12
Fachbereich
Institut für Mathematik
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Prof. Dr. Andreas Bernig

I am professor for differential geometry. My main research interest is in integral geometry, more precisely the theory of valuations on vector spaces and manifolds, their algebraic structures and applications for kinematic formulas. Two sample publications in this area are

 
  • Andreas Bernig, J. H. G. Fu, Gil Solanes: Integral geometry of complex space forms Geometric and Functional Analysis 24 (2014), 403-492.
  • Andreas Bernig, J. H. G. Fu: Hermitian Integral Geometry Annals of Mathematics 173 (2011), 907-945.
Besides integral geometry, I am interested in other areas such as Riemann and Finsler geometry, metric geometry, geometric inequalities. 




Sommersemester 2024 


VL Algebraische Integralgeometrie II

Mi 14 - 16 Uhr, Raum 109c






Oberseminar Geometrische Analysis


Di 14-16 Uhr ct, Raum 903











Research interests   

  • Integral Geometry (Valuations, Kinematic formulas)
  • Finsler Geometry (Holmes-Thompson and Busemann volumes, Hilbert geometries)
  • Riemannian geometry (in particular, questions related to curvature)
  • Geometric inequalities (isoperimetric inequality, Brunn-Minkowski, Blaschke-Santaló, Alexandrov-Fenchel, Mahler conjecture etc.)
  • Geometric Measure Theory (Legendrian cycles, Metric Measure Theory)

Born 1974 at Leipzig (Germany).

Studies

Postdoctoral experience

  • 2000-2001: University of Münster (Germany), with Prof. L. Bröcker
  • 2001-2003: University of Zürich (Switzerland), with Prof. V. Schroeder
  • 2003-2004: University of Freiburg (Germany), with Prof. V. Bangert
  • 2004-2007: University of Fribourg (Switzerland), with Prof. R. Kellerhals
  • 2005: Habilitation at the University of Fribourg: Legendrian currents, support functions and tensor-valued measures on singular spaces
  • 2007-2009: SNFS-Professorship at the University of Fribourg, Project Invariants of singular spaces
  • October 2009-present: Professor (W3) for Differential Geometry at the Goethe-University Frankfurt am Main 
  • 2013: Declined offer for a professorship in Differential Geometry/Global Analysis from the University of Vienna.
  • 2017-2019: Dean of the Faculty Computer Science and Mathematics

Prizes and scholarships

  • 1991 and 1992: First prize at the German mathematical olympiad.
  • 1993-1998: Scholarship of the Studienstiftung des Deutschen Volkes
  • 1996-1997: Scholarship of the Deutscher Akademischer Austauschdienst (DAAD)
  • 2001-2004: Scholarship of the Deutsche Forschungsgemeinschaft (DFG)

 

Nr.

Title

Journal

Co-author(s)
 44 Hard Lefschetz theorem and Hodge-Riemann relations for convex valuations Preprint

 J. Kotrbaty, Th. Wannerer
 43 The Weyl tube theorem for Kähler manifolds Preprint  J.. Fu, G. Solanes, Th. Wannerer

42

 Crofton formulas in pseudo-Riemannian space forms Compositio Mathematica, 158 (2022), 1935–1979 D. Faifman, G. Solanes

41

 Uniqueness of curvature measures in pseudo-Riemannian geometry The Journal of Geometric Analysis 31(2021), 11819–11848 D. Faifman, G. Solanes

40

 Additive kinematic formulas for flag area measures
 Mathematische Annalen 381(2021), 1615-1652 Judit Abardia-Evéquoz

39

 Unitarily invariant valuations and Tutte's sequence Proceedings of the AMS 149(2) (2021), 829-841  

38

 Curvature measures of pseudo-Riemannian manifolds J. Reine Angew. Math., 788 (2022) 77-127
 D. Faifman, G. Solanes

37

 Flag area measures Mathematika, 65 (2019), 958-989 J. Abardia-Evéquoz, S. Dann

36

 Dual area measures and local additive kinematic formulas Geometriae Dedicata, 203(1) (2019), 85-110  

