Postdoctoral researcher
Tsinghua University – Imperial College London
April 2026 – present
Curriculum vitae
Marco Rampazzo
Algebraic geometer working on derived categories, birational geometry, and mathematical realizations of gauged linear sigma models.
Yau Mathematical Sciences Center, Tsinghua University
C-551, Shuangqing Complex Building · Haidian District · Beijing
Profile
Research and teaching
I am an algebraic geometer working on derived categories, birational geometry, and mathematical realizations of gauged linear sigma models, with a parallel interest in agent-based AI systems for long-horizon mathematical research. I currently hold a joint postdoctoral position at Tsinghua University and Imperial College London and am based at Tsinghua in Beijing. My teaching and mentoring experience spans foundational undergraduate courses, master’s research supervision, and an 18-hour PhD course on derived categories of rational homogeneous varieties.
Experience
Academic positions
Postdoctoral researcher
University of Antwerp
February 2025 – September 2025
Postdoctoral researcher
University of Bologna
February 2021 – January 2025
Teaching assistant
University of Bologna
October 2021 – January 2022
Teaching assistant
University of Stavanger
October 2020 – December 2020
PhD student in Mathematics
University of Stavanger
September 2016 – September 2020
Education
Degrees
PhD in Mathematics
University of Stavanger · Supervisor: Michał Kapustka
Equivalences between Calabi–Yau manifolds and roofs of projective bundles
May 2021
Master’s degree in Physics
University of Milan
July 2016
Bachelor’s degree in Physics
University of Milan
December 2013
Research
Research interests
Derived categories and semiorthogonal decompositions of Fano varieties
Exceptional collections, semiorthogonal decompositions and mutations provide powerful tools to understand derived categories of coherent sheaves and categorical resolutions of singularities, and to investigate the geometric information that they carry. The derived category is a very rigid invariant for a Fano variety, but the choice of an appropriate subcategory can lead to the construction of more subtle birational invariants. This approach can be extended to singular varieties by constructing semiorthogonal decompositions of the categorical resolution of singularities.
Birational equivalences, K-equivalence, and the DK conjecture
While the derived category is known to be an invariant up to isomorphism for smooth Fano and general type varieties, its behavior as a birational invariant in broader settings (e.g. flops and related constructions) remains the subject of open conjectures. In particular, there is substantial evidence suggesting that certain birational transformations, known as K-equivalences, should induce equivalences at the level of derived categories.
Gauged linear sigma models, phase transitions, and mathematical physics
In physics, gauged linear sigma models are supersymmetric gauge theories that exhibit multiple phases. Unlike the original abelian models, non-abelian GLSMs can have several “geometric” phases, each corresponding to the geometry of a smooth projective variety. Conjecturally, the physical relationship between these phases is reflected mathematically by Fourier–Mukai functors inducing equivalences, or embeddings, between the derived categories of the associated varieties.
Varieties with two projective-bundle structures
The classification of simple K-equivalences, i.e. crepant birational maps between smooth projective varieties which admit a common resolution whose morphism to either side is a single blowup along a smooth center, is closely related to the classification of special Fano varieties called roofs. These are varieties of Picard rank two, whose extremal contractions are projective bundles, and such that there is a line bundle which restricts to O(1) on the fibers of both contractions. Although the roof condition is rather restrictive, the classification is still an open problem.
In progress
Current research projects
Reconstruction of del Pezzo surfaces from semiorthogonal components
With Xun Lin and Shizhuo Zhang. Categorical Torelli theorems for low-degree del Pezzo surfaces, recovering their geometry from the semiorthogonal complement of the structure sheaf and investigating their conic bundle structures via spinor modifications.
Verra threefolds and spinor modifications
With Shizhuo Zhang. Kuznetsov’s spinor modifications intrinsically describe birational maps between conic bundles that preserve the Kuznetsov component up to Morita equivalence. We classify those inducing isomorphisms of Verra threefolds, proving a Torelli-type statement.
The last primitive double-mirror Calabi–Yau pair?
With Michał Kapustka and Prajwal Samal. A GLSM construction for a primitive, non-birational pair of Calabi–Yau varieties, together with a derived equivalence obtained by comparing the relevant phases and their categorical models.
A categorical resolution for the degree-33 Schubert variety in the Cayley plane
With Giovanni Mongardi, Luigi Martinelli, Michał Kapustka, and Prajwal Samal.We consider a pair of Calabi–Yau varieties which admits a description through a candidate homological-projective-duality pair of categorical resolutions of singularities.
