Geometric Analysis

Prof. Dr. Franz Schuster

Office Hours:		Monday 10:30 - 11:30
Phone:		+43-1-58801/10475
Fax:		+43-1-58801/10496
Email:		schuster@dmg.tuwien.ac.at
Address:		Institut für Diskrete Mathematik und Geometrie, TU Wien Wiedner Hauptstrasse 8–10, 1040 Wien, Austria
Room:		5th floor, Section A, DA 05 L22

Short Curriculum Vitae

• 2003: Master degree (Dipl.-Ing.), Vienna University of Technology
• 06/2003-02/2007: Researcher, FWF Project  Affinely associated bodies
• 01/2005-06/2005: Visiting Scholar, Università degli Studi di Firenze
• 2005: Doctor of Technical Sciences, Vienna University of Technology
• 03/2006-08/2006: Visiting Scholar, Albert-Ludwigs-Universität Freiburg
• 03/2007-02/2009: Researcher, FWF Project  Valuations on convex bodies
• 06/2008: Best Paper Award 2007 of the Faculty of Mathematics, Vienna University of Technology
• 03/2009-07/2012: Assistant Professor at the Vienna University of Technology
• 06/2010: Best Paper Award 2009 of the Faculty of Mathematics, Vienna University of Technology
• 07/2010: Habilitation in Analysis and Geometry, Vienna University of Technology
• 10/2010: Hlawka-Prize of the Austrian Academy of Sciences
• 05/2012: ERC Starting Grant of the European Research Council
• 06/2012: START-Prize of the Austrian Science Fund (FWF)
• 08/2012-03/2013: Associate Professor at the Vienna University of Technology
• Since 04/2013: Full Professor at the Vienna University of Technology
• 09/2013: Förderungspreis of the Austrian Mathematical Society
• 11/2013: Best Paper Award 2012 of the Faculty of Mathematics, Vienna University of Technology
• Since 03/2020: Department Head, Institute of Discrete Mathematics and Geometry, Vienna University of Technology

Conference Organization

• 07/2016: Conference on Convex and Discrete Geometry in Vienna
• 09/2013: Conference on Convex Geometry at the CIEM in Castro Urdiales, Spain
  
• 02/2013: Conference on Integral Geometry and its Applications in Oberwolfach
  
• 09/2011: Conference on Convex and Integral Geometry at the Goethe University Frankfurt
  
• 01/2010: Mini-Workshop on Valuations and Integral Geometry in Oberwolfach
  
• 07/2009: Conference on Convex and Discrete Geometry in Vienna
• 10/2008: Special Session on Convex and Integral Geometry in Middletown, CT
  

Class Notes

• Harmonische Analysis und Geometrie (in German)
  
• Lie Algebren und Darstellungstheorie (in German)
  
• Analysis auf Mannigfaltigkeiten (in German)
  
• Integralgeometrie (in German)
  
• Kompakte Lie Gruppen und Darstellungstheorie (in German)
  

Research Projects

PhD Students

• 03/2010 - 02/2012: Thomas Wannerer
  Thesis: "SO(n) equivariant Minkowski Valuations"
• 11/2010 - 12/2012: Manuel Weberndorfer
  Thesis: "Reverse Affine Isoperimetric Inequalities"
• 04/2011 - 06/2013: Lukas Parapatits
  Thesis: "Minkowski Valuations and the Special Linear Group"
• 11/2012 - 01/2015: Florian Besau
  Thesis: "Binary Operations and Floating Bodies in Spherical Convexity"
• 02/2013 - 03/2016: Astrid Berg
  Thesis: "Volume Inequalities for Minkowski Valuations"
• 09/2014 - 02/2016: Felix Dorrek
  Thesis: "Area measures, Minkowski endomorphisms and j-projection bodies"
• 12/2016 - 11/2019: Thomas Hack
  Thesis: "Spherical isoperimetric inequalities"
• 05/2017 - 07/2020: Philipp Kniefacz
  Thesis: "Rearrangement and Sobolev inequalities via projection averages"
• 08/2018 - 10/2021: Georg Hofstätter
  Thesis: "Isoperimetric problems for Minkowski valuations"
• Since 04/2021: Simon Ellmeyer
  
• Since 12/2021: Leo Brauner
  

Preprints and Work in progress

• Affine Quermassintegrals and Even Minkowski Valuations
  Jointly with G. Hofstätter.
• Affine invariant bivaluations
  Jointly with S. Alesker.