35

 Kinematic formulas for tensor valuations Journal Reine Angewandte Mathematik, 736 (2018), 141-191 D. Hug

34

 Valuation theory of indefinite orthogonal groups Journal of Functional Analysis 273 (2017), 2167-2247 D. Faifman

33

 Kinematic formulas on the quaternionic plane Proceedings of the London Mathematical Society 115 (2017), 725-762 G. Solanes

32

 Natural operations on differential forms on contact manifolds Differential Geometry and its applications 50 (2017), 34-51  

31

 Convolution of valuations on manifolds Journal of Differential Geometry, 107 (2017), 203-240 S. Alesker

30

 Generalized translation invariant valuations and the polytope algebra Advances in Mathematics 290 (2016), 36-72 D. Faifman

29

 Spin(9)-invariant valuations on the octonionic plane Israel Journal of Mathematics 214 (2016), 831-855 F. Voide

28

 Classification of invariant valuations on the quaternionic plane Journal of Functional Analysis 267 (2014), 2933-2961 Gil Solanes

27

 Integral geometry of complex space forms Geometric and Functional Analysis 24 (2014), 403-492 J. H. G. Fu, Gil Solanes

26

 Centroid bodies and the convexity of area functionals Journal of Differential Geometry 98 (2014), 357-373  

25

 The isoperimetrix in the dual Brunn-Minkowski theory Advances in Mathematics 254 (2014), 1-14  
24
 Invariant valuations on quaternionic vector spaces Journal de l'Institut de Mathématiques de Jussieu 11 (2012), 467-499
23
 The product on smooth and generalized valuations American Journal of Mathematics 134 (2012), 507-560

S. Alesker
22
 Hermitian Integral Geometry Annals of Mathematics 173 (2011), 907-945

J. H. G. Fu
21
 Harmonic analysis of translation invariant valuations Geometric and Functional Analysis 21 (2011), 751-773

S. Alesker, F. Schuster
20
 Projection bodies in complex vector spaces Advances in Mathematics 227 (2011), 830-846

J. Abardia
19
 Integral Geometry under G_2 and Spin(7) Israel Journal of Mathematics 184 (2011), 301-316  
18
 Volume entropy of Hilbert geometries Pacific Journal of Mathematics 245 (2010), 201-225

G. Berck, C. Vernicos
17
 A Hadwiger-type theorem for the special unitary group Geometric and Functional Analysis 19 (2009), 356-372  
16
 Hilbert geometry of polytopes Archiv der Mathematik 92 (2009), 314-324  
15
 A product formula for valuations on manifolds with applications to the integral geometry of the quaternionic line Commentarii Mathematici Helvetici 84 (2009), 1-19  
14
 Tangent spaces and Gromov-Hausdorff limits of subanalytic spaces Journal Reine Angewandte Mathematik 608 (2007), 1-15 A. Lytchak
13
 The normal cycle of a compact definable set Israel Journal of Mathematics 159 (2007), 373-411  
12
 Valuations on manifolds and Rumin cohomology Journal of Differential Geometry 75 (2007), 433-457 L. Bröcker
11
 Valuations with Crofton formula and Finsler geometry

Advances in Mathematics 210 (2007), 733-753

  
10
 Convolution of convex valuations Geometriae Dedicata 123 (2006), 153-169 J. H. G. Fu
9
 Support functions, projections and Minkowski addition of Legendrian cycles Indiana University Mathematics Journal 55 (2006), 443-464  
8
 Curvature tensors of singular spaces Differential Geometry and its applications 24 (2006), 191-208  
7
 Gromov-Hausdorff limits in definable families Illinois Journal of Mathematics 49 (2005), 475-485  
6
 Variations of Curvatures of Subanalytic Spaces and Schläfli-type Formulas Annals of Global Analysis and Geometry 24 (2003), 67-93  
5
 Non standard metric products Beiträge Algebra Geometrie 44 (2003), 499-510

