Lorenz Schwachhöfer

Research Interests

List of publications and preprints

• Articles in scientific journals

  • Domenico Fiorenza, Hông Vân Lê, Lorenz J. Schwachhöfer, Luca Vitagliano, Strongly homotopy Lie algebras and deformations of calibrated submanifolds, Asian Journal of Mathematics, Vol. 25 no. 3, 341-368 (2021), [online version]
  
  
  • Domenico Fiorenza, Kotaro Kawai, Hông Vân Lê, Lorenz J. Schwachhöfer, Almost formality of manifolds of low dimension, Annali della Scuola Normale Superiore di Pisa, Vol. 22 no. 1, 79-107 (2021), DOI Number: 10.2422/2036-2145.201905_002 [online version]
  
  
  • Florio M. Ciaglia, Jürgen Jost, Lorenz J. Schwachhöfer, Differential geometric aspects of parametric estimation theory for states on finite-dimensional C^*-algebras, Entropy Vol. 22(11), 1132 (30 p.) (2020), [online version]
  
  
  • Florio M. Ciaglia, Jürgen Jost, Lorenz J. Schwachhöfer, From the Jordan Product to Riemannian Geometries on Classical and Quantum States, Entropy Vol. 22(6), 637 (27 p.) (2020), [online version]
  
  
  • Hông Vân Lê, Lorenz J. Schwachhöfer, Lagrangian submanifolds in strictly nearly Kähler 6-manifolds, Osaka Journal of Mathematics. Vol. 56 no. 3, 601-629 (2019) [online version]
  
  
  • Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz J. Schwachhöfer, Parametrized measure models, Bernoulli Journal, Vol. 24, No. 3, 1692-1725 (2018). [online version]
  
  
  • Kotaro Kawai, Hông Vân Lê, Lorenz J. Schwachhöfer, Frölicher-Nijenhuis cohomology on G2- and Spin(7)-manifolds, Internat. J. Math. 29 (2018), no. 12, [online version]
  
  
  • Kotaro Kawai, Hông Vân Lê, Lorenz J. Schwachhöfer, Frölicher-Nijenhuis bracket and geometry of G_2-and Spin(7)-manifolds, Annali di Matematica Pura ed Applicata (4) 197 (2018), no. 2, 411-432 [online version]
  
  
  • Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz J. Schwachhöfer, Information geometry and sufficient statistics, Probab. Theory Related Fields 162 no. 1-2, 327-364 (2015) [online version]
  
  
  • Roger Bielawski, Lorenz J. Schwachhöfer, Hypercomplex limits of pluricomplex structures and the Euclidean limit of hyperbolic monopoles, Ann. Global Anal. Geom. 44 no. 3, 245-256, (2013) [online version]
  
  
  • Roger Bielawski, Lorenz J. Schwachhöfer, Pluricomplex geometry and hyperbolic monopoles, Comm. Math. Phys. 323 no. 1, 1-34 (2013) [online version]
  
  
  • Roger Bielawski, Lorenz J. Schwachhöfer, Sheaves on P^1 x P^1, bigraded resolutions, and coadjoint orbits of loop groups, Proc. Amer. Math. Soc. 141 no. 12, 4155-4167 (2013) [online version]
  
  
  • Lorenz J. Schwachhöfer, On the Solvability of the Transvection group of Extrinsic Symplectic Symmetric Spaces, Journal of Geometry and Physics, Vol. 61, 2098 - 2107 (2011) [online version]
  
  
  • Tom Krantz, Lorenz J. Schwachhöfer, Extrinsically Immersed Symplectic Symmetric Spaces, Annals of Global Analysis and Geometry, Vol. 37, No. 4, 379 - 391 (2010) [online version]
  
  
  • Lorenz J. Schwachhöfer, Kristopher Tapp, Cohomogeneity one disk bundles with normal homogeneous collars, Proceedings of the London Mathematical Society (3), Vol. 99 No. 3, 609 - 632 (2009), [online version]
  
  
  • Michel Cahen, Lorenz J. Schwachhöfer, Special Symplectic Connections, Journal of Differential Geometry, Vol. 83, no.2, 229-271 (2009) [online version]
  
  
  • Lorenz J. Schwachhöfer, Kristopher Tapp, Homogeneous Metrics with nonnegative curvature, Journal of Geometric Analysis Vol. 19, 929-943 (2009), [online version]
  
