Dennis Eriksson
Professor in Mathematics
Algebraic geometry • Arakelov theory • Complex geometry • AI for mathematics
Department of Mathematical Sciences • Chalmers University of Technology and the University of Gothenburg • 412 58 Gothenburg, Sweden • dener [аt] chalmers.se • he/him/his • Please call me Dennis
- I think a lot about invariants in arithmetic and complex geometry.
- Lately: genus one mirror symmetry, BCOV invariants, hypersurface singularities, arithmetic analogues.
- Also curious about what AI can and cannot do in mathematics.
- I take master students.
Publications
Spectrum of singularities, analytic torsion and Calabi–Yau degenerations
The Deligne-Riemann-Roch isomorphism
Genus one mirror symmetry for intersection of two cubics in $\mathbb{P}^5$
Base change conductors through intersection theory and quotient singularities
The spectral genus of an isolated hypersurface singularity and its relation to the Milnor number and analytic torsion
Complex Chern–Simons bundles in the relative setting
Deligne-Riemann-Roch and intersection bundles
On genus one mirror symmetry in higher dimensions and the BCOV conjectures
Nonproper intersection products and generalized cycles
Spaces of norms, determinant of cohomology and Fekete points in non-Archimedean geometry
BCOV invariants of Calabi–Yau manifolds and degenerations of Hodge structures
Global representation of Segre numbers by Monge–Ampère products
Kähler quantisation of vortex moduli
Singularities of metrics on Hodge bundles and their topological invariants
Discriminants and Artin conductors
Erratum to: Discriminants and Artin conductors (J. Reine Angew. Math. 712 (2016), 107–121)
A logarithmic interpretation of Edixhoven's jumps for Jacobians
Degenerating Riemann surfaces and the Quillen metric
Un isomorphisme de type Deligne–Riemann–Roch
On the Brauer–Manin obstruction for zero-cycles on curves
Nothing in this category.
Postdocs
-
Yanbo Fang (Current, 2026–present)
PhD students
-
Tudor Sharpe (Current, 2026–present)
-
Gabriel Abánades Joglar (Current, 2025–present)
-
Anthony Mäkelä (Current, 2025–present, Co-supervisor)
-
Douglas Molin (Completed 2026, Co-supervisor)
Thesis Selmer group actions on $p$-adic automorphic cohomology
-
Mykola Pochekai (Completed 2024)
Thesis Hodge Theory in Combinatorics and Mirror Symmetry
-
Jiacheng Xia (Completed 2021, Co-supervisor)
Thesis Some Cases of Kudla’s Modularity Conjecture for Unitary Shimura Varieties
-
Manh Hung Tran (Completed 2020)
Thesis The density of rational points and invariants of genus one curves
Master students
-
Samuel Plumeyer (Current)
Thesistentative Tubular neighborhoods in geometry
-
Sebastian Jansson (Current)
Thesistentative Hurwitz numbers and modular forms
-
Liu Xudong (2024)
Thesis The geometry of bielliptic surfaces
-
Felix Frelot (2022)
Thesis The Torelli theorem
-
Robert Antonio Pop Gorea (2021)
Thesis Analogies between geometry and number theory
-
Magnus Fries (2020)
Thesis Mirror symmetry at genus one of elliptic curves
-
Mattias Lindby (2016)
Thesis Elliptic curves and their $L$-series: the role of complex multiplication
Bachelor students
-
Louis Dao·Anna Davoodi·Erik Samuelsson (2024, with Adam Keilthy)
Thesis How do we know that a computer program does what it says it does?
Teaching
This year2026–2027
- Quarter 2 Algebraic geometry MMA321 Lecture notes (PDF)preliminary version·Algebraic Geometry Workbench
- Quarter 3 Algebraic structures MMG500·MVE150
Courses
UndergraduateChalmers
Preparatory Calculus; Calculus for Civil Engineering; Multivariable Calculus.
Master levelChalmers, Hangzhou, Paris
Algebraic Geometry; reading courses in algebraic topology and homological algebra.
