Thomas Wannerer

Publications

• An intersection product for the polytope algebra
   
• Complex and quaternionic analogues of Busemann's random simplex and intersection inequalities, with C. Saroglou
   
• Hard Lefschetz theorem and Hodge-Riemann relations for convex valuations, with A. Bernig and J. Kotrbatý
   
• The Fourier transform on valuations is the Fourier transform, with D. Faifman
  J. Funct. Anal. 288 (2025), no. 3, Paper No. 110741, 42 pp.
   
• 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
   
• Integral geometry on the octonionic plane, with J. Kotrbatý
  Indiana Univ. Math. J., to appear
   
• The Weyl tube theorem for Kähler manifolds, with A. Bernig, J. H. G. Fu, and G. Solanes
   
• 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
   
• 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., (2020), https://doi.org/10.1016/j.jfa.2020.108665
   
• Classification of angular curvature measures and a proof of the angularity conjecture
  Amer. J. Math., 144 (2022), no. 5, 1331–1366
   
• Riemannian curvature measures, with J. H. G. Fu
  Geom. Funct. Anal., 29 (2019), 343–381
   
• Integral geometry of exceptional spheres, with G. Solanes
  J. Differential Geom., 117 (2021), 137–191
   
• 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) equivariant Minkowski valuations
  Indiana Univ. Math. J. 60 (2011), 1655–1672
   
• GL(n) contravariant Minkowski valuations, with F. E. Schuster
  Trans. Amer. Math. Soc. 364 (2012), 815–826
   

Grants

• since 2024: DFG, Lorentzian polynomials and equality in log-concave inequalities, (WA 3510/4-1)
• since 2020: DFG, Curvature Measures in Convex and Integral Geometry, (WA 3510/3-1)
• 2019: DFG, Conference on Convex, Discrete and Integral Geometry, (WA 3510/2-1)
• 2016-2020: DFG, The Transfer Principle of Integral Geometry and Isoperimetric Inequalities, (WA 3510/1-1)

Editorial work

• since 2023: Editorial board, Beiträge zur Algebra und Geometrie

Conference organization

• Interactions between convex geometry and spectral analysis, ISM summer school, Université de Montréal, Canada, July 28 – August 1, 2025
• Seminar on the log-Brunn–Minkowski conjecture, Podebradý, Czechia, February 12–14, 2025
• Positivity and Inequalities in Convex and Complex Geometry, Oberwolfach Mini-Workshop, October 29–November 3, 2023
• Conference on Convex, Discrete and Integral Geometry, FSU Jena, September 16–20, 2019
• Convexity Day, Max Planck Institute for Mathematics in the Sciences, September 9, 2019
• Parallel workshop on Convex and Integral Geometry at Differential Geometry and its Applications, Hradec Králové, September 1–7, 2019
• Conference on Convex and Integral Geometry, Goethe-Universität Frankfurt am Main, September 25–29, 2017
• Workshop on Integral Geometry and Valuation Theory, ETH Zürich, June 17–19, 2015

Invited talks

• Combinatorial Synergies East, MPI for Mathematics in the Sciences, Leipzig, March 19–21, 2025
• Workshop on Convex Geometry and its Applications, MFO, December 15–20, 2024
• Lluis Santaló School "Convex Geometry, Differential Geometry and Harmonic Analysis: Building Synergies", Santander, Spain, July 29 – August 2, 2024
• Oberseminar Differentialgeometrie, Max Planck Institute for Mathematics, Bonn, April 18, 2024
• Geometry Seminar, Shaanxi Normal University, September 19, 2023
• INdAM meeting: Convex Geometry - analytic aspects, Cortona, June 26–30, 2023
• Salzburg Mathematics Colloquium, Paris Lodron Universität Salzburg, May 9, 2023
• Asymptotic Geometric Analysis Seminar, Tel Aviv University, March 19, 2023
• Workshop on Stochastic Geometry, Osnabrück University, November 23–25, 2022
• Workshop on Integral and Metric Geometry, BIRS-CMO, May 1–6, 2022
• Workshop on Convex Geometry and its Applications, MFO, December 12–17, 2021
• Stochastic Geometry Seminar, Charles University, Prague, December 7, 2021
• Conference on Convex, Integral and Stochastic Geometry, Bad Herrenalb (Black Forest), 5–10 September 2021
• Seminar, University of Ioannina, May 5, 2021
• Convex Geometry Seminar, TU Wien, January 28, 2021
• Oberseminar Differentialgeometrie, Max Planck Institute for Mathematics, Bonn, December 12, 2020
• Workshop on Convex Geometry and its Applications, MFO, December 9–15, 2018
• Geometrietag, TU Dresden, December 7–8, 2018
• Summer School New Perspectives on Convex Geometry, CIEM, Castro Urdiales, September 3–7, 2018
• Geometry Seminar, Courant Institute of Mathematical Sciences, March 20, 2018
• Geometry Seminar, University of Toronto, March 12, 2018
• Conference on Convex, Discrete and Integral Geometry, Banach Center, Bedlęwo, June 4–9, 2017
• Sächsischer Geometrietag, TU Chemnitz, December 8–9, 2016
• Mathematics colloquium, Osnabrück University, November 16, 2016
• Conference on Convex and Discrete Geometry, TU Vienna, July 4–8, 2016
• Perspectives on Integral Geometry, University of Georgia, May 30–June 4, 2016
• Seminari de Geometria, Universitat Autònoma de Barcelona, January 10, 2016
• 7. Thüringer Geometrietag, Friedrich-Schiller-Universität Jena, December 4–5, 2015
• Asymptotic Geometric Analysis Mini-Symposium, Case Western Reserve University, August 15–16, 2015
• Geometry Seminar, University of Georgia, February 27, 2015
• Workshop on Tensor Valuations in Stochastic Geometry and Imaging, Sandbjerg Estate, September 21–26, 2014
• Conference on Geometry and Dynamics of Finsler Manifolds, CIRM, June 16–20, 2014
• Convex Geometry Seminar, TU Wien, April 3, 2014
• Asymptotic Geometric Analysis Seminar, Tel Aviv University, December 8, 2013
• Conference on Convex Geometry, Castro Urdiales, September 23–27, 2013
• Workshop on Integral Geometry and its Applications, MFO, February 3–9, 2013
• Geometry Seminar, University of Georgia, January 11, 2013
• Workshop on Convex Geometry and its Applications, MFO, December 9–15, 2012
• Erasmus Workshop on Hermitian Integral Geometry, Goethe-Universität Frankfurt am Main, July 17–19, 2012
• Topics in Geometric Analysis seminar, Max Planck Institute for Gravitational Physics, June 11, 2012
• Workshop on Convexity and Asymptotic Geometric Analysis, CRM, Université de Montréal, April 16–20, 2012
• Analysis Seminar, ETH Zürich, February 28, 2012
• Conference on Integral and Convex Geometric Analysis and Related Topics, Chern Institute of Mathematics, December 14–18, 2011
• Conference on Convex and Integral Geometry, Goethe-Universität Frankfurt am Main, September 26–30, 2011
• AG Stochastische Geometrie, Karlsruhe Institute of Technology, July 17, 2011
• Oberseminar Geometrische Analysis, Goethe-Universität Frankfurt am Main, June 14, 2011
• Workshop on Harmonic Analysis in Convex Geometry, BIRS, May 15–20, 2011
• Mini-Workshop on Valuations and Integral Geometry, MFO, January 17–23, 2010