Sven Möller

Emmy-Noether Junior Research Group Leader
Bereich Algebra und Zahlentheorie
Fachbereich Mathematik
Universität Hamburg, Germany

Visiting Professor
Arbeitsgruppe Algebra
Fachbereich Mathematik
Technische Universität Darmstadt, Germany

Contact Information

Universität Hamburg:
business Geomatikum, Room 314 (directionsopen_in_new, mapopen_in_new)
alternate_email math@moeller-sv...
alternate_email sven.moeller@uni-ha... (for internal use)
lock public PGP key (encrypted mails are welcome)
link Link to this webpage: www.moeller-sven.de
phone+49 40 42838 5183
mail Mailing address

Technische Universität Darmstadt:
business S2|15 310 (directionsopen_in_new, mapopen_in_new)
alternate_email math@moeller-sv...
alternate_email smoeller@mathematik.tu-da... (for internal use)
lock public PGP key (encrypted mails are welcome)
link Link to this webpage: www.moeller-sven.de
phone+49 6151 16 22148
mail Mailing address

Research Projects and News

I am broadly interested in representation theory, number theory, algebraic geometry and mathematical physics. In particular, I study vertex algebras, conformal field theory, automorphic forms, infinite-dimensional Lie algebras and their connections. Here is a popular science summary of some of my recent work.

Together with Claudia Alfes I organised a workshop on Modular Forms and Representation Theory in 2022.

Funded research projects:

• Principal investigator: SFB 1624 Higher Structures, Moduli Spaces and Integrability
• Principal investigator: Emmy Noether Programme Vertex Algebras Associated with 2- and 4-dimensional Conformal Field Theories
• Key researcher: cluster of excellence Quantum Universe

Research Group

Ph.D. students:

• Hannes Knötzele

Curriculum Vitæ

Academic CV file_downloadPDF
(last updated: Mar. 2023)

Selected Publications

1. Hilbert Schemes of Points in the Plane and Quasi-Lisse Vertex Algebras with N=4 Symmetry.
   Submitted, 2023. (arXiv:2309.17308 [math.RT]).
   With Tomoyuki Arakawa and Toshiro Kuwabara.
   (Video of talk by meopen_in_new)
2. Dimension Formulae and Generalised Deep Holes of the Leech Lattice Vertex Operator Algebra.
   Ann. of Math., 197(1):221–288, 2023. (arXiv:1910.04947 [math.QA]).
   With Nils R. Scheithauer.
   (Video of talk by Nils R. Scheithaueropen_in_new, popular science summaryopen_in_new)
   [Typo: entry 45 in Table 2 should read “A_5,1 E_7,3”.]
3. Construction and Classification of Holomorphic Vertex Operator Algebras.
   J. Reine Angew. Math. (Crelle's Journal), 759:61–99, 2020. (arXiv:1507.08142 [math.RT]).
   With Jethro van Ekeren and Nils R. Scheithauer.
   (Videos of talks by Jethro van Ekerenopen_in_new and Nils R. Scheithaueropen_in_new)

All Publications

My publications on Google Scholar open_in_new, the arXiv open_in_new (incomplete: zbMath open_in_new, MathSciNet open_in_new)

1. Computing G-Crossed Extensions and Orbifolds of Vertex Operator Algebras.
   Submitted, 2024. (arXiv:2409.16357 [math.QA])
   With César Galindo and Simon Lentner.
2. Equivalence Relations on Vertex Operator Algebras, I: Genus.
   Submitted, 2024. (arXiv:2408.07117 [hep-th]).
   With Brandon C. Rayhaun.
3. Hilbert Schemes of Points in the Plane and Quasi-Lisse Vertex Algebras with N=4 Symmetry.
   Submitted, 2023. (arXiv:2309.17308 [math.RT]).
   With Tomoyuki Arakawa and Toshiro Kuwabara.
   (Video of talk by meopen_in_new)
4. Classification of Self-Dual Vertex Operator Superalgebras of Central Charge at Most 24.
   Submitted, 2023. (arXiv:2303.17190 [math.QA]).
   With Gerald Höhn.
   (Video of talk by Gerald Höhn and meopen_in_new)
5. A Geometric Classification of the Holomorphic Vertex Operator Algebras of Central Charge 24.
   Algebra Number Theory, 18(10):1891–1922, 2024. (arXiv:2112.12291 [math.QA]).
   With Nils R. Scheithauer.
6. Systematic Orbifold Constructions of Schellekens' Vertex Operator Algebras from Niemeier Lattices.
   J. Lond. Math. Soc., 106(4):3162–3207, 2022. (arXiv:2010.00849 [math.QA]).
   With Gerald Höhn.
   [Typo: genus I in Table 1 should read, e.g., “II_6,0(2₁⁺¹ 4₅^-1 8_II⁺⁴)”.]
7. Schellekens' List and the Very Strange Formula.
   Adv. Math., 380:107567, 2021. (arXiv:2005.12248 [math.QA]).
   With Jethro van Ekeren, Ching Hung Lam and Hiroki Shimakura.
   (Video of talk by Jethro van Ekerenopen_in_new)
8. Dimension Formulae and Generalised Deep Holes of the Leech Lattice Vertex Operator Algebra.
   Ann. of Math., 197(1):221–288, 2023. (arXiv:1910.04947 [math.QA]).
   With Nils R. Scheithauer.
   (Video of talk by Nils R. Scheithaueropen_in_new, popular science summaryopen_in_new)
   [Typo: entry 45 in Table 2 should read “A_5,1 E_7,3”.]
9. Natural Construction of Ten Borcherds-Kac-Moody Algebras Associated with Elements in M₂₃.
   Comm. Math. Phys., 383(1):35–70, 2021. (arXiv:1905.09629 [math.QA]).
   [Typo: in Remark 3.11 (2), the first factor of the codomain of χ should be overlined.]
10. Orbifold Vertex Operator Algebras and the Positivity Condition.
    In: Research on Algebraic Combinatorics and Representation Theory of Finite Groups and Vertex Operator Algebras.
    RIMS Kôkyûroku, (2086):163–171, 2018. (arXiv:1803.03702 [math.QA]).
11. Dimension Formulae in Genus Zero and Uniqueness of Vertex Operator Algebras.
    Int. Math. Res. Not., 2020(7):2145–2204, 2020. (arXiv:1704.00478 [math.QA]).
    With Jethro van Ekeren and Nils R. Scheithauer.
    [Typo: erroneous minus sign in the exponential of equation (7).]
12. A Cyclic Orbifold Theory for Holomorphic Vertex Operator Algebras and Applications.
    Ph.D. thesis, Technische Universität Darmstadt, 2016. (arXiv:1611.09843 [math.QA]).
    [Typo: in the third displayed formula after Proposition 7.2.1 both b_n+1 should be b₁, and analogously in the inline formula that follows.]
13. Construction and Classification of Holomorphic Vertex Operator Algebras.
    J. Reine Angew. Math. (Crelle's Journal), 759:61–99, 2020. (arXiv:1507.08142 [math.RT]).
    With Jethro van Ekeren and Nils R. Scheithauer.
    (Videos of talks by Jethro van Ekerenopen_in_new and Nils R. Scheithaueropen_in_new)

Mailing Address

Sven Möller
Bereich Algebra und Zahlentheorie
Fachbereich Mathematik
Universität Hamburg
Bundesstraße 55
20146 Hamburg
Germany

Sven Möller
Arbeitsgruppe Algebra
Fachbereich Mathematik
Technische Universität Darmstadt
Schloßgartenstraße 7
64289 Darmstadt
Germany