Research

PhD position FWF project "Classification problems for valuations on convex functions"

I am currently looking for a PhD student for the project "Classification problems for valuations on convex functions (PAT4205224)" starting fall 2025. If you are interested or would like some more information on the position, please contact me

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 

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)