Name: Workshop on Algebraic Geometry and Physics 2025. Moduli Spaces in (Super)Geometry and Mathematical Physics. A celebration of Ugo Bruzzo's 70th birthday
Start: 2025-10-06T09:30:00-03:00
End: 2025-10-10T19:00:00-03:00
Location: Littoral Hotel

Workshop on Algebraic Geometry and Physics 2025. Moduli Spaces in (Super)Geometry and Mathematical Physics. A celebration of Ugo Bruzzo's 70th birthday

from Monday, 6 October 2025 (09:30) to Friday, 10 October 2025 (19:00)

Monday, 6 October 2025
09:30 Moduli of stable super maps - Daniel Hernández Ruipérez (Universidad de Salamanca, Spain)
Moduli of stable super maps
- Daniel Hernández Ruipérez (Universidad de Salamanca, Spain)
09:30 - 10:30
We construct the moduli of stable supermaps as an algebraic superstack with superschematic and separated diagonal. We prove that its bosonic reduction is an affine linear scheme over the stack of stable spin maps, so that it is not proper except in a few particular cases. We also compute the virtual dimension of the moduli superstack of stable supermaps, and prove that it coincides with previous calculations when the target of the supermaps is bosonic.
10:30 Coffee break
Coffee break
10:30 - 11:00
11:00 Moduli of framed sheaves on Hirzebruch surfaces - Valeriano Lanza (Universidade Federal Fluminense, Brazil)
Moduli of framed sheaves on Hirzebruch surfaces
- Valeriano Lanza (Universidade Federal Fluminense, Brazil)
11:00 - 12:00
In this talk, I shall survey three papers devoted to the study of moduli spaces of framed sheaves on Hirzebruch surfaces, two of which were written in collaboration with Ugo Bruzzo. These contributions pursue a common objective: the construction of a quiver-theoretic description of such moduli spaces, starting from the monadic description previously established by Bartocci, Bruzzo, and Rava. To date, this objective has been fully realized only in the rank-$1$ case—corresponding to Hilbert schemes of points on suitable line bundles over $\mathbb{P}^1$—and in the so-called minimal case, where minimality refers to a bound on the numerical invariants of the sheaves that guarantees the non-emptiness of the moduli space. In the concluding part of the talk, I will discuss possible directions for future research on the subject.
12:00 Lunch Break
Lunch Break
12:00 - 15:00
15:00 Higgs Grassmannians - Beatriz Graña Otero (Universidad de Salamanca, Spain)
Higgs Grassmannians
- Beatriz Graña Otero (Universidad de Salamanca, Spain)
15:00 - 16:00
We consider a Higgs bundle $(E, \phi)$. Its Higgs Grassmiannans are subschemes of the usual Grassmannian bundles of $E$ that parameterise Higgs quotients of $(E, \phi)$. We recall how to define them, present some results about their structure, and explain how they can be used to prove some results about Higgs bundles satisfying a strong semistability condition.
16:00 Coffee break
Coffee break
16:00 - 16:30
16:30 Linear data for the nested Hilbert scheme of points on affine spaces and varieties - Pedro H. dos Santos (Universidade Federal de Pernambuco (UFPE), Brazil)
Linear data for the nested Hilbert scheme of points on affine spaces and varieties
- Pedro H. dos Santos (Universidade Federal de Pernambuco (UFPE), Brazil)
16:30 - 17:30
In this talk we realize the nested Hilbert scheme of points on affine spaces and varieties as quiver varieties. In addition, we provide a schematic construction to a set-theoretical result concerning the nested Hilbert schemes of points on $\mathbb A^2$ with quotients supported on curves, provided by Santos; we compute interesting examples and an explicit formula for the tangent space to these latter schemes. This construction generalizes previous work of Jardim, von Flach and Lanza, about the nested Hilbert schemes of points on $\mathbb A^2$ and also of Henni and Jardim, about the Hilbert schemes of points on $\mathbb A^n$, for $n\geq 3.$
Tuesday, 7 October 2025
09:30 On characteristic classes for bundles on quantum spaces - Giovanni Landi (Università degli Studi di Trieste, Italy)
On characteristic classes for bundles on quantum spaces
- Giovanni Landi (Università degli Studi di Trieste, Italy)
09:30 - 10:30