T. Foertsch, V. Schroeder
4
 Courbures intrinsèques dans les Catégories analytico-géométriques Annales de l'Institut Fourier 53 (2003), 1897-1924 L. Bröcker
3
 Scalar Curvature of definable CAT-Spaces Advances in Geometry 3 (2003), 23-43  
2
 Lipschitz-Killing Invariants Mathematische Nachrichten 245 (2002), 5-25 L. Bröcker
1
 Scalar Curvature of definable Alexandrov Spaces Advances in Geometry 2 (2002), 29-55  

Other texts



Vorlesungsplan bis 2027




WS 23/24Goethe-Universität FrankfurtBlockseminar Mikrolokale Analysis
WS 23/24Goethe-Universität FrankfurtVL Distributionentheorie
WS 23/24
Goethe-Universität Frankfurt
VL Mathematik für Studierende der Physik 3
WS 23/24Goethe-Universität FrankfurtOberseminar Geometrische Analysis
SS 23 Goethe-Universität Frankfurt Oberseminar Geometrische Analysis
SS 23
 Goethe-Universität Frankfurt Proseminar Fourierreihen
SS 23 Goethe-Universität Frankfurt Analysis auf Mannigfaltigkeiten
WS 22/23 Goethe-Universität Frankfurt
 Seminar zur algebraischen Integralgeometrie
WS 22/23 Goethe-Universität Frankfurt Algebraische Integralgeometrie
WS 22/23 Goethe-Universität Frankfurt
 Funktionentheorie und gewöhnliche Differentialgleichungen
WS 22/23 Goethe-Universität Frankfurt Oberseminar Geometrische Analysis
SS22 Goethe-Universität Frankfurt Vorlesung Analysis 2
SS22 Goethe-Universität Frankfurt VL Konvex- und Integralgeometrie
SS22 Goethe-Universität Frankfurt Oberseminar Geometrische Analysis
WS 21/22 Goethe-Universität Frankfurt Vorlesung Analysis 1
WS 21/22 Goethe-Universität Frankfurt Vorlesung Allgemeine Relativitätstheorie
WS 21/22 Goethe-Universität Frankfurt Oberseminar Geometrische Analysis
SS21 Goethe-Universität Frankfurt