PhD levelGraduate school
$K$-theory (with M. Goffeng); $p$-adic methods (with A. Södergren, S. Herrero); reading courses in algebraic number theory, Arakelov theory, Hodge theory, derived geometry, and Gromov–Witten theory.
Recognition
Teaching Award, three timesChalmers
Prize for best teacher in the Civil Engineering programme. Nominated for the Chalmers pedagogical prize in 2020.
Examining
Bachelor Thesis ExaminerChalmers & University of Gothenburg
Examiner for bachelor theses in mathematics; approximately 80 students and 20 projects every year.
Pedagogical work
Ämnesstråkansvarig, mathematicsCivil Engineering programme, Chalmers
Responsible for the mathematics strand through the rebuild of the programme, in which all of its mathematics courses were redesigned.
Pedagogical Research PublicationPrimus 28 (2018), no. 8
Communicating to Learn Multivariable Calculus: Students' Blackboard Presentations as a Means for Enhancing Mathematics Learning. With Hans Malmström.
Innovation GrantChalmers
Approx. €70,000 for developing digital teaching tools. I applied for and led the project.
Pedagogical Studies in Higher Education (15 hp)Chalmers
Formal qualification in university-level teaching and learning, including student assessment, curriculum design, and learning theories.
Curriculum vitae
Open the CV as a PDF Last updated 9 October 2026
My research grows out of arithmetic geometry, where algebraic geometry, number theory, and complex analysis meet. This area combines tools from Grothendieck's algebraic geometry with ideas from complex differential geometry, and I use this interaction to study structural invariants of algebraic varieties. In recent years, these methods have naturally connected my work to mathematical aspects of mirror symmetry — a conjectural framework originating in string theory that continues to influence several areas of modern geometry — as well as to questions about singularities. Across these topics, my work studies how algebraic geometry, and in particular intersection theory, serves as a meeting point for arithmetic ideas, complex geometric methods, Hodge theory, singularities, and mirror symmetry.
About me
I am a Swedish mathematician with extensive international research experience, and a strong interest in collaboration, communication and education. Outside mathematics, I enjoy language learning and cultural travel.
Languages
- Swedish
- English
- French
- German
- Chinese
- Japanese
- Polish
Select Significant Publications
Deligne-Riemann-Roch and intersection bundles
On genus one mirror symmetry in higher dimensions and the BCOV conjectures
Complex Chern–Simons bundles in the relative setting
BCOV invariants of Calabi–Yau manifolds and degenerations of Hodge structures
Spaces of norms, determinant of cohomology and Fekete points in non-Archimedean geometry
Some Select Research Grants
Research in ParisInstitut Henri Poincaré
2 month invitation.
Vergstiftelsen Postdoc GrantPostdoc grant
Grant, approx. €200,000, to hire a postdoc for two years, in the project "The hunt for new invariants in the intersection of arithmetic and algebraic".
Vetenskapsrådet Research Project GrantPI
Approx. €350,000.
Vetenskapsrådet Postdoc GrantPI
Salary for two years.
G.S. Magnussons Grantmobility grant
Approx. €30,000.
Svensk-Franska stifelsenmobility grant
Approx. €6,000.
Knut och Alice Wallenberg FoundationVisiting Professor Grant
For Gerard Freixas i Montplet, one year visiting professor at Chalmers.
Research in ParisInstitut Henri Poincaré
Two-month funded visit.
Trimester Program OrganizerHIM Bonn
Group-leader: "$p$-adic methods in Arakelov geometry and Shimura varieties".
Positions
Professor (Gothenburg)Chalmers University of Technology
Department of Mathematical Sciences.
Associate Professor (Docent) (Gothenburg)Chalmers University of Technology
Department of Mathematical Sciences.
Assistant Professor (Gothenburg)Chalmers University of Technology
Visitor MPIMax Planck Institute for Mathematics, Bonn
January–April.
Junior Trimester Program (Organiser)Hausdorff Institute for Mathematics
Trimester: Algebraic geometry ($p$-adic methods in Arakelov geometry and Shimura varieties).
Postdoctoral ResearcherMax Planck Institute for Mathematics
January–December.
Postdoctoral ResearcherUniversity of Gothenburg
Teaching assistant 2011–2012.
