November Our monograph Deformations of path algebras of quivers with relations will be published as a single volume by Astérisque
July We just posted a new paper on partially wrapped Fukaya categories of orbifold surfaces
April Under Notes & Miscellanea I uploaded my handwritten notes (147 pages) for D. Auroux's Fall 2016 Eilenberg Lectures on Fukaya categories and mirror symmetry
I am a postdoctoral fellow at MSRI/SLMath from January–May 2024 for the spring programme on Noncommutative Algebraic Geometry
My main research centres around noncommutative algebraic geometry, representation theory and mathematical physics. I am developing new techniques in the deformation theory of algebraic structures to describe and study
deformations of associative and A∞ algebras via reduction systems
deformations of Abelian or derived categories of coherent sheaves and noncommutative algebraic geometry
(strict) deformation quantization
noncommutative deformations of singularities and their singularity categories
geometry of noncommutative varieties
deformations of Fukaya categories and mirror symmetry
A∞ structures and deformations of graded algebras
noncommutative deformation theory (i.e. deformations over a noncommutative base).
Together with Zhengfang Wang I developed a combinatorial approach to the deformation theory of associative algebras (in this paper). Jointly with Daniel Labardini Fragoso I am developing a visual applet implementing this method to help with the combinatorics when studying particular examples: QUIVERed.
I am also working on a (for now) separate line of research concerning
categorical techniques in theoretical physics, in particular the categorification of scattering amplitudes.
I am currently a postdoc at the University of Cologne in the group of Sibylle Schroll.
born in Germany, 10 years of school education in Germany
one year of high school in the UK
MA(Hons) Philosophy & Mathematics (undergraduate) at the University of Edinburgh
one year of volunteer work ("Zivildienst") in Takasaki, Japan
MSc Mathematical Sciences at the University of Tokyo (with Toshiyuki Kobayashi)
PhD Mathematics (defended December 2018) from the University of Münster, Germany — my advisers were Elizabeth Gasparim and Lutz Hille
9-month postdoc at the MPIM in Bonn where my mentor was Catharina Stroppel
2-year postdoc at the University of Freiburg with Katrin Wendland
currently postdoc at the University of Cologne with Sibylle Schroll
My CV is available as PDF.
A∞ deformations of partially wrapped Fukaya categories of surfaces, with S. Schroll, Z. Wang
Deformation quantization and singularity categories, with M. Kalck, Z. Wang
A new structure sheaf on the spectrum of a module category, with A. Siqveland
Singular Hochschild cohomology of affine toric varieties, with M. Filip, Z. Wang
Partially wrapped Fukaya categories of orbifold surfaces, with S. Schroll, Z. Wang [arXiv]
A∞ deformations of extended Khovanov arc algebras and Stroppel's Conjecture, with Z. Wang [arXiv]
Towards a categorification of scattering amplitudes, with P. Oak, A. Pal, K. Ray, H. Treffinger [arXiv]
Deformations of path algebras of quivers with relations, with Z. Wang, forthcoming in Astérisque [arXiv]
Hochschild cohomology and deformation theory via reduction systems, Oberwolfach Rep. 21, 1117–1120 (2024) [doi]
Deformations of categories of coherent sheaves via quivers with relations, with Z. Wang, Algebr. Geom. 11 (1), 1–36 (2024) [doi] [arXiv]
Strict quantization of polynomial Poisson structures, with P. Schmitt, Comm. Math. Phys. 398 (3), 1085–1127 (2023) [doi] [arXiv]
Learning scattering amplitudes by heart, with K. Ray, Phys. Lett. B 820, 136594 (2021) [doi] [arXiv]
PhD project
Quantizations of local surfaces and rebel instantons, with E. Gasparim, J. Noncommut. Geom. 16 (1), 311–351 (2022) [doi] [arXiv]
Deformation–obstruction theory for diagrams of algebras and applications to geometry, with Y. Frégier, J. Noncommut. Geom. 14 (3), 1019–1047 (2020) [doi] [arXiv]
Classical deformations of noncompact surfaces and their moduli of instantons, with E. Gasparim, J. Pure Appl. Algebra 223 (6), 2543–2561 (2019) [doi] [arXiv]
A Lie theoretical construction of a Landau–Ginzburg model without projective mirrors, with E. Ballico, E. Gasparim, L. Grama, L. A. B. San Martin, Manuscripta Math. 158 (1–2), 85–101 (2019) [doi] [arXiv]
Master's project
Deformations of the discrete Heisenberg group, Proc. Japan Acad. Ser. A Math. Sci. 89 (4), 55–59 (2013) [doi] [arXiv]
Graduate research
Isomorphisms of moduli spaces, with C. C. Amilburu, B. Callander and E. Gasparim, in Proceedings Second Latin Congress on Symmetries in Geometry and Physics, Mat. Contemp. 41, 1–16 (2012) [doi] [arXiv]
Moduli of vector bundles on non-compact surfaces and their deformations, PhD thesis, University of Münster (2018)
Deformations of the discrete Heisenberg group, Master's thesis, University of Tokyo (2012)
Handwritten notes for D. Auroux's Eilenberg Lectures Fukaya categories and mirror symmetry (Columbia University, 2016)
Extended Khovanov arc algebras: Quivers, Hochschild cohomology and A∞ deformations