Vorlesung Riemannsche Geometrie
SS21 Goethe-Universität Frankfurt

Blockseminar zum Thema
Kählermannigfaltigkeiten
S20/21 Goethe-Universität Frankfurt Forschungssemester
SS20 Goethe-Universität Frankfurt Vorlesung Analysis 2
SS20 Goethe-Universität Frankfurt Vorlesung Analysis auf Mannigfaltigkeiten
SS20 Goethe-Universität Frankfurt Oberseminar Geometrische Analysis
WS 19/20 Goethe-Universität Frankfurt Oberseminar Geoemtrische Analysis
WS 19/20 Goethe-Universität Frankfurt Vorlesung Maß- und Integrationstheorie
WS 19/20 Goethe-Universität Frankfurt Vorlesung Symplektische Geometrie
WS 19/20 Goethe-Universität Frankfurt Proseminar Analysis: Fourierreihen
WS 19/20 Goethe-Universität Frankfurt Blockseminar: From symplectic measurements to the Mahler conjecture
SS19 Goethe-Universität Frankfurt Oberseminar Geometrische Analysis
SS19 Goethe-Universität Frankfurt Vorlesung Darstellung kompakter Liegruppen
WS 18/19 Goethe-Universität Frankfurt Blockseminar über Minimalflächen
WS 18/19 Goethe-Universität Frankfurt Oberseminar Geometrische Analysis
WS 18/19 Goethe-Universität Frankfurt Analysis 2
SS18 Goethe-Universität Frankfurt Oberseminar Geometrische Analysis
SS18 Goethe-Universität Frankfurt Analysis 1
WS 17/18 Goethe-Universität Frankfurt Oberseminar Geometrische Analysis
WS 17/18 Goethe-Universität Frankfurt Seminar zur Integralgeometrie
WS 17/18 Goethe-Universität Frankfurt Vorlesung Algebraische Integralgeometrie
SS 17 Goethe-Universität Frankfurt Oberseminar Geometrische Analysis
SS 17 Goethe-Universität Frankfurt Konvex- und Integralgeometrie
WS 16/17 Goethe-Universität Frankfurt Forschungssemester
WS 16/17 Goethe-Universität Frankfurt Oberseminar Geometrische Analysis
SS 16 Goethe-Universität Frankfurt Analysis 1
SS 16 Goethe-Universität Frankfurt Symplektische Geometrie
SS 16 Goethe-Universität Frankfurt Seminar zur Differentialgeometrie
SS 16 Goethe-Universität Frankfurt Oberseminar Geometrische Analysis
WS 15/16 Goethe-Universität Frankfurt Oberseminar Geometrische Analysis
WS 15/16 Goethe-Universität Frankfurt Vorlesung Riemannsche Geometrie
WS 15/16 Goethe-Universität Frankfurt Proseminar Ausgewählte Themen der Analysis
SS 15 Goethe-Universität Frankfurt Oberseminar Geometrische Analysis
SS 15 Goethe-Universität Frankfurt Analysis auf Mannigfaltigkeiten
SS 15 Goethe-Universität Frankfurt Seminar Darstellung kompakter Lie-Gruppen
WS 14/15 Goethe-Universität Frankfurt Oberseminar Geometrische Analysis
WS 14/15 Goethe-Universität Frankfurt Funktionentheorie und gewöhnliche Differentialgleichungen
WS 14/15 Goethe-Universität Frankfurt Darstellung kompakter Lie-Gruppen
SS 14 Goethe-Universität Frankfurt Seminar über Differentialgeometrie
SS 14 Goethe-Universität Frankfurt Oberseminar Geometrische Analysis
SS 14 Goethe-Universität Frankfurt Finslergeometrie
SS 14 Goethe-Universität Frankfurt Analysis 2
WS 13/14 Goethe-Universität Frankfurt Analysis 1
WS 13/14 Goethe-Universität Frankfurt Oberseminar Geometrische Analysis
SS13 Goethe-Universität Frankfurt Forschungssemester
WS12/13 Goethe-Universität Frankfurt Mathematik für Physiker 3
WS 12/13 Goethe-Universität Frankfurt Geometrische Variationsprobleme
WS 12/13 Goethe-Universität Frankfurt Oberseminar Geometrische Analysis

SS 12

Goethe-Universität Frankfurt

Elementare Differentialgeometrie

SS12

Goethe-Universität Frankfurt

Geometrische Maßtheorie

SS 12

Goethe-Universität Frankfurt

Proseminar ausgewählte Themen der Analysis

SS12

Goethe-Universität Frankfurt

Oberseminar Geometrische Analysis

WS 11/12

Goethe-Universität
Frankfurt

Geometrische Ungleichungen

WS 11/12

Goethe-Universität Frankfurt

Konvex- und Integralgeometrie

WS 11/12

Goethe-Universität Frankfurt

Seminar über Geometrische Analysis

WS 11/12

Goethe-Universität Frankfurt

Oberseminar Geometrische Analysis
SS 11 Goethe-Universität Frankfurt Analysis auf Mannigfaltigkeiten
SS 11 Goethe-Universität Frankfurt Liegruppen
WS 10/11 Goethe-Universität Frankfurt Höhere Analysis
WS 10/11 Goethe-Universität Frankfurt Riemannsche Geometrie
SS 10 Goethe-Universität Frankfurt Proseminar Konvexe Mengen und Funktionen
SS 10 Goethe-Universität Frankfurt Analysis 2
WS 09/10 Goethe-Universität Frankfurt Mathematik für Studierende der Physik 1
WS 08/09 Universität Ulm Erasmusvorlesung (8 Stunden) Modern integral geometry
WS 08 Universität Fribourg Riemannian geometry
WS 08 Universität Fribourg Seminar Courbes et surfaces
SS 08 Universität Fribourg Seminar Polytopes
WS 07/08 Universität Fribourg Géométrie Intégrale
WS 06/07 Universität Fribourg Seminar Courbes et surfaces
SS 06 Universität Fribourg Algèbre et Géométrie II
WS 05/06 Universität Fribourg Algebraic Geometry
SS 03 Universität Zürich Geometric Measure Theory
WS 02/03 Universität Zürich Seminar Euklidische, sphärische und hyperbolische Geometrie
SS 01 Universität  Münster Seminar Metric Geometry
     