Calabi–Yau orbifold fibrations and stacky GLSMs
With Will Donovan. Total spaces of homogeneous bundles on Grassmannians can lead to GLSM phase transitions whose second geometric phase is an orbifold fibration. We investigate one such case and its relation to a derived category of modules over the even part of a Clifford algebra.
Mathematical research-agent systems
Codex-native, agent-based control layers for long-horizon mathematical reasoning, building on the Danus and Rethlas systems and improving the memory layer to optimize the retrieval of mathematical facts.
Bibliography
Publications and preprints
PhD thesis: Equivalences between Calabi–Yau manifolds and roofs of projective bundles
doi:10.31265/usps.78Fano fibrations and DK conjecture for relative Grassmann flips
doi:10.4171/PRIMS/61-4-7Fullness of the Kuznetsov–Polishchuk exceptional collection for the spinor tenfold
doi:10.1007/s10468-023-10246-6New counterexamples to the birational Torelli theorem for Calabi–Yau manifolds
doi:10.1090/proc/16745The generalized roof F(1, 2, n): Hodge structures and derived categories
doi:10.1007/s10468-022-10173-yMukai duality via roofs of projective bundles
doi:10.1112/blms.12597Torelli problem for Calabi–Yau threefolds with GLSM description
doi:10.4310/CNTP.2019.v13.n4.a2Categorical resolutions and birational geometry of nodal Gushel–Mukai varieties
arXiv:2602.14109Window categories for a simple 9-fold flop of Grassmannian type
arXiv:2510.06184Derived equivalence for the simple flop of type D5
arXiv:2410.20446Calabi–Yau fibrations, simple K-equivalence and mutations
arXiv:2006.06330Reconstruction of a del Pezzo surface from the orthogonal complement of its structure sheaf
The last primitive double-mirror Calabi–Yau pair?
Academic talks
Invited talks
Window categories and Calabi–Yau threefolds
YMSC Postdoctoral Seminar
Beijing · July 4, 2026
Semiorthogonal decompositions for Fano varieties
Seminar of Algebra, Jagiellonian University
Kraków · December 11, 2025
On the derived category of nodal Gushel–Mukai fourfolds
IMPAN Seminar of Algebraic Geometry
Kraków · December 9, 2025
Double-mirror Calabi–Yau threefolds in Grassmannians
Algebraic Geometry Seminar, Jagiellonian University
Kraków · December 1, 2025
Window categories and birational maps
IMPANGA seminar
Warsaw · November 14, 2025
Flips, flops and window categories
Algebraic geometry seminar
Guangzhou · November 6, 2025
Full exceptional collections on G/B
Workshop “Semiorthogonal decompositions for representations of algebraic groups”
Bielefeld · September 3, 2025
Derived categories and nodal Gushel–Mukai fourfolds
MAGIC Seminar
London · May 19, 2025
Gushel–Mukai fourfolds and flops
Algebraic Geometry Seminar
Pohang · April 8, 2025
Derived categories and flops
Number Theory and Algebraic Geometry Seminar
Leuven · April 2, 2025
Exceptional collections for algebraic varieties
Analysis & Geometry Seminar
Antwerp · February 26, 2025
Derived categories and birational transformations
Algebra, Geometry and Number Theory Seminar
Antwerp · November 22, 2024
An introduction to derived categories of homogeneous varieties
IMPAN colloquium
Kraków · May 16, 2024
Derived categories of generalized Grassmannians
IMPANGA seminar
Warsaw · May 11, 2024
Generalized Grassmann flips vs pushforwards of hyperplane sections
MIST workshop on Derived Categories
Hong Kong · March 9, 2024
DK conjecture for generalized Grassmann flips
Algebraic Geometry Seminar, Jagiellonian University
Kraków · February 9, 2024
Full exceptional collections for homogeneous varieties
Seminar of Algebra and Number Theory, University of Augsburg
Augsburg · November 30, 2023
Simple K-equivalence and semiorthogonal decompositions
Modern Perspectives on Birational Geometry
Taipei · July 29–August 4, 2023
K-equivalence and derived categories
Derived Categories and Birational Geometry
Milan · June 30–July 1, 2022
Derived categories and GLSM phase transitions
SAXAG seminar
Leipzig · June 23, 2022
Homogeneous roofs of projective bundles and semiorthogonal decompositions
IMPANGA seminar
Warsaw · June 3, 2022
L-equivalence for Calabi–Yau pairs in generalized Grassmannians
Grothendieck Ring and Derived Category: a Gathering
Turin · April 27–28, 2022
Semiorthogonal decompositions and homogeneous varieties