We study the quantization of spaces whose K-theory in the classical limit is the ring of dual numbers $\mathbb{Z}[t]/(t^2)$. For a compact quantum space, we give sufficient conditions that guarantee there is a morphism of abelian groups from $K_0 \to \mathbb{Z}[t]/(t^2)$, compatible with the tensor product of bimodules. Applications include the standard quantum sphere $S^2_q$ and a quantum 4-sphere $S^4_q$ coming from quantum symplectic groups. For the former the K-theory is generated by the Euler class of a monopole bundle while for the latter, the K-theory is generated by the Euler class of the instanton bundle.
10:30 Coffee break
Coffee break
10:30 - 11:00
11:00 On the Noether-Lefschetz theory in projective toric orbifolds - William D. Montoya (Universidade Estadual de Campinas, Brazil)
On the Noether-Lefschetz theory in projective toric orbifolds
- William D. Montoya (Universidade Estadual de Campinas, Brazil)
11:00 - 12:00
In 2012, Bruzzo and Grassi proved a Noether-Lefschetz theorem for toric varieties, which claims that for a (2k+1)-dimensional projective toric orbifold with suitable conditions on a very general quasi-smooth hypersurface $X$, each $(k,k)$-cohomology class on $X$ comes from the ambient toric variety. The Noether-Lefschetz locus is the locus of quasi-smooth hypersurfaces with the same degree such that there exists a $(k,k)$-cohomology class that does not come from the ambient toric variety. In this talk, I will present the main results about the Noether-Lefschetz loci in toric varieties based on my joint work with Prof. Ugo Bruzzo in recent years.
12:00 Lunch break
Lunch break
12:00 - 15:00
15:00 Automorphisms of quartic surfaces and Cremona transformations - Carolina Araujo (IMPA, Brazil)
Automorphisms of quartic surfaces and Cremona transformations
- Carolina Araujo (IMPA, Brazil)
15:00 - 16:00
In this talk, I will address the following question, attributed to Gizatullin: ``Which automorphisms of a smooth quartic surface in projective 3-space are restrictions of Cremona transformations of the ambient space?'' Corti and Kaloghiros have introduced a general framework that is extremely useful for approaching this problem, namely, a special version of the Sarkisov program for Calabi-Yau pairs. I will report on recent progress on Gizatullin’s problem obtained using this theory, in collaborations with Alessio Corti and Alex Massarenti, and with Daniela Paiva and Sokratis Zikas.
16:00 Coffee break
Coffee break
16:00 - 16:30
16:30 Cox Gorenstein algebras - Rodrigo Gondim (Federal University of Pernambuco, Brazil)
Cox Gorenstein algebras
- Rodrigo Gondim (Federal University of Pernambuco, Brazil)
16:30 - 17:30
We study $G$-graded Artinian algebras having Poincaré duality and their Lefschetz properties. We prove the equivalence between the toric setup and the $G$-graded one. We prove a Hessian criterion in the $G$-graded setup. We provide an application to toric geometry.
Wednesday, 8 October 2025
09:30 Enumerative geometry of flag varieties and prime numbers - Giordano Cotti (Universidade de Lisboa, Portugal)
Enumerative geometry of flag varieties and prime numbers
- Giordano Cotti (Universidade de Lisboa, Portugal)
09:30 - 10:30
Enumerative geometry, as formulated in Gromov--Witten theory, encodes curve-counting information on smooth projective varieties. Such data can be organized in different ways, giving rise to rich geometric structures and invariants, including quantum cohomology and quantum spectra. In the work \emph{G.~Cotti, ``Coalescence Phenomenon of Quantum Cohomology of Grassmannians and the Distribution of Prime Numbers,'' IMRN, 2022}, an unexpected connection was observed between the quantum cohomology of Grassmannians and the distribution of prime numbers. In this talk, I will present recent progress extending this perspective to the enumerative geometry of more general partial flag varieties, highlighting how the relation with prime numbers persists in a broader setting.
10:30 Coffee break
Coffee break
10:30 - 11:00
11:00 Splitting of supervector bundles on projective superspaces - Charles Almeida (Universidade Federal de Minas Gerais, Brazil)
Splitting of supervector bundles on projective superspaces
- Charles Almeida (Universidade Federal de Minas Gerais, Brazil)
11:00 - 12:00
In this talk, we will introduce basic concepts of superalgebraic geometry and explore why certain classical foundational results, such as the Birkhoff-Grothendieck splitting criterion, do not extend naturally to the supergeometric setting. We then present a splitting criterion for supervector bundles and give some examples of supervector bundles with vanishing cohomology that do not split. Joint work with Ugo Bruzzo (SISSA).
12:00