     
     

Upcoming events  

Past events

Third party funding

  • BE 2484/10-1 (DFG) Kohomologische Methoden in der Integralgeometrie, 01.10.2023-30.09.2026
  • BE 2484/8-1 (DFG) Convex and Integral Geometry (Konferenz)
  • BE 2484/5-2  (DFG) Kinematic Formulas in Hermitian space forms and Applications, 1.7.2016-31.5.2021
  • BE 2484/6-1 (DFG) Volumes in normed vector spaces and Finsler manifolds, 15.11.2014-15.11.2017
  • BE 2484/5-1 (DFG) Kinematic Formulas in Hermitian space forms and Applications, 1.10.2012-30.9.2014
  • BE 2484/4-1 (DFG) Convex and Integral Geometry (Konferenz)
  • BE 2484/3-1 (gemeinsames DFG-Projekt mit Prof. Tobias Weth) Geometrische Ungleichungen in Analysis und Integralgeometrie, 1.5.2011-30.4.2014

Service as referee

  • Acta Mathematica Hungarica, Advances in Calculus of Variations, Advances in Geometry, Advances in Mathematics, American Journal of Mathematics, Annals of Global Analysis and Geometry, Annales scientifiques de l'Ecole normale supérieure, Annales Polonici Mathematici, Ann. Acad. Sci. Fenn. Math., Analysis and Geometry in Metric Spaces, Archiv der Mathematik, Axioms, Bulletin of the London Mathematical Society, Calculus of variations and PDE, Canadian Journal of Mathematics, Communications in Contemporary Mathematics, Communications in Pure and Applied Mathematics, Compositio Mathematica, Comptes rendus Mathematique, Discrete & Computational Geometry, Duke Mathematical Journal, European Journal of Mathematics, Forum Mathematicum, GAFA, GAFA Seminar Notes, Geometriae Dedicata, Indiana University Mathematics Journal, International Mathematics Research Notices, Inventiones Mathematicae, Israel Journal of Mathematics, Journal für die Reine und Angewandte Mathematik, Journal of Differential Geometry, Journal of Functional Analysis, Journal of Function Spaces, Journal of Geometric Analysis, Journal of Geometry, Journal of Mathematical Analysis and Applications, Journal of the EMS, Journal of the LMS, Journal of Topology and Analysis, manuscripta mathematica, Mathematische Annalen, Mathematical Inequalities & Applications, Mathematical Proceedings, Michigan Mathematical Journal, Monatshefte für Mathematik, Proceedings of the London Mathematical Society, Publicationes Mathematicae Debrecen, Studia Mathematica, Transactions of the American Mathematical Society

Invited talks on Conferences and Workshops

Month
 Conference/Workshop
 Title
July 2023,

Jena, Workshop Modern valuation theory
https://modernval2023.uni-jena.de		 The Weyl principle in pseudo-Riemannian geometry
June 2023,

 Cortona, Conference Convex Geometry - Analytic aspects
https://events.dimai.unifi.it/Cortona23/ 		Intrinsic volumes of Kähler manifolds
June 2023
Nijmegen/Niederlande
workshop "Singularities and Curvature
in General Relativity"
(https://www.math.ru.nl/SCGR2023/)



 Mini Course"Curvature measures of singular spaces in the Riemannian and pseudo-Riemannian setting",