Seminar of Algebra and Geometry, University of Bologna
Bologna · June 15, 2021
Computing Hodge numbers of Calabi–Yau varieties in Grassmannians
Seminar of Algebra, Jagiellonian University
Kraków · April 11, 2019
A gauged linear sigma model description for a pair of non-birational Calabi–Yau threefolds
Motives of Calabi–Yau Manifolds
Kraków · May 19–21, 2018
Contributed talks
Hodge structures and derived categories of Fano varieties in Grassmannians
Recent Advances in Classical Algebraic Geometry
Kraków · June 27–July 2, 2022
Mukai roofs and K3 surfaces
Algebraic Geometry Days
Stavanger · November 25–26, 2019
Derived equivalence of Mukai roofs: the case of K3 surfaces of degree 12
Nasjonalt Algebramøte 2019
Oslo · November 7–8, 2019
A GLSM description for a pair of non-birational Calabi–Yau threefolds
Nasjonalt Matematikermøte 2018, PhD day
Bergen · September 12, 2018
Academic activity
Teaching, mentoring, and service
Graduate teaching and mentoring
- Master’s research project in homological algebra
Supervisor within Wendy Lowen’s master’s course · Antwerp, spring 2025 - Master’s thesis graduation committee
Committee member · Antwerp, spring 2025 - Derived categories of rational homogeneous varieties
Organizer and instructor, 18-hour PhD course · Bologna, March–April 2024
Undergraduate teaching
- Course instructor: Linear algebra · Stavanger, fall 2019
- Exercise classes / tutoring: Linear Algebra · fall 2021
- Discrete Mathematics and Linear Algebra · fall 2020
- Probability and Statistics · spring 2020
- Linear algebra · fall 2018
- Linear algebra · fall 2017
Academic organization and outreach
Hodge atoms seminar
Organizer with Will Donovan
Beijing · 2026
Mathematics Research Day
Panelist in a discussion on the day-to-day life of mathematical researchers
Antwerp · March 26, 2025
Bridgeland stability conditions seminar
Organizer with Simone Billi, Francesco Denisi, Franco Giovenzana, Annalisa Grossi, and Mihai Pavel · seminar archive
Bologna · Chemnitz · Nancy · fall 2021
The mathematics of gauged linear sigma models
Organizer and speaker
Toulouse · spring 2019
Mobility
Research visits
Long-term visits
Jagiellonian University and IMPAN
Guest · Funding: Jagiellonian University and IMPAN
Kraków · November–December 2025
Paul Sabatier University
Guest · Funding: Norwegian Research Council mobility grant
Toulouse · February–May 2019
Short-term visits
Sun Yat-sen University
Guest
Guangzhou · August 19–22, 2026
IMPAN
Guest · Funding: IMPAN
Kraków · February 2–6, 2026
Sun Yat-sen University
Guest · Funding: Sun Yat-sen University
Guangzhou · November 3–7, 2025
Imperial College London
Guest · Funding: Imperial College London
London · May 19–23, 2025
Institute for Basic Science
Guest · Funding: Institute for Basic Science
Pohang · April 7–11, 2025
University of Antwerp
Guest · Funding: University of Antwerp
Antwerp · November 21–23, 2024
Jagiellonian University
Guest · Funding: INdAM–GNSAGA and Jagiellonian University
Kraków · May 6–17, 2024
The Chinese University of Hong Kong
Guest · Funding: The Chinese University of Hong Kong
Hong Kong · March 8–13, 2024
Jagiellonian University
Guest · Funding: Jagiellonian University
Kraków · February 5–9, 2024
University of Augsburg
Guest · Funding: University of Augsburg
Augsburg · November 28–December 1, 2023
Max Planck Institute for Mathematics in the Sciences
Guest · Funding: MPI MiS
Leipzig · June 22–24, 2022
Computer algebra and AI
Research software, AI, and industry collaborations
Research software
AG-flops-scripts
With Will Donovan, Wahei Hara, and Michał Kapustka. Open-source Python tools for homogeneous-bundle cohomology, Ext groups, tilting bundles, and window-category computations.
2025
Borel–Weil–Bott calculator
Web application computing the cohomology of irreducible homogeneous bundles on rational homogeneous varieties.
2022
Industry collaborations
Humanos s.r.l.
Graph-based retrieval-augmented generation, LLM recommendation systems, and virtual assistants using multiple LLM agents.
December 2024 – September 2025
Hello Human s.r.l.
NLP, LLM recommendation systems, feature extraction, and sentiment analysis.
July 2023 – December 2024
Algoretico s.r.l.s.
Recommendation systems, reinforcement learning, and rectification problems in multiview geometry.
January 2022 – June 2023