Postdoctoral ResearcherUniversity of Tokyo
JSPS Research FellowUniversity of Tokyo
Education
PhD in MathematicsUniversité d'Orsay, Paris 11, Paris
Thesis: Formule de Lefschetz fonctorielle et applications géométriques, under the supervision of Damian Rössler.
Undergraduate and master studies in MathematicsUniversity of Gothenburg, Gothenburg + Paris 13, Paris
Thesis: Some more or less explicit class field theory. Under the supervision of Peter Hegarty.
Academic & Organizational Responsibilities
PhD Student Admissions CommitteeChalmers
Member of the PhD committee deciding future PhD students.
Programme Board MemberChalmers
Member of the "Programråd" for Samhällsbyggnadsteknik.
Group Leader (Junior Trimester Program)Hausdorff Institute for Mathematics
Organized and led the Junior Trimester Program: $p$-adic methods in Arakelov geometry and Shimura varieties.
High School Outreach CoordinatorGothenburg region
Contact person for high school research projects in mathematics.
Main Organizer / Co-Organizer (International Workshops)International workshops
N-cube (2015, 2016, 2018, 2025); Freixit 2024; Number theory and dynamical systems (2016); Algebraic Geometry (Bonn, 2018); Workshop: Arithmetic intersection theory and Shimura varieties (2014).
Thesis Committees & ExaminationParis and Gothenburg
Rapporteur and Member of jury for Andres Gomez (Aarhus 2026); Member of jury for Juan Felipe Castro Cárdenas (Paris 2026); Rapporteur for Dai Imaike (Kyoto 2024); Rapporteur and Member of jury for Dorian Ni (Paris 2022); Member of jury for Bertrand Duma (Paris 2012); Diskutant/Opponent at licentiate defense for Ida Säfström (Gothenburg 2010).
Professional Service and Journal RefereeingInternational Journals
Regular ad-hoc referee for journals including: Inventiones Mathematicae, IMRN, Algebra & Number Theory, Journal of Differential Geometry, JEMS, JHEP, JGP, Selecta Mathematica, and Pacific Journal of Mathematics. Also served as a referee for various international conference proceedings.
Teaching and Pedagogical Qualifications
UndergraduateChalmers
Preparatory Calculus; Calculus for Civil Engineering; Multivariable Calculus.
Master levelChalmers, Hangzhou, Paris
Algebraic Geometry; reading courses in algebraic topology and homological algebra.
PhD levelGraduate school
$K$-theory (with M. Goffeng); $p$-adic methods (with A. Södergren, S. Herrero); reading courses in algebraic number theory, Arakelov theory, Hodge theory, derived geometry, and Gromov–Witten theory.
Teaching Award, three timesChalmers
Prize for best teacher in the Civil Engineering programme. Nominated for the Chalmers pedagogical prize in 2020.
Bachelor Thesis ExaminerChalmers & University of Gothenburg
Examiner for bachelor theses in mathematics; approximately 80 students and 20 projects every year.
Pedagogical Research PublicationPrimus 28 (2018), no. 8
Communicating to Learn Multivariable Calculus: Students' Blackboard Presentations as a Means for Enhancing Mathematics Learning. With Hans Malmström.
Innovation GrantChalmers
Approx. €70,000 for developing digital teaching tools. I applied for and led the project.
Pedagogical Studies in Higher Education (15 hp)Chalmers
Formal qualification in university-level teaching and learning, including student assessment, curriculum design, and learning theories.