 March 2023
 Leipzig: Geometrietag (https://www.math.uni-leipzig.de/geometrietag/) The Weyl principle in pseudo-Riemannian geometry
November 2022 Osnabrück: Stochastic Geometry Workshop (https://www.math-conf.uni-osnabrueck.de/stochastic-geometry-workshop/) 
 Algebraic integral geometry
April 2022 TU Vienna: Mini-symposium Geometric Probability and Valuation Theory Crofton formulas for pseudo-Riemannian space forms
December 2021 Oberwolfach: Workshop Convex Geometry and its Applications Intrinsic volumes on Kaehler manifolds

September 2021

 Bad Herrenalb: Conference on Convex, Integral and Stochastic Geometry Intrinsic volumes of Kähler manifolds

March 2021

 HIM Bonn: Workshop High dimensional measures: geometric and probabilistic aspects Intrinsic volumes on pseudo-Riemannian manifolds

September 2019

 Jena: Conference on convex, discrete and integral geometry The Weyl principle in pseudo-Riemannian geometry
September 2019 MPI Leipzig: Convexity day The normal cycle
September 2019

Hradec Králové: Differential Geometry and its Applications

Dual area measures and hermitian integral geometry
December 2018 Oberwolfach: Conference on Convex geometry and its applications Flag area measures
September 2018 EPF Lausanne: Summer school Generalized curvatures Mini-course on Lipschitz-Killing curvatures
December 2017 Magdeburg:  Geometrietag Natural operators on contact manifolds
September 2017 Bad Herrenalb: Conference Geometry and Physics of Spatial Random Systems
Tensor valuations and local additive kinematic formulas
June 2017 Bedlewo:  Conference Convex, Discrete and Integral Geometry Convolution of valuations
October 2016 Rome: Workshop Analytic aspects of convexity A Hadwiger-type theorem for non-definite orthogonal groups
December 2015 Jena: Geometrietag Hermitian integral geometry
June 2015 Zurich: Workshop on Integral Geometry and Valuation Theory Valuations and curvature measures on manifolds
February 2015 Congreso RSME Granada Integral geometry of transitive group actions
June 2014 CIRM Luminy: Geometry and dynamics on Finsler manifolds Minimality of k-planes in normed spaces
January 2014 Toulouse: Workshop on Busemann-Petty problems Minimality of k-planes in normed spaces
September 2013 Castro Urdiales: Conference on Convex Geometry Kinematic formulas for tensor valuations
September 2013 Freudenstadt: Geometry and Physics of Spatial Random Systems Kinematic formulas for tensor valuations
March 2013 Banff: Interplay of convex geometry and Banach space theory Minimality of k-planes in normed spaces
June 2012 35. Süddeutsches Kolloquium über Differentialgeometrie   Hermitesche Integralgeometrie
April 2012 CRM Montreal: Workshop on Convexity and asymptotic geometric analysis Algebraic integral geometry
December 2011 Chern Institute, Tianjin: International conference on Integral and Convex Geometric Analysis and Related Topics Integral geometry of complex space forms
July 2011 Bad Herrenalb: Workshop on Geometry and Physics of Spatial Random Systems Recent developments in tensor valuations
Juni 2010 Bad Herrenalb: Workshop on Convex and Stochastic Geometry Valuations, bivaluations and geometric inequalities
November 2009 Oberwolfach: Conference on Convex geometry and its applications First steps in quaternionic integral geometry
July 2009 Vienna: Conference on Convex and Discrete Geometry Integral geometry of transitive group actions
June 2009 Tel Aviv: The state of Geometry and Functional Analysis Algebraic integral geometry
March 2009 Blaubeuren: 15th Workshop on Stochastic geometry, Stereology, and Image Analysis Algebraic integral geometry
July 2008 Oberwolfach: Conference Geometry Volume entropy of Hilbert metrics
January 2008 Wien: Workshop Convex and Stochastic Geometry A Hadwiger-type theorem for the special unitary group
April 2007 Jerusalem: Workshop Valuations The principal kinematic formula in hermitian vector spaces
October 2006 Oberwolfach: Meeting Geometry The principal kinematic formula in hermitian vector spaces
December 2005 Lausanne: Workshop Integral and Random Geometry Integral geometry, currents and cohomology
September 2005 Passau: Conference Real Algebraic and Analytic Geometry Support functions and the construction of the normal cycle
August 2005 Lausanne: XXth Rolf Nevanlinna Colloquium Valuations on manifolds and the Rumin-de Rham complex
September 2004 Oberwolfach: meeting Geometry Curvature tensors of singular spaces
June 2004 Salamanca: conference Real Algebraic and Analytic Geometry Tangent cones and Gromov-Hausdorff limits of subanalytic spaces,
April 2003 Trento: conference Geometric Measure Theory A proof of Schläfli's formula with normal cycles
April 2003 Pisa: conference Real Algebraic and Analytic Geometry Distributional invariants of singular spaces
September 2003 Münster: workshop Singular spaces - metric, curvature and characteristic classes Generalized Curvatures,
March 2002 Oberwolfach: Meeting Real algebraic and analytic geometry Variations of Lipschitz-Killing curvatures
February 2002 Oberwolfach: Meeting Positivity of Polynomials Barrier functions for positive matrices and polynomials,
December 2001 Madrid: conference Real Geometry Intrinsic Curvatures in Analytic-Geometric Categories
June 2001 Rennes: Conference Real Algebraic and Analytic Geometry Differential Geometry of definable Sets
May 2000 Chambéry: Workshop Espaces singuliers et Géométrie Spectrale Géométrie Intégrale

