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Dr. Markus Upmeier


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Akad. Rat a. Z.

E-Mail: markus.upmeier@math.uni-augsburg.de
Telefon: +49 821 598 - 2228
Fax: +49 821 598 - 2241
Raum: L1-3024
Hausanschrift: Universitätsstrasse 14
86159 Augsburg


Research Interests

  • (Generalized) differential cohomology, Deligne cohomology
  • Higher algebraic structures in differential geometry using (higher) category theory
  • Almost Kähler and Complex Geometry

Publications

  • The Canonical 2-Gerbe of a Complex Manifold, arXiv:1601:04819, 2016.
  • Extremal K-contact metrics (joint with Mehdi Lejmi), arXiv:1410.1370, Mathematische Zeitschrift, December 2015, Volume 281, Issue 3, pp 673-687.
  • Refinements of the Chern-Dold Character: Cocycle Additions in Differential Cohomology, arXiv:1404:2027, Journal of Homotopy and Related Structures, pp 1-17, 2015.
  • Products in Generalized Differential Cohomology, arXiv:1112.4173v2, Algebraic & Geometric Topology 15-1 (2015), 65--83.
  • Algebraic Structure and Integration in Generalized Differential Cohomology, PhD Thesis, University of Göttingen, PDF, 2013.
  • A Bicategory Approach to Differential Cohomology, arXiv:1211.6832, 2012.
  • Miraculous Cancellation Formulas for twisted indices of Dirac Operators, Diploma Thesis, University of Göttingen, PDF, 2010.

Notes and Slides from Talks

  • Differential Geometry Seminar ULB, Introduction to Generalized Differential Cohomology, 11.02.2014, Notes
  • Differential Geometry Seminar ULB, Introduction to Ordinary Differential Cohomology, Notes
  • Differential Geometry Seminar ULB, Expository talk on Generalized Cohomology Theory, Notes
  • Seminar Mathematical Physics, Marburg, Differential Cohomology and Gauge Theory, Notes
  • Meeting of the Graduiertenkollegs GK1463 (Hannover), GK1493 (Göttingen), and GK1670 (Hamburg). Differential Cohomology and Gauge Theory, Notes
  • YTM2012, Copenhagen, Products in Generalized Differential Cohomology, Slides
  • Tutzing, Seminar Optimal Transportation, Variations of Kantorovich-duality, first applications to optimal transportation, Notes
  • RTG 1493 Meeting, Goßlar. Generalized Differential Cohomology, Slides

Lehre / Teaching