
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 infinitedimensional spaces and moduli spaces in lowdimensional topology and algebraic geometry. This includes investigating string theory implications
for the geometry of CalabiYau, 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.

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

Homological Lie brackets on moduli spaces and pushforward operations in twisted Ktheory, arXiV:2101.10990, 2021.

Vertex Falgebra structures on the complex oriented homology of Hspaces (with J. Gross), preprint, 2021.

Canonical orientations for moduli spaces of G2instantons with gauge group SU(m) or U(m) (with D. Joyce),
arXiv:1811.02405, 2018.
Journal Publications

Orientation data for moduli spaces of coherent sheaves over CalabiYau 3folds (with D. Joyce),
Advances in Mathematics (accepted), arXiv:2001.00113, 2020.

On spin structures and orientations for gaugetheoretic moduli spaces (with D. Joyce),
Advances in Mathematics (accepted),
arXiv:1908.03524, 2019.

A categorified excision principle for elliptic symbol families,
Quarterly Journal of Mathematics,
doi.org/10.1093/qmath/haaa063, 2021.

On orientations for gaugetheoretic moduli spaces (with D. Joyce and Y. Tanaka),
Advances in Mathematics, Vol. 362, 4 March 2020.

Connections on central extensions, lifting gerbes, and finitedimensional obstruction vanishing (with I. Biswas),
Proceedings Geometry at the Frontier (accepted),
arXiv:1910.10402, 2019.

Closed almostKähler 4manifolds of constant nonnegative Hermitian holomorphic sectional curvature are Kähler (with M. Lejmi),
Tohoku Math. J., Vol. 72, No. 4, December, 2020.

Integrability theorems and conformally constant Chern scalar curvature metrics in almost Hermitian geometry (with M. Lejmi),
Communications in Analysis and Geometry, Vol. 28, pp. 16031645, 2020.

Chern's contribution to the Hopf problem: An exposition based on Bryant's paper (with A. Tralle),
Differential Geom. Appl., 2017.

The canonical 2gerbe of a holomorphic vector bundle, Theory Appl. Categ. 32, pp. 10281049, 2017.

Refinements of the ChernDold character: cocycle additions in differential cohomology,
J. Homotopy Relat. Struct., volume 11, no. 2, pp. 291307, 2016.

Extremal Kcontact metrics (with M. Lejmi), Mathematische Zeitschrift, volume 281, no. 3, pp. 673687, 2015.

Algebraic structure and integration maps in cocycle models for differential cohomology,
Algebraic & Geometric Topology, volume 15, no. 1, pp. 6583, 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 7dimensional gauge theory,
Geometry and Analysis Seminar, Mathematical Institute, University of Oxford,
January 28, 2019. Slides

Canonical Orientations for the Moduli Space of G2instantons,
Centre for Quantum Geometry of Moduli Spaces, Nielsen Retreat,
October 23, 2018. Slides

Orientations for Moduli Spaces in HigherDimensional Gauge Theory,
talk at the CUNY Graduate Center, New York, September 13, 2018.
Slides

Canonical Orientations for the Moduli Space of G2instantons,
Simons Collaboration Meeting
"Special Holonomy: Progress and Open Problems 2018", Stony Brook,
September 11, 2018. Handout

Orientations for Moduli Spaces in HigherDimensional Gauge Theory,
Conference "Analytic and Algebraic Geometry" at ICTS Bangalore, March 2018.
Handout, Video

Almost Kähler 4manifolds of Constant Holomorphic
Sectional Curvature are Kähler,
Workshop "Informal Geometry" in Valle d'Aosta, January 2018.
Slides

Almost Kähler 4manifolds 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 infinitedimensional moduli spaces,
Kickoff Meeting of the DFG priority programme "Geometry at Infinity",
November 9, 2017.

Almost Kähler 4manifolds of Constant Holomorphic
Sectional Curvature are Kähler,
Geometry and Analysis Seminar, Mathematical Institute, University of Oxford, October 30, 2017.

Almost Kähler 4manifolds 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
Click to Expand

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 nonuniform convergence
corresponding Mathematica notebook
Nondifferentiability
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 