  
  • Michel Cahen, Simone Gutt, Nicolas Richard, Lorenz J. Schwachhöfer, Extrinsic symplectic symmetric spaces, Journal of Geometry and Physics Vol. 59, No.4, 409 - 425 (2009) [online version]
  
  
  • Lorenz J. Schwachhöfer, A remark on left invariant metrics on compact Lie groups, Archiv der Mathematik, Vol. 90, No.2, 158 - 162 (2008) [online version]
  
  
  • Pierre Bieliavsky, Michel Cahen, Simone Gutt, John Rawnsley, Lorenz J. Schwachhöfer, Symplectic Connections, International Journal of Geometric Methods in Modern Physics Vol. 3, No. 3, p. 375-420 (2006) [online version]
  
  
  • Michel Cahen, Lorenz J. Schwachhöfer, Special symplectic connections and Poisson geometry, Letters in Mathematical Physics, Vol. 69, No. 1, p. 115 - 137 (2004) [pdf] [ps] [dvi]
  
  
  • Lorenz J. Schwachhöfer, Wilderich Tuschmann, Metrics of positive Ricci curvature on quotient spaces, Mathematische Annalen, Vol. 330, No.1, 59 - 91 (2004) [pdf] [ps] [dvi]
  
  
  • Lorenz J. Schwachhöfer, Homogeneous connections with special symplectic holonomy, Mathematische Zeitschrift, Vol. 238, No.4, 655 - 688 (2001) [pdf] [ps] [dvi]
  
  
  • Lorenz J. Schwachhöfer, Connections with irreducible holonomy representations, Advances in Mathematics, Vol. 160, No.1, 1 - 80 (2001) [pdf] [ps] [dvi]
  
  
  • Lorenz J. Schwachhöfer, Riemannian, Symplectic and Weak Holonomy, Annals of Global Analysis and Geometry, Vol. 18, No. 3, 291-308 (2000) [pdf] [ps] [dvi]
  
  
  • Sergey A. Merkulov, Lorenz J. Schwachhöfer, Classification of irreducible holonomies of torsion-free affine connections, Annals of Mathematics, Vol. 150, No.1, 77 - 149 (1999); Addendum: Classification of irreducible holonomies of torsion-free affine connections, Annals of Mathematics, Vol. 150, No.3, 1177 - 1179 (1999)
  
  
  • Quo-Shin Chi, Lorenz J. Schwachhöfer, Exotic Holonomy on Moduli Spaces of Rational Curves, Differential Geometry and its Applications, Vol. 8, No. 2, 105 - 134 (1998) [online version]
  
  
  • Lorenz J. Schwachhöfer, On affine connections whose holonomy is a tensor representation, Zeitschrift für Analysis und ihre Anwendungen, Vol. 16, No.1, 119 - 130 (1997) [pdf] [ps] [dvi]
  
  
  • Quo-Shin Chi, Sergey A. Merkulov, Lorenz J. Schwachhöfer, Exotic Holonomy $E_7^{(a)}$, International Journal of Mathematics, Vol. 8, No. 5, 583 - 594 (1997) [pdf] [ps] [dvi]
  
  
  • Quo-Shin Chi, Sergey A. Merkulov, Lorenz J. Schwachhöfer, On the Existence of infinite series of exotic holonomies, Inventiones Mathematicae, Vol. 126, No. 2, 391 - 411 (1996) [pdf] [ps] [dvi]
  
  
  • Lorenz J. Schwachhöfer, On Homogeneous Connections with Exotic Holonomy, Geometriae Dedicata, Vol. 62, 193 - 208 (1996) [pdf] [ps] [dvi]
  
  
  • Lorenz J. Schwachhöfer, Connections with Exotic Holonomy, Transactions of the American Mathematical Society, Vol. 345, No. 1, 293 - 321 (1994) [pdf] [ps] [dvi]



• Contributions to refereed conference proceedings

  • Lorenz J. Schwachhöfer, Tight models of de-Rham algebras of highly connected manifolds, in: Differential Geometry in the Large, O. Dearricott, W. Tuschmann, Y. Nikolayevsky, T. Leistner, D. Crowley (Eds.), London Mathematical Society Lecture Note Series, Cambridge University Press (2020) [online version]
  
  
  • Kotaro Kawai, Hông Vân Lê, Lorenz J. Schwachhöfer, Frölicher-Nijenhuis bracket on manifolds with special holonomy, in: Lectures and Surveys on G2-Manifolds and Related Topics, S. Karigiannis, N. Leung, J. Lotay (Eds.), Fields Institute Communications, 201-215, (2020) [online version]
  