12:00 - 12:30

12:30 Lunch break
Lunch break
12:30 - 15:00

15:00 Free afternoon
Free afternoon
15:00 - 19:00

19:00 Conference dinner
Conference dinner
19:00 - 21:00
Thursday, 9 October 2025
09:30 Stability conditions for coherent systems on integral curves - Renato Vidal Martins (Universide de Campinas, Brazil)
Stability conditions for coherent systems on integral curves
- Renato Vidal Martins (Universide de Campinas, Brazil)
09:30 - 10:30
In this talk, we briefly introduce stability conditions, which we apply to the category of coherent systems on an integral curve $C$. We define Bridgeland stability conditions on its derived category. We also study the semistability of certain objects with respect to these conditions. We use some results we got to address the problem of finding bounds for the dimension of the space of global sections of torsion-free sheaves on $C$. It's a joint work with Marcos Jardim and Leonardo Roa-Leguizamon.
10:30 Coffee break
Coffee break
10:30 - 11:00
11:00 The Hilbert scheme of points and its motive - Michele Graffeo (Sissa, Italy)
The Hilbert scheme of points and its motive
- Michele Graffeo (Sissa, Italy)
11:00 - 12:00
The Hilbert scheme of points on a quasi-projective variety is a classical object in algebraic geometry. However, its geometry is nowadays still not completely accessible. On the other hand, the motive of a variety $X$ is an invariant attached to $X$ carrying a lot of information about its geometry, and it is considered as a universal Euler characteristic. In a joint project with Monavari, Moschetti and Ricolfi we give general formulas to compute the motive of the Hilbert scheme of points, provided the knowledge of a finite amount of data (that we give explicitly in some cases). In my seminar I will present our formulas and I will show many applications.
12:00 Lunch break
Lunch break
12:00 - 15:00
15:00 On the Factorization of Lucas Polynomials via Lucas Atoms - Gessica Alecci (Politecnico di Torino, Italy)
On the Factorization of Lucas Polynomials via Lucas Atoms
- Gessica Alecci (Politecnico di Torino, Italy)
15:00 - 16:00
In 2020, Sagan and Tirrell introduced Lucas atoms, which are irreducible factors of Lucas polynomials. Their main goal was to investigate when certain combinatorial rational functions are actually polynomials. In a joint work with Miska, Murru, and Romeo, we present Lucas atoms in a more natural way than the original definition, providing straightforward proofs of their main properties. Moreover, we fully characterize the p-adic valuations of Lucas atoms for any prime p, thereby answering a question left open by Sagan and Tirrell. Finally, we show that the sequence of Lucas atoms is not holonomic, in contrast to the Lucas sequence, which satisfies a linear recurrence of order two.
16:00 Coffee break
Coffee break
16:00 - 17:00
17:00 On the exceptional set of crepant resolutions of abelian singularities - Fábio Arceu Ferreira (Federal University of Rio Grande do Norte, Brazil)
On the exceptional set of crepant resolutions of abelian singularities
- Fábio Arceu Ferreira (Federal University of Rio Grande do Norte, Brazil)
17:00 - 18:00
Let $G$ be a finite abelian subgroup of $\mathsf{SL}(n, \mathbb{C})$, and suppose there exists a toric crepant resolution $ \phi: X \longrightarrow \mathbb{C}^n / G$ of the quotient variety $\mathbb{C}^n / G$. Let $\mathsf{Exc}(\phi) = E_1 \cup \dots \cup E_s$ be the decomposition of the exceptional set of $\phi$ into irreducible components. In this seminar, I will show that for every $i$ there exists an open subset $U_i$ of $X$ such that $E_i \subset U_i$, and $U_i$ is isomorphic to the total space of the canonical bundle $\omega_{E_i}$ of $E_i$. Furthermore, $X = U_1 \cup \dots \cup U_s$. This contributes to the collection of results aimed at solving a classical problem, i.e., to determine which submanifolds of a complex manifold have a neighborhood isomorphic to a neighborhood of the zero section of their normal bundle.