Publications

• Spherical Centroid Bodies
  AMERICAN JOURNAL OF MATHEMATICS, in press.
  Jointly with F. Besau, T. Hack, and P. Pivovarov.
• Blaschke-Santalo inequalities for Minkowski and Asplund endomorphisms
  INTERNATIONAL MATHEMATICS RESEARCH NOTICES, in press.
  Jointly with G. Hofstätter.
• Fixed points of Minkowski valuations
  ADVANCES IN MATHEMATICS 392 (2021), 108017, 33 pp.
  Jointly with O. Ortega-Moreno.
• Sharp Sobolev inequalities via projection averages
  THE JOURNAL OF GEOMETRIC ANALYSIS, 31 (2021), 7436–7454.
  Jointly with P. Kniefacz.
• Lutwak-Petty Projection Inequalities for Minkowski Valuations and their Duals
  JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 490 (2020), 124190, 24 pp.
  Jointly with A. Berg.
• Affine vs. Euclidean Isoperimetric Inequalities
  ADVANCES IN MATHEMATICS 356 (2019), 106811, 26 pp.
  Jointly with C. Haberl.
• Minkowski Valuations and Generalized Valuations
  JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY (JEMS) 20 (2018), 1851-1884.
  Jointly with T. Wannerer.
• Log-Concavity Properties of Minkowski Valuations
  TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 370 (2018), 5245-5277.
  Jointly with A. Berg, L. Parapatits and M. Weberndorfer.
• Projection Functions, Area Measures and the Alesker-Fourier Transform
  JOURNAL OF FUNCTIONAL ANALYSIS 273 (2017), 2026-2069.
  Jointly with F. Dorrek.
• A Hadwiger-type theorem for general tensor valuations
  In: Tensor Valuations and their Applications in Stochastic Geometry and Imaging
  (M. Kiderlen and E. Vedel Jensen, eds.), Springer Lecture Notes in Mathematics 2177, 157-184 (2017).
  
• Binary Operations in Spherical Convex Geometry
  INDIANA UNIVERSITY MATHEMATICS JOURNAL 65 (2016), 1263-1288.
  Jointly with F. Besau.
• Even Minkowski Valuations
  AMERICAN JOURNAL OF MATHEMATICS 137 (2015), 1651-1683.
  Jointly with T. Wannerer.
• A Characterization of Blaschke Addition
  ADVANCES IN MATHEMATICS 254 (2014), 396-418.
  Jointly with R.J. Gardner and L. Parapatits.
• Volume Inequalities for Asymmetric Wulff Shapes
  JOURNAL OF DIFFERENTIAL GEOMETRY 92 (2012), 263-283.
  Jointly with M. Weberndorfer.
• The Steiner Formula for Minkowski Valuations
  ADVANCES IN MATHEMATICS 230 (2012), 978-994.
  Jointly with L. Parapatits.
• An Asymmetric Affine Polya-Szegoe Principle
  MATHEMATISCHE ANNALEN 352 (2012), 517-542.
  Jointly with C. Haberl and J. Xiao.
• The Sine Transform of Isotropic Measures
  INTERNATIONAL MATHEMATICS RESEARCH NOTICES 2012, 717-739.
  Jointly with G. Maresch.
• GL(n) contravariant Minkowski valuations
  TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 364 (2012), 815-826.
  Jointly with T. Wannerer.
• Harmonic Analysis of Translation Invariant Valuations
  GEOMETRIC AND FUNCTIONAL ANALYSIS 21 (2011), 751-773.
  Jointly with S. Alesker and A. Bernig.
• Crofton Measures and Minkowski Valuations
  DUKE MATHEMATICAL JOURNAL 154 (2010), 1-30.
• General $L_p$ Affine Isoperimetric Inequalities
  JOURNAL OF DIFFERENTIAL GEOMETRY 83 (2009), 1-26.
  Jointly with C. Haberl.
• Asymmetric Affine $L_p$ Sobolev Inequalities
  JOURNAL OF FUNCTIONAL ANALYSIS 257 (2009), 641-658.
  Jointly with C. Haberl.
• Valuations and Busemann-Petty Type Problems
  ADVANCES IN MATHEMATICS 219 (2008), 344-368.
• Convolutions and Multiplier Transformations of Convex Bodies
  TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 359 (2007), 5567-5591.
• Rotation Invariant Minkowski Classes of Convex Bodies
  MATHEMATIKA 54 (2007), 1-13.
  Jointly with R. Schneider.
• Rotation Equivariant Minkowski Valuations
  INTERNATIONAL MATHEMATICS RESEARCH NOTICES 2006, Article ID 72894, 20 pages.
  Jointly with R. Schneider.
• Volume Inequalities and Additive Maps of Convex Bodies
  MATHEMATIKA 53 (2006), 211-234.
• An Arithmetic Proof of John's Ellipsoid Theorem
  ARCHIV DER MATHEMATIK 85, 82 - 88 (2005).
  Jointly with P.M. Gruber.