Publications
Below are my research articles in reverse chronological order.
- An intersection product for the polytope algebra
Canad. J. Math., in press.
- Hard Lefschetz theorem and Hodge–Riemann relations for convex valuations, with A. Bernig and J. Kotrbatý
Ann. of Math. (2), in press.
- Translation invariant curvature measures of convex bodies, with J. Schuhmacher
Adv. Math., in press.
- The Weyl tube theorem for Kähler manifolds, with A. Bernig, J. H. G. Fu, and G. Solanes
Geom. Topol. 30 (2026), 2713–2772.
- Complex and quaternionic analogues of Busemann's random simplex and intersection inequalities, with C. Saroglou
Math. Ann. 393 (2025), no. 2, 1797–1825.
- The Fourier transform on valuations is the Fourier transform, with D. Faifman
J. Funct. Anal. 288 (2025), no. 3, Paper No. 110741, 42 pp.
- Minkowski valuations in affine convex geometry, with J. Henkel
Int. Math. Res. Not. IMRN 2025, no. 1, Paper No. rnae268, 35 pp.
- Dually Lorentzian polynomials, with J. Ross and H. Süss
Monatsh. Math. 208 (2025), no. 3, 495–524.
- Integral geometry on the octonionic plane, with J. Kotrbatý
Indiana Univ. Math. J. 74 (2025), no. 2, 407–465.
- From harmonic analysis of translation-invariant valuations to geometric inequalities for convex bodies, with J. Kotrbatý
Geom. Funct. Anal. 33 (2023), 541–592.
- On mixed Hodge–Riemann relations for translation-invariant valuations and Aleksandrov–Fenchel inequalities, with J. Kotrbatý
Commun. Contemp. Math. 24 (2022), no. 7, Paper No. 2150049, 24 pp.
- Classification of angular curvature measures and a proof of the angularity conjecture
Amer. J. Math. 144 (2022), no. 5, 1331–1366.
- Integral geometry of exceptional spheres, with G. Solanes
J. Differential Geom. 117 (2021), 137–191.
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The Weyl principle on the Finsler frontier, with D. Faifman
Selecta Math. 27 (2021), no. 2, Paper No. 27, 30 pp.
- On the extendability by continuity of angular valuations on polytopes
J. Funct. Anal. 279 (2020), Paper No. 108665.
- Riemannian curvature measures, with J. H. G. Fu
Geom. Funct. Anal. 29 (2019), 343–381.
- Minkowski valuations and generalized valuations, with F. E. Schuster
J. Eur. Math. Soc. 20 (2018), 1851–1884.
- Even Minkowski valuations, with F. E. Schuster
Amer. J. Math. 137 (2015), 1651–1683.
- Aleksandrov–Fenchel inequalities for unitary valuations of degree 2 and 3, with J. Abardia
Calc. Var. Partial Differential Equations 54 (2015), 1767–1791.
- Integral geometry of unitary area measures
Adv. Math. 263 (2014), 1–44.
- The module of unitarily invariant area measures
J. Differential Geom. 96 (2014), 141–182.
- On the inverse Klain map , with L. Parapatits
Duke Math. J. 162 (2013), 1895–1922.
- GL(n) contravariant Minkowski valuations, with F. E. Schuster
Trans. Amer. Math. Soc. 364 (2012), 815–826.
- GL(n) equivariant Minkowski valuations
Indiana Univ. Math. J. 60 (2011), 1655–1672.