Seminar talks

Month University Title
November 2022:  UA Barcelona Integral geometry of complex space forms and Tutte's sequence 1,3,13,68,399,..."
March 2022 Tel Aviv Integral geometry of complex space forms
October 2021 TU Vienna Integral geometry of complex space forms and Tutte's sequence 1,3,13,68,399,...
July 2021 Tübingen Intrinsic volumes on pseudo-Riemannian manifolds (online)
July 2021 Chemnitz Intrinsic volumes on pseudo-Riemannian manifolds (online)
February 2020 Florence A Chern-Gauss-Bonnet theorem for metrics with changing signature
February 2017 Cleveland Integral geometry of the complex projective space
February 2017 Toronto Integral geometry of the complex projective space
January 2017 Jena Integral geometry of the complex projective space
March 2016 TU Vienna Klain-Schneider continuous valuations
October 2015 TU Vienna Convolution of valuations
May 2015 Oldenburg Volumina in normierten Vektorräumen
April 2015 Giessen Algebraic integral geometry
March 2015 UA Barcelona Convolution of valuations and the polytope algebra
November 2014 Münster Integral geometry of the complex projective space
May 2013 KIT Karlsruhe Centroid bodies and the convexity of area functionals
April 2013 UA Barcelona The measured centroid body and convexity of area functionals
April 2013 Osnabrück Algebraic integral geometry
March 2013 Polytechnic Institute, NYU A duality for isoperimetric problems
November 2012 Stuttgart Integralgeometrie transitiver Gruppen
October 2012 Fribourg Algebraic integral geometry
July 2012 Kiel Kinematische Formeln und Bewertungen
March 2012 Tel Aviv Algebraic integral geometry
January 2012 Marburg Algebraic integral geometry
April 2011 Chambéry Géométrie intégrale algébrique
August 2010 TU Vienna The complex projection body
June 2009 Strasbourg Géométrie intégrale des espaces hermitiens
May 2009 Münster Algebraic integral geometry
April 2009 Chambéry Géométrie intégrale des espaces hermitiens
March 2009 Vienna Currents, forms and valuations
February 2009 Ulm Hermitesche Integralgeometrie
October 2008 Dijon Géométrie intégrale des espaces hermitiens
May 2008 Barcelona Hermitian integral geometry
February 2008 Jena Valuations and Rumin cohomology
January 2007 Münster Integralgeometrie und Kohomologietheorien
January 2007 Regensburg Integralgeometrie und Kohomologietheorien
February 2006 Athens, GA Smooth valuations, Rumin cohomology and the Hard Lefschetz Theorem
January 2006 Strasbourg Valuations lisses et cohomologie de Rumin-de Rham
April 2005 Zurich Valuations on manifolds and the Rumin- de Rham complex
December 2004 Nice Tenseurs de courbure des ensembles singuliers
November 2004 Marseille Limites de Gromov-Hausdorff dans les familles définissables
November 2004 Fribourg (CH) Altes und Neues zur Minkowskiaddition
May 2004 Chambéry Espaces tangents des ensembles sous-analytiques
March 2004 Rennes Espaces tangents des ensembles sous-analytiques
November 2003 Bern Collapsing of Riemannian manifolds
November 2003 Fribourg (CH) Krümmungen singulärer Räume
May 2003 Neuchâtel Courbure des espaces lisses et singuliers
February 2003 HU Berlin Curvatures of singular spaces
January 2003 Rennes Formule de Schläfli et courbures des ensembles sous-analytiques
November 2002 Louvain-la-Neuve Barrier Functions on Convex sets
November 2002 Freiburg and Augsburg Schläfli's Formula and Curvatures of Singular Spaces
October 2002 Bern Schläfli's Formula and Curvatures of Singular Spaces
April 2002 Paris 7 Variations des courbures et formule de Schläfli
December 2000 Zürich Scalar Curvature of Singular Spaces
May 2000 Duisburg Konstruktionen in der Reellen Algebraischen Geometrie
March 2000 Rennes and Dijon Courbure des ensembles singuliers
January 2000 Chambéry Mesures de courbures
September 1997 Dortmund Konstruktionen in der Reellen Algebraischen Geometrie
 