Informal Categorification Seminar, Columbia University
Minicourse Deformation theory via L∞ algebras
Higher Structures in Deformation Theory, University of Freiburg
Deformations of categories of coherent sheaves via quivers with relations
LAGOON Seminar
Minicourse Deformations of path algebras of quivers with relations (slides first, second, fourth talk)
New Trends in Representation Theory, Hausdorff Research Institute for Mathematics in Bonn)
Advances in Representation Theory of Algebras (ARTA X)
1–5 September 2025
University of Cologne
Cologne Representation Theory Day 2
1 October 2024
University of Cologne
Cologne Representation Theory Day
17 October 2023
University of Cologne
τ-Research School
5–8 September 2023
University of Cologne
Quivers, Representation Theory and Physics
7–9 September 2022
University of Cologne
Higher Structures in Deformation Theory
31 August – 2 September 2022
University of Freiburg
GEOQUANT 2021 — Geometry & Quantization
International school "Deformation quantization and convergence" and international conference (hybrid events)
2–13 August 2021
University of Freiburg
Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)
(since 2023)
Oberseminar Algebra und Geometrie
University of Münster (2017/2018)
Simetrias & Representações
State University of Campinas, Brazil (2013–2015)
A Weinstein sector of type D on an orbifold surface
(from Partially wrapped Fukaya categories of orbifold surfaces)
The extended Khovanov arc algebra K₂²
(from A∞ deformations of extended Khovanov arc algebras and Stroppel's Conjecture)
A vanishing cycle and its two thimbles in a symplectic Lefschetz fibration with two critical points (from my PhD thesis)
14 intermediate t-structures on the derived category of the A₃ quiver 1 → 2 → 3 and their hearts (shaded) and projective objects (circled)
(from Learning scattering amplitudes by heart)
Fukaya categories of orbifold surfaces from deformation theory
Geometry and Topology Seminar, Uppsala University
Associative algebras from Fukaya categories of orbifold surfaces
Geometric Models in Representation Theory and Beyond, NTNU Trondheim
Module varieties via one-sided Gröbner bases
Köln Algebra Seminar, University of Cologne
Deformations of gentle algebras and gluing of Fukaya categories of surfaces
Paris Algebra Seminar, Institut de Mathématiques de Jussieu – Paris Rive Gauche
From Fukaya categories of orbifold surfaces to representation theory of associative algebras
Seminar Geometric Methods in Mathematics, TU Dresden
Utility and usability of projective resolutions
The Mathematics of Post-Quantum Cryptography, Max Planck Institute for Mathematics, Bonn
Associative algebras from orbifold surfaces
New Developments in Representation Theory of Algebras, Okinawa Institute of Science and Technology, Japan
Associative algebras from Fukaya categories
Colloquium in Honour of Lutz Hille, Bielefeld University
Partially wrapped Fukaya categories of orbifold surfaces
Oberseminar Algebra und Algebraische Geometrie, Paderborn University
Deformation theory via reduction systems and applications
International Conference on Representation of Algebras (ICRA 21), Shanghai
Derived equivalences of associative algebras via Fukaya categories
BIREP Seminar, Bielefeld University
Hochschild cohomology and deformation theory via reduction systems
Hochschild (Co)Homology and Applications, Mathematisches Forschungsinstitut Oberwolfach
Combinatorial deformation quantization via the Koszul complex
Seminar Noncommutative Projective Schemes, MSRI/SLMath
Noncommutative geometry via quivers with relations
Introductory Workshop: Noncommutative Algebraic Geometry, MSRI/SLMath
A∞ deformations of extended Khovanov arc algebras
Seminar on Quantum groups, Hopf algebras and monoidal categories, UCLouvain
Introduction to representation and character varieties
Seminar Factorization Homology, University of Bonn
The Diamond Lemma
Seminar Operads, University of Bonn
Hochschild cohomology and A∞ deformations of extended Khovanov arc algebras
Algebras and Representation Theory in Germany (ARTIG 2), University of Stuttgart
Koszul duality for operads
Seminar Operads, University of Bonn
A categorical perspective on scattering amplitudes
Oberseminar Algebra, Zahlentheorie und algebraische Geometrie, University of Freiburg
A∞ deformations of extended Khovanov arc algebras and Stroppel's Conjecture
Algebraic Geometry Seminar, University of Luxembourg
From cluster categories to scattering amplitudes
Algebra Group Seminar, University of Cologne
Extended Khovanov arc algebras: Quivers, Hochschild cohomology and A∞ deformations (video first talk, second talk by Zhengfang Wang)
Informal Categorification Seminar, Columbia University
A∞ deformations of extended Khovanov arc algebras and Stroppel’s Conjecture
FD Seminar
Strict deformation quantization of polynomial Poisson structures
Seminar semiklassische Analysis und Darstellungstheorie, University of Cologne
Deformations of path algebras of quivers with relations
Oberseminar Geometry, Algebra and Topology, University of Münster
The Bardzell–Chouhy–Solotar resolution
Algebra Group Seminar, University of Cologne