Friday, 10 October 2025
09:30 Towards an algebraic proof for the Codimension One Theorem - Rafael Holanda (Universidade Federal de Pernambuco, Brazil)
Towards an algebraic proof for the Codimension One Theorem
- Rafael Holanda (Universidade Federal de Pernambuco, Brazil)
09:30 - 10:30
In 1996, David Cox proved that for a given projective toric variety of dimension $n$, its homogeneous coordinate ring modulo $n+1$ forms with the same ample degree, that do not vanish simultaneously, must have dimension one in the component of the critical degree of the forms. This result, known as the Codimension One Theorem, was generalized by Cattani-Cox-Dickenstein and even further by Cox-Dickenstein. We will discuss these generalizations and their geometric ingredients involved in their proofs. We will conclude with an algebraic proof of Cox's theorem in the case of a product of projective spaces.
10:30 Coffee break
Coffee break
10:30 - 11:00
11:00 Non-Kähler Hodge--Lefschetz theory and the Bianchi identity - Arpan Saha (Universidade Estadual de Campinas, Brazil)
Non-Kähler Hodge--Lefschetz theory and the Bianchi identity
- Arpan Saha (Universidade Estadual de Campinas, Brazil)
11:00 - 12:00
Being Kähler imposes severe constraints on the cohomology of compact complex manifolds such as the Hard Lefschetz property, and the question of how far this generalises beyond the class of Kähler manifolds has been of great interest for a while. In this talk, I shall report on ongoing joint work with Mario García Fernández and Raúl González Molina that abstracts out the definition of a variation of Hodge--Lefschetz structure and provides evidence that, under certain natural assumptions, such a structure exists more generally on distinguished subspaces within moduli spaces of Bismut--Ricci-flat metrics that are pluriclosed up to source terms. In particular, these distinguished subspaces may be regarded as replacements for the Kähler cone, with affine structure modelled on a subspace of the (1,1) Aeppli cohomology of the compact complex manifold.
12:00 Lunch break
Lunch break
12:00 - 15:00
15:00 Coherent Systems on Surfaces - Leonardo Roa-Leguizamón (Universidade Estadual de Campinas, Brazil)
Coherent Systems on Surfaces
- Leonardo Roa-Leguizamón (Universidade Estadual de Campinas, Brazil)
15:00 - 16:00
Let $X$ be a smooth, irreducible, projective surface. A coherent system on $X$ is a pair $(E, V)$ where $E$ is a coherent sheaf on $X$ and $V$ is a finite-dimensional vector space. Associated to coherent systems there is a notion of stability that depends on a parameter $\alpha \in \mathbb{Q}[m]$. In this talk, we describe the moduli space of coherent systems for $\alpha \gg 0$, present topological and geometric properties of this moduli space, and describe the structure of chambers and walls for coherent systems on the projective plane when $\dim(V) = 2$. This is joint work with L. Costa, I. Macías-Tarrío, and a joint work with O. Mata-Gutiérrez, and H. Torres-López.
16:00 Coffee break
Coffee break
16:00 - 16:30
16:30 Some results on Donagi-Markman cubics for Hitchin systems - Peter Dalakov (American University in Bulgaria, Bulgaria)
Some results on Donagi-Markman cubics for Hitchin systems
- Peter Dalakov (American University in Bulgaria, Bulgaria)
16:30 - 17:30
will review some results on Donagi-Markman cubics (infinitesimal period maps) for the pure and generalised Hitchin system. I will discuss how these fit into the context of special Kaehler geometry, and also will discuss some work in progress. Joint with Ugo Bruzzo.