  
  • Jürgen Jost, Hông Vân Lê, Lorenz J. Schwachhöfer, The Cramér-Rao inequality on singular statistical models in: Geometric science of information, Lecture Notes in Comput. Sci., (Springer) vol. 10589, 554-560 (2017), [online version]
  
  
  • Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz J. Schwachhöfer, Invariant geometric structures on statistical models in: Geometric science of information, Lecture Notes in Comput. Sci., (Springer) vol. 9389, 150-158 (2015), [online version]
  
  
  • Lorenz J. Schwachhöfer, Holonomy groups and algebras, in: Global differential geometry, Springer Proc. Math., 17, 3-37 (2012) [pdf] [ps]
  
  
  • Lorenz J. Schwachhöfer, Nonnegative curvature on disk bundles, Proceedings of the Conference ``Variational Problems in Differential Geometry'', 127-141 London Math. Soc. Lecture Note Ser., 394, 127-141 (2012) [online version]
  
  
  • Martin Panak, Lorenz J. Schwachhöfer, Bochner-Kähler metrics and connections of Ricci type, Proceedings of the 10th International Conference on Differential Geometry and Its Applications 2007, Differential geometry and its applications, 339-352 (2008) [online version]
  
  
  • Michel Cahen, Simone Gutt, Lorenz J. Schwachhöfer, Construction of Ricci-type connections by reduction and induction, in: "The Breadth of Symplectic and Poisson Geometry", Festschrift in Honour of Alan Weinstein, Birkhäuser Verlag, p. 41 - 58 (2004) [online version]
  
  
  • Lorenz J. Schwachhöfer, Special connections on symplectic manifolds, Proceedings of the 24th Winter School ``Geometry and Physics'', January 2004, Srní, Czech Republic, in: Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II, Nr. 75, 197 - 223 (2005) [pdf] [ps] [dvi]
  
  
  • Lorenz J. Schwachhöfer, Lower Curvature Bounds and Cohomogeneity One Manifolds, Proceedings of the "8th International Conference on Differential Geometry and its Applications", Silesian University, Opava, Czech Republic, August 2001, in: Differential Geometry and its Applications, Vol. 17, 209 - 228 (2002) [pdf] [ps] [dvi]
  
  
  • Lorenz J. Schwachhöfer, Symplectic connections via integration of Poisson structures, Proceedings of the "Rencontres Mathématiques de Glanon" (2002) [pdf] [ps]
  
  
  • Lorenz J. Schwachhöfer, Irreducible holonomy groups, Proceedings of the 20th Winter School ``Geometry and Physics'', January 2000, Srní, Czech Republic, in: Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II, Nr. 66, 59 - 81 (2001) [pdf] [ps] [dvi]
  
  
  • Sergey A. Merkulov, Lorenz J. Schwachhöfer, Twistor solution of the holonomy problem, pp. 395 - 402, The Geometric Universe, Science, Geometry and the work of Roger Penrose, S.A. Hugget (ed.), Oxford University Press (1998) [pdf] [ps] [dvi]
  
  
  • Lorenz J. Schwachhöfer, On the classification of holonomy groups, Proceedings of the "Third Arbeitstagung of the Second Series" (1997), Max-Planck-Institut für Mathematik, Bonn [pdf] [ps] [dvi]



• Preprints

  • Lorenz J. Schwachhöfer, On the Ricci curvature of normal metrics on Biquotients, arXiv:math.DG/0702612
  
  
  • Lorenz J. Schwachhöfer, Holonomy, [pdf] [ps] [dvi]
  
  
  • Lorenz J. Schwachhöfer, Wilderich Tuschmann, Almost nonnegative curvature and cohomogeneity one, Preprint 62, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig
  
  
  • Lorenz J. Schwachhöfer, Homogeneous connections with special symplectic holonomy, Preprint 783, Erwin-Schrödinger-Institut, Vienna
  
  

• Monographs

  • Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz J. Schwachhöfer, Information Geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (Springer, 2017)



• Theses

  • Habilitationsschrift: On the classification of holonomy representations (1998, Universität Leipzig) [pdf] [ps] [dvi]
  
  
  • Ph.D. thesis: Connections with exotic holonomy (1992, University of Pennsylvania, Philadelphia) [pdf] [ps] [dvi]