Deformations and spectra in noncommutative algebraic geometry
Spectral Methods in Algebra, Geometry and Topology, Hausdorff Research Institute for Mathematics, Bonn
From formal to actual deformations of associative algebras I, II
Algebra Group Seminar, University of Cologne
Minicourse Deformation theory via L∞ algebras (videos)
Higher Structures in Deformation Theory, University of Freiburg
Varieties of reduction systems and PBW deformations
Aachen–Bochum–Cologne Darstellungstheorie Seminar, RWTH Aachen University
Introduction to deformation theory
Algebra Group Seminar, University of Cologne
Deformations of categories of coherent sheaves via quivers with relations (video)
Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)
Combinatorial deformations of associative algebras and applications to geometry
Forschungsseminar Algebra/Algebraische Geometrie, Freie Universität Berlin
A combinatorial approach to deformation quantization
Séminaire de Mathématiques, Université Haute-Alsace, Mulhouse
Deformations of diagrams of algebras and applications to geometry
Deformation Theory Seminar, University of Pennsylvania
Strict deformation quantizations of polynomial Poisson structures
Deformation Quantization Seminar, University of Würzburg
Chern classes of tautological bundles and Nakajima operators
Seminar Heisenberg algebras and Hilbert schemes of points on surfaces, University of Freiburg
Hilbert schemes of points on surfaces: the moduli problem
Seminar Heisenberg algebras and Hilbert schemes of points on surfaces, University of Freiburg
From quiver representations to scattering amplitudes and back
Oberseminar Differentialgeometrie, University of Freiburg
Scattering amplitudes from derived categories and cluster categories
Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)
Introduction to deformation theory
Basic Notions Seminar, University of Freiburg
Minicourse Deformations of path algebras of quivers with relations (videos 1, 2, 3, 4)
New Trends in Representation Theory, Hausdorff Research Institute for Mathematics, Bonn
Covariant quantization of strings
Seminar String theory, University of Freiburg
Perspectives on GIT
Seminar Higgs bundles, University of Freiburg
Introduction to homological mirror symmetry
Basic Notions Seminar, University of Freiburg
Deformations of path algebras of quivers with relations
Oberseminar Algebra und Zahlentheorie, University of Freiburg
The derived category of projective space
Seminar Derived categories, University of Freiburg
Deformations of path algebras of quivers with relations from a geometric perspective
Oberseminar Differentialgeometrie, University of Freiburg
Poisson manifolds, star products and deformation quantization after Kontsevich
Valeurs zêta multiples en quantification par déformation, Institut Montpelliérain A. Grothendieck, Montpellier
Minicourse An introduction to algebraic deformation theories
Working Group in Deformation Theory, ICPT, Trieste
Deformations of Abelian categories in algebra, geometry & physics
Algebra, Geometry & Physics Seminar, Max Planck Institute for Mathematics, Bonn
L∞ algebras for deformations of Abelian categories and applications to geometry
Higher Differential Geometry Seminar, Max Planck Institute for Mathematics, Bonn
Deformations of Abelian categories and applications to geometry
Oberseminar Geometrie und Topologie, University of Mainz
Local holomorphic Euler characteristic and instanton charge
Oberseminar Algebra, Geometry & Topology, University of Münster
Brauer groups, Azumaya algebras and twisted sheaves
Seminar Derived categories of singular surfaces, University of Hannover
Categorical resolutions of singularities
Seminar Derived categories of singular surfaces, Free University of Berlin
L∞ algebra for deformations of categories of quasi-coherent sheaves
Interactions between commutative algebra, representation theory, and algebraic geometry — A conference in memoriam Ragnar-Olaf Buchweitz, University of Münster
Diagrams of algebras, categories of coherent sheaves and deformations
Bielefeld Representation Theory Seminar (BIREP), University of Bielefeld
Diagrams of algebras, categories of coherent sheaves and their deformation theory
Forschungsseminar Algebra/Algebraische Geometrie, Free University of Berlin
Anahita Pouralijanki (Master's, ongoing)
Simon Rottmann (Master's 2024)
Deformation theory and classification of 4-dimensional algebras
University of Cologne
Homological algebra I
Seminar "Introduction to homological algebra"
Representation theory of quivers
Algebra
Linear algebra II (main lecturer)
Linear algebra I
Seminar "Topics in representation theory: From matrix problems to quiver representations and back"
Hyperbolic geometry
Elementary differential geometry
University of Freiburg
Differential geometry II — The simple Lie algebras and singularities
Undergraduate seminar "Big theorems and beautiful proofs"
Seminar "Crystallographic groups"
Complex analysis
Undergraduate seminar "Representation theory of quivers"
Algebraic topology
State University of Campinas
Calculus 2
Calculus 1
s.barmeier ⟨æт⟩ gmail.com
Mathematical Institute
University of Cologne
Weyertal 86-90
50931 Köln
Germany