Supervision
Yanbo Fang (Current, 2026–present)
Tudor Sharpe (Current, 2026–present); Gabriel Abánades Joglar (Current, 2025–present); Anthony Mäkelä (Current, 2025–present, Co-supervisor); Douglas Molin (Completed 2026, Co-supervisor); Mykola Pochekai (Completed 2024); Jiacheng Xia (Completed 2021, Co-supervisor); Manh Hung Tran (Completed 2020)
Samuel Plumeyer (Current); Sebastian Jansson (Current); Liu Xudong (2024); Felix Frelot (2022); Robert Antonio Pop Gorea (2021); Magnus Fries (2020); Mattias Lindby (2016)
Louis Dao, Anna Davoodi, Erik Samuelsson (2024)
Recent Selected Seminars
Mini-course (invited)Xiamen, China
How many rational points? The work of Abel prize winner Gerd FaltingsGothenburg, Sweden
Colloquium
Genus one mirror symmetry for toric varietiesIBS, Pohang, South Korea
Algebraic geometry seminarBologna, Italy
On smooth fillings of Calabi–Yau varieties
Séminaire de géométrie "Anniversaire Paul 80"Paris, France
The spectral genus and an inequality for the Milnor number
Spring school in Arakelov Geometry and related topicsHangzhou, China
Relative intersection theory and Arakelov geometry, minicourse
Algebraic geometry seminarStockholm, Sweden
From counting genus one curves to questions about singularities
Masterclass: Arakelov geometry on Shimura varietiesCopenhagen, Denmark
Eisenstein series and enumerative geometry
Genus one mirror symmetry and the arithmetic Riemann–Roch theoremPrinceton, Marseille, Oxford, Stockholm
Selected Conferences
Conference in honour of Ken-Ichi Yoshikawa's 60th birthdayKyoto, Japan
Invited
Arakelov geometry intercity conferenceWestlake University, Hangzhou, China
Archimedean heights and bad reduction of Calabi–Yau manifolds
AI for MathematicsGothenburg, Sweden
The very confident intern — how I use LLMs in my mathematical research
Kähler Geometry: Past, Present and FutureBanff, Canada
On a conjecture of Deligne for the determinant of the cohomology
Hodge theory in a broad senseStockholm, Sweden
On smooth fillings of Calabi–Yau families
Around Local Index TheoryParis, France
Intersection bundles and the Cappell–Miller torsion for Riemann surfaces. Mini-course on joint work with Gerard Freixas i Montplet.
Algebra and FriendsBorås, Sweden
Milnor Number Inequalities in Hypersurface Singularities
Complex Geometry WorkshopAarhus, Denmark
On some singularity invariants from analytic torsion
Arakelov geometry intercity conferenceRegensburg, Germany
Genus one mirror symmetry and the arithmetic Riemann–Roch theorem
Workshop AlkageGrenoble
On an invariant for Calabi–Yau manifolds through analytic torsion
The full publication list is on its own tab, so it is not repeated here.
AI for math
I use large language models in my own work, and I am interested in where they help, where they mislead, and what either fact means for how mathematics actually gets done. This page collects what comes out of that: things I have built, talks I have given, and notes as I write them.
The Common Room
A noticeboard of small browser games about mathematics and academic life. Plain HTML, CSS and JavaScript - no frameworks, no build step, nothing to install, and no image files: every sound is synthesised as it plays. I wrote them with an LLM sitting next to me, which is rather the point. They are the working example behind everything else on this page.
Open The Common Room Eight games and one scene
Math Collab
A shared whiteboard, calls with screen share, and chat that understands LaTeX - something like WhatsApp, but built for doing mathematics together rather than just talking about it.
Open Math Collab Whiteboard, screen share, LaTeX chat
Algebraic Geometry Workbench
An interactive companion to my MMA321 Algebraic Geometry course: curve and surface explorers, a blow-up lab, exercises and practice quizzes.
Open the Workbench Curve and surface explorers, blow-up lab, quizzes
Coming up
My most productive colleague doesn’t have an officeAlgebra and Geometry division meeting, Gothenburg
Short talk on how I use AI in mathematics, for research and for apps.
AI for MathematicsInstitut Mittag-Leffler, Djursholm
Conference, 14-18 June. Attending.
Talks
The very confident intern - how I use LLMs in my mathematical researchAI for Mathematics, Gothenburg
More about me
- Work: https://www.chalmers.se/en/persons/dener/
- arXiv: https://arxiv.org/search/?query=Eriksson%2C+Dennis&searchtype=author&abstracts=show&order=-announced_date_first&size=50
- Publications: https://scholar.google.com/citations?user=DwAUqycAAAAJ&hl=sv&oi=ao
- ORCID: https://orcid.org/0000-0003-0646-6613