Postdocs

  • PD Dr. Judit Abardia-Evequoz
  • Dr. Jan Kotrbatý
  • Dr.  Léo Mathis 

Doctoral students

  • Since January 2019 Frederik Herget
  • 2020 Jonas Knörr: Smooth valuations on convex functions
  • 2016 Mykhailo Saienko: Tensor valued valuations and curvature measures in euclidean spaces
  • 2013 Floriane Voide: Spin(9)-invariant valuations
  • 2010 Christoph Thäle: Geometry of Iteration Stable Random Tessellations

Master/Diploma students

  • 2019 Lucas Schäfer: Algebraische Operationen auf Bewertungen
  • 2018 Jonas Knörr: Lokale additive kinematische Formeln auf der quaternionischen Ebene
  • 2017 Frank Steinke: Krümmungsmaße in quaternionischen Vektorräumen
  • 2014 Patrick Mentrup: Systolen auf Finslermannigfaltigkeiten
  • 2012 Mykhailo Saienko: SU(n)-invariant curvature measures
  • 2009 Floriane Voide: La conjecture de Mahler
  • 2006 Cathrine Marro: Das Holmes-Thompson-Volumen

Former research associates

  • Dr. Florian Besau (now TU Vienna)
  • Prof. Dr. Thomas Wannerer (now University of Jena)
  • Dr. Gautier Berck
  • Dr. Olaf Mordhorst 

Vorlesungen im Sommersemester 2024

Prof. Dr. Andreas Bernig


Institut für Mathematik
Goethe-Universität Frankfurt

Robert-Mayer-Str. 10

D-60325 Frankfurt am Main

Büro: Raum 821


Postanschrift:

Goethe-Universität Frankfurt am Main

Fachbereich Informatik und Mathematik

Institut für Mathematik

D-60629 Frankfurt am Main


Phone: ++49-69-798-28953           

Fax: ++49-69-798-28856

Email: bernig@math.uni-frankfurt.de


Sprechzeiten: Di 13:45 - 14:15 Uhr.

Sprechzeiten während der vorlesungsfreien Zeit nach Vereinbarung