Severin Barmeier

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.

Short biography

• 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.

In progress

• 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

Preprints

1. Partially wrapped Fukaya categories of orbifold surfaces, with S. Schroll, Z. Wang [arXiv]

2. A∞ deformations of extended Khovanov arc algebras and Stroppel's Conjecture, with Z. Wang [arXiv]

3. Towards a categorification of scattering amplitudes, with P. Oak, A. Pal, K. Ray, H. Treffinger [arXiv]

Publications

4. Deformations of path algebras of quivers with relations, with Z. Wang, forthcoming in Astérisque [arXiv]

5. Hochschild cohomology and deformation theory via reduction systems, Oberwolfach Rep. 21, 1117–1120 (2024) [doi]

6. Deformations of categories of coherent sheaves via quivers with relations, with Z. Wang, Algebr. Geom. 11 (1), 1–36 (2024) [doi] [arXiv]

7. Strict quantization of polynomial Poisson structures, with P. Schmitt, Comm. Math. Phys. 398 (3), 1085–1127 (2023) [doi] [arXiv]

8. Learning scattering amplitudes by heart, with K. Ray, Phys. Lett. B 820, 136594 (2021) [doi] [arXiv]

PhD project

9. Quantizations of local surfaces and rebel instantons, with E. Gasparim, J. Noncommut. Geom. 16 (1), 311–351 (2022) [doi] [arXiv]

10. Deformation–obstruction theory for diagrams of algebras and applications to geometry, with Y. Frégier, J. Noncommut. Geom. 14 (3), 1019–1047 (2020) [doi] [arXiv]

11. Classical deformations of noncompact surfaces and their moduli of instantons, with E. Gasparim, J. Pure Appl. Algebra 223 (6), 2543–2561 (2019) [doi] [arXiv]

12. 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

13. Deformations of the discrete Heisenberg group, Proc. Japan Acad. Ser. A Math. Sci. 89 (4), 55–59 (2013) [doi] [arXiv]

Graduate research

14. 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]

Theses

• 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)

• 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)

Conferences, workshops and research schools

• 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

Research seminars

• 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)

Upcoming

• [13 Dec 2024] From Fukaya categories of orbifold surfaces to representation theory of associative algebras
  Seminar Geometric Methods in Mathematics, TU Dresden

• [13 Jan 2025] Paris Algebra Seminar, Institut de Mathématiques de Jussieu – Paris Rive Gauche

2024

• 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

2023

• 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

2022

• 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

2021

• 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

2020

• 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

2019

• 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

Supervision

• Anahita Pouralijanki (Master's, ongoing)

• Simon Rottmann (Master's 2024)
  Deformation theory and classification of 4-dimensional algebras

Courses

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

Author profiles

• arXiv

• MathSciNet

• zbMATH

• ORCİD

• ResearchGate

Email

s.barmeier ⟨æт⟩ gmail.com

Address

Mathematical Institute
University of Cologne
Weyertal 86-90
50931 Köln
Germany