Contact Publications Talks & Slides Teaching




About

I am a postdoctoral researcher at the Mathematical Institute of the University of Oxford and Stipendiary Lecturer at St Anne's College. Previously, I was visiting assistant professor (Akad. Rat a.Z.) at the University of Augsburg. I have recently been awarded a Heisenberg Fellowship which I plan to hold at the University of Freiburg.

My research is supported by the DFG priority programme Geometry at Infinity where I lead the project Gerbes in Renormalization and Quantization. I am a member of the Simons Collaboration on Special Holonomy in Geometry, Analysis, and Physics.

I am the organizer of the Oxford Geometry and Analysis Seminar.

I am interested in applications of algebraic topology to infinite-dimensional spaces and moduli spaces in low-dimensional topology and algebraic geometry. This includes investigating string theory implications for the geometry of Calabi-Yau, G2, and Spin(7)-manifolds and quantizing gauge theory invariants.

I received my Ph.D. in September 2013 from the University of Göttingen, advised by Thomas Schick. My current CV is here.

Contact

Email: upmeier [at] maths [dot] ox [dot] ac [dot] uk   Mail:  The Mathematical Institute
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road, OX2 6GG Oxford
Phone: +44 (0) 1865 615187

Publications

Preprints

  1. Homological Lie brackets on moduli spaces and pushforward operations in twisted K-theory, arXiV:2101.10990, 2021.
  2. Vertex F-algebra structures on the complex oriented homology of H-spaces (with J. Gross), preprint, 2021.
  3. Canonical orientations for moduli spaces of G2-instantons with gauge group SU(m) or U(m) (with D. Joyce), arXiv:1811.02405, 2018.

Journal Publications

  1. Orientation data for moduli spaces of coherent sheaves over Calabi-Yau 3-folds (with D. Joyce),
    Advances in Mathematics (accepted), arXiv:2001.00113, 2020.
  2. On spin structures and orientations for gauge-theoretic moduli spaces (with D. Joyce),
    Advances in Mathematics (accepted), arXiv:1908.03524, 2019.
  3. A categorified excision principle for elliptic symbol families,
    Quarterly Journal of Mathematics, doi.org/10.1093/qmath/haaa063, 2021.
  4. On orientations for gauge-theoretic moduli spaces (with D. Joyce and Y. Tanaka),
    Advances in Mathematics, Vol. 362, 4 March 2020.
  5. Connections on central extensions, lifting gerbes, and finite-dimensional obstruction vanishing (with I. Biswas), Proceedings Geometry at the Frontier (accepted), arXiv:1910.10402, 2019.
  6. Closed almost-Kähler 4-manifolds of constant non-negative Hermitian holomorphic sectional curvature are Kähler (with M. Lejmi), Tohoku Math. J., Vol. 72, No. 4, December, 2020.
  7. Integrability theorems and conformally constant Chern scalar curvature metrics in almost Hermitian geometry (with M. Lejmi), Communications in Analysis and Geometry, Vol. 28, pp. 1603-1645, 2020.
  8. Chern's contribution to the Hopf problem: An exposition based on Bryant's paper (with A. Tralle),
    Differential Geom. Appl., 2017.
  9. The canonical 2-gerbe of a holomorphic vector bundle, Theory Appl. Categ. 32, pp. 1028-1049, 2017.
  10. Refinements of the Chern-Dold character: cocycle additions in differential cohomology,
    J. Homotopy Relat. Struct., volume 11, no. 2, pp. 291-307, 2016.
  11. Extremal K-contact metrics (with M. Lejmi), Mathematische Zeitschrift, volume 281, no. 3, pp. 673-687, 2015.
  12. Algebraic structure and integration maps in cocycle models for differential cohomology,
    Algebraic & Geometric Topology, volume 15, no. 1, pp. 65-83, 2015.

Other Publications

  • PhD thesis, Algebraic Structure and Integration in Generalized Differential Cohomology, Open Access Link.
  • Diploma thesis, A Generalized Miraculous Cancellation Formula for Indices of Dirac Operators, PDF.
  • M. Upmeier, A Bicategory Approach to Differential Cohomology, arXiv:1211.6832, 2012.

