable Mackey-Zimmer theorem 

       Studia Math., 266. 241-289, 2022.

       [arXiv] - [blog] - [journal]

      J. Symbolic Comput., 104: 855-873, 2021.

       [arXiv] - [journal] - [video]

  • (with T. TaoAn uncountable Moore-Schmidt theorem

       Ergodic Theory Dynam. Systems, 43(7): 2376-2403, 2023.

       [arXiv] - [blog] - [journal]

       Mathematical Aspects of Computer and Information Sciences, MACIS 2019, Springer Lecture Notes in Computer           Science 11989: 364-381, 2020.

       [arXiv] - [journal]

  • (with S.-M. Grad)  A perturbational duality approach in vector optimization

       unpublished preprint

       [arXiv]

  • (with M. Carl)  A transfer principle for second-order arithmetic, and applications

       J. Log. Anal., 10, Paper No. 8, 32 pp, 2018.

       [arXiv] - [journal]

       ​unpublished preprint

       [arXiv]

         J. Convex Anal., 26(2): 593–603, 2019. 

       [arXiv] - [journal]

       J. Optim. Theory Appl., 186(2): 644–666, 2020.   

       [arXiv] - [journal] 

  • (with M. Kupper and M. Streckfuss)  Measures and integrals in conditional set theory  

       Set-Valued Var. Anal., 26(4): 947–973, 2018. 

       [arXiv] - [journal] 

  • (with M. Kupper and P. Luo)  Multidimensional quadratic BSDEs with separated generators

       Electron. Commun. Probab., 22, Paper No. 58, 10 pp, 2017.  

       [arXiv] - [journal] 

  • (with S. Drapeau)  Conditional Preference Orders and their Numerical Representations

      J. Math. Econom., 63: 106–118, 2016. 

       [arXiv] - [journal] 

  • Sheaves and conditional sets

       unpublished preprint

       [arXiv] - [recent video]

  • (with S. Drapeau, M. Karliczek, M. Kupper)  The algebra of conditional sets and the concepts of conditional topology and compactness

      ​ J. Math. Anal. Appl. 437(1): 561–589, 2016.  

       [arXiv] - [journal] 

  • A Theory of Conditional Sets

       PhD thesis, 2014.

       [thesis]

  • (with J. Geiser), Iterative operator splitting with time overlapping algorithms 

       Wave Propagation in Materials for Modern Applications, Ed. A. Petrin, INTECH Open Access Publisher, 2010.

       [book chapter]

bottom of page