Research

Preprints

• A Paley-Wiener-Schwartz Theorem for smooth valuations on convex functions [arXiv]

• Zonal valuations on convex bodies [arXiv]

• Polynomial valuations on convex functions and their maximal extensions [arXiv]
  (joint with Jacopo Ulivelli)

• A geometric decomposition for unitarily invariant valuations on convex functions [arXiv]

• Equivariant valuations on convex functions [arxiv]
  (joint with Georg Hofstätter)

• The homogeneous decomposition of dually translation invariant valuations on Lipschitz functions on the sphere [arXiv]
  (joint with Andrea Colesanti and Daniele Pagnini)

• Singular valuations and the Hadwiger theorem on convex functions [arXiv] 

• Unitarily invariant valuations on convex functions [arXiv] 

Publications

• Smooth valuations on convex bodies and finite linear combinations of mixed volumes [link,arXiv]
  Proceedings of the London Mathematical Society 130: e70057 (2025).

• From valuations on convex bodies to convex functions [link,arXiv]
  Mathematische Annalen 390: 5987–6011 (2024)
  (joint with Jacopo Ulivelli)

• Smooth valuations on convex functions [link,arXiv]
  Journal of Differential Geometry 126(2): 801-835 (2024).

• Monge-Ampère operators and valuations [link,arXiv]
  Calculus of Variations and Partial Differential Equations 63, 89 (2024).

• Equivariant endomorphisms of convex functions [link,arXiv]
  Journal of Functional Analysis 285(1) (2023), Paper No. 109922.
  (joint with Georg C. Hofstätter)

• The support of dually epi-translation invariant valuations on convex functions [link,arXiv]
  Journal of Functional Analysis 281(5) (2021), Paper No. 109059.

Talks

2025 

07/2025 Local functionals and valuations on convex functions
Focused Workshop on Current Trends in Geometric Valuation Theory, Budapest (Hungary)

05/2025 A Paley–Wiener–Schwartz Theorem for valuations on convex functions
2025 Szeged Workshop on Convexity, Szeged (Hungary)

2024

12/2024 A Paley–Wiener–Schwartz Theorem for valuations on convex functions
Convex Geometry and its Applications, Oberwolfach (Germany)

06/2024 Unitarily invariant valuations on convex functions
Convex Geometry in Florence, Florence (Italy)

03/2024 Complex Monge-Ampère operators and functional Hermitian intrinsic volumes
High dimensional phenomena: geometric and probabilistic aspects, Hausdorff Research Institute, Bonn (Germany)

02/2024 From valuations on sets to valuations on functions
Stochastic Geometry Seminar, Charles University Prague (Czech Republic)  

2023

09/2023 Valuations and Monge-Ampère operators
Conference on Convex Geometry and Geometric Probability, Salzburg (Austria)

09/2023 Valuations and distributions,
Meeting of the Austrian Mathematical Society 2023, Graz (Austria)

07/2023 Algebraic Integral Geometry for Monge-Ampère operators
Modern Valuation Theory, Jena (Germany)

06/2023 Valuations and Monge-Ampère operators
Convex geometry - Analytic aspects, Cortona (Italy)

06/2023 Valuations, distributions, and Monge-Ampère operators
Geometric Valuation Theory - from convex sets to functions, Castro Urdiales (Spain)

06/2023 Valuations, distributions, and Monge-Ampère operators
seminar, TU Wien (Austria)

05/2023 Valuations and distributions
seminar, Tel Aviv University (Israel)

02/2023 From valuations on convex bodies to valuations on convex functions
seminar, University of Georgia UGA, Athens (USA)

02/2023 Valuations and distributions
seminar, University of Georgia UGA, Athens (USA)

01/2023 From valuations on sets to valuations on functions
Vienna Geometric Analysis Seminar,  Wien (Austria)

2022

09/2022 Translation equivariant curvature measures on convex functions and Monge-Ampère-type operators
seminar, Friedrich Schiller University Jena (Germany)

06/2022 Algebraic structures on valuations on functions
geOmetry, anaLysis & convExity (OLE), Sevilla (Spain)

05/2022 Unitarily invariant valuations on convex functions
Szeged Workshop on Convexity, Szeged (Hungary)

04/2022 Unitarily invariant valuations on convex functions
Mini-Symposium on Geometric Probability and Valuation Theory, Vienna (Austria)

2021

11/2021 A geometric decomposition for unitarily invariant valuations on convex functions II.
seminar, TU Wien (Austria)

11/2021 A geometric decomposition for unitarily invariant valuations on convex functions
seminar, TU Wien (Austria)

09/2021 Smooth valuations on convex functions
Young Topologists and Geometers, joint meeting of DMV-OeMG, Einbeck (Germany)

09/2021 Smooth valuations on convex functions
Conference on Convex, Integral and Stochastic Geometry, Bad Herrenalb (Germany)

01/2021 Smooth and mixed Hessian valuations on convex functions
seminar, TU Wien (Austria)

2019

11/2019 Smooth valuations on convex functions
seminar, Friedrich Schiller University Jena (Germany)

11/2019 Smooth valuations on convex functions
seminar, Goethe-University Frankfurt (Germany)