Recent Talks and Slides

  • Instanton moduli spaces in gauge theory and their differential topology, Bath Algebra, Geometry and Number Theory Seminar, November 10, 2020.
  • Spin structures and orientation data for CY3, Abstract, CUNY Graduate Center, Geometric Analysis Seminar, New York, September 12, 2019.
  • Orientation problems for PDEs and instanton moduli spaces, Abstract, Oberseminar Differentialgeometrie, Universität Freiburg, July 8, 2019. Slides
  • Orientation problems for PDEs and instanton moduli spaces, Abstract, Seminar Geometry und Topology, Universität Stuttgart, July 2, 2019. Slides
  • Orientation problems and gauge theory, SPP Conference "Geometry at Infinity", Münster, April 3, 2019. Slides
  • Orientation problems in 7-dimensional gauge theory, Geometry and Analysis Seminar, Mathematical Institute, University of Oxford, January 28, 2019. Slides
  • Canonical Orientations for the Moduli Space of G2-instantons, Centre for Quantum Geometry of Moduli Spaces, Nielsen Retreat, October 23, 2018. Slides
  • Orientations for Moduli Spaces in Higher-Dimensional Gauge Theory, talk at the CUNY Graduate Center, New York, September 13, 2018. Slides
  • Canonical Orientations for the Moduli Space of G2-instantons, Simons Collaboration Meeting "Special Holonomy: Progress and Open Problems 2018", Stony Brook, September 11, 2018. Handout
  • Orientations for Moduli Spaces in Higher-Dimensional Gauge Theory, Conference "Analytic and Algebraic Geometry" at ICTS Bangalore, March 2018. Handout, Video
  • Almost Kähler 4-manifolds of Constant Holomorphic Sectional Curvature are Kähler, Workshop "Informal Geometry" in Valle d'Aosta, January 2018. Slides
  • Almost Kähler 4-manifolds of Constant Holomorphic Sectional Curvature are Kähler , Conference "Constant Scalar Curvature Metrics in Kähler and Sasaki Geometry", CIRM Marseille, January 18, 2018. Slides
  • Gerbes in renormalization and quantization of infinite-dimensional moduli spaces, Kickoff Meeting of the DFG priority programme "Geometry at Infinity", November 9, 2017.
  • Almost Kähler 4-manifolds of Constant Holomorphic Sectional Curvature are Kähler, Geometry and Analysis Seminar, Mathematical Institute, University of Oxford, October 30, 2017.
  • Almost Kähler 4-manifolds of Constant Holomorphic Sectional Curvature are Kähler, Oberwolfach workshop "Analysis, Geometry and Topology of Positive Scalar Curvature Metrics", August 9, 2017. OWR Report (p. 2258)
  • Chern's Contribution to the Hopf Problem, Workshop "Hopf 2017" in Marburg, March 29, 2017. Handout

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Current Teaching

Semester Course Institution
Trinity 2021 Index Theory of Elliptic Operators TCC Graduate Course Center
Trinity 2021 Group Theory St Anne's College, Oxford
Hilary 2021 Groups and Group Actions St Anne's College, Oxford
Hilary 2021 Integration St Anne's College, Oxford
Hilary 2021 Linear Algebra II St Anne's College, Oxford
Michaelmas 2020 Linear Algebra I St Anne's College, Oxford
Michaelmas 2020 Metric Spaces and Complex Analysis St Anne's College, Oxford
Additional Files: Branches and branch cuts
corresponding Mathematica notebook
Trinity 2020 Geometry of Surfaces
(Video Solutions)
Mathematical Institute, Oxford
Additional Files: Dreibein animation
corresponding Mathematica notebook
Trinity 2020 Number Theory St Peter's College, Oxford
Trinity 2020 Analysis III St Peter's College, Oxford
Hilary 2020 Analysis II St Peter's College, Oxford
Additional Files: Uniform versus non-uniform convergence
corresponding Mathematica notebook

Non-differentiability
corresponding Mathematica notebook
Michaelmas 2019/20 Geometry of Surfaces Mathematical Institute, Oxford
Additional Files: Gauss map animation
corresponding Mathematica notebook
Michaelmas 2019/20 Differential Equations I Keble College, Oxford
Additional Files: Picard iteration example 1
corresponding Mathematica notebook

Picard iteration example 2

Method of characteristics animation
corresponding Mathematica notebook
Michaelmas 2019/20 Linear Algebra I Keble College, Oxford