Mini-workshop on flag supermanifolds, related supergeometries and applications

Feb 13, 2026, 9:00 AM → Feb 14, 2026, 5:00 PM Europe/Rome

Room 205 (13/2) & Stasi (14/2) (IGAP (13/2) & ICTP (14/2))

Ugo Bruzzo (UFMG & IGAP), Michele Graffeo (SISSA), Ugo Bruzzo (SISSA)

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The workshop aims at providing some highlights on recent developments in supergeometry, especially about flag supermanifolds, moduli spaces of supergeometric structures, and foundations of algebraic supergeometry.

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Registration

Registration is free, but mandatory.

Deadline for Registration: January 31, 2026

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How to reach us

From Piazza Oberdan take bus 6 toward Grignano/Miramare.
Get off at “Strada Statale 14 della Venezia Giulia 9” (ICTP stop).
Walk uphill for about 5 minutes, following the signs toward IGAP, to reach the entrance.

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Speakers

Ugo Bruzzo (UFMG, Belo Horizonte & IGAP)

Sergio Cacciatori (Univ. Insubria, Como)

Daniel Hernández Ruipérez (Univ. Salamanca)

Michele Graffeo (SISSA & IGAP, Trieste)

Simone Noja (Univ. Bari)

Emanuele Pavia (University of Luxembourg)

Ivan Penkov (Constructor University, Bremen)

Elizaveta Vishnyakova (UFMG, Belo Horizonte)

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Scientific committee

Daniel Hernández Ruipérez (Univ. Salamanca)

Ivan Penkov (Constructor University, Bremen)

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Organizers

Ugo Bruzzo (UFMG, Belo Horizonte & IGAP​)

Michele Graffeo (SISSA & IGAP) 

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Supported by

SISSA, IGAP, PRIN 2022 Geometry of algebraic structures: moduli, invariants, deformations

Friday, February 13

9:30 AM → 10:00 AM Registration

10:00 AM → 11:00 AM Linear embeddings of complex supergrassmannians

In the early 1980-ies I. Skornyakov and I proved that a two-sided complex supergrassmannian is not superprojective.
This demonstrated that the role of supergrassmannians in algebraic supergeometry cannot be the same as the role of grassmannians in algebraic geometry. In particular, it motivated the sudy of embeddings of one supergrassmannian into another supergrassmannian.This study has been delayed for 40 years, and in this talk I will explain if and how one supergrassmannian can be embedded into another supergrassmannian so that the pullback of the Berezinian canonical sheaf from the larger supergrassmannian is isomorphic to the canonical sheaf of the smaller supergrassmannian. I call such embeddings linear and will outline a classification of linear embedddings of (possibly isotropic) supergrassmannians into other (possibly isotropic) supergrassmannians. A possible application is a classification of linear ind-supergrassmannians. The Sato supergrassmannian is a linear supergrassmannian.

Speaker: Prof. Ivan Penkov (Constructor University Bremen)

11:00 AM → 11:30 AM Coffee Break

11:30 AM → 12:30 PM Graded coverings of supermanifolds and their applications

In geometry, the notion of a covering space is classical and well estab-
lished. A familiar example is the universal covering: p : ℝ → S¹, given by
t ↦ exp(it). Analogous constructions also appear in algebra, for instance
in the theory of modules over rings, where one encounters flat or torsion-
free coverings. Despite arising in different contexts, these coverings share a
common underlying idea: an object from a given category is covered by ob-
jects belonging to a smaller (or different) category in such a way that certain
universal properties are satisfied.
In the paper “Super Atiyah classes and obstructions to splitting of su-
permoduli space”, Donagi and Witten introduced a construction of the first
obstruction class to the splitting of a supermanifold. Later we observed that
the infinite prolongation of the Donagi–Witten construction satisfies univer-
sal properties common for other coverings. In other words, this construction
yields a covering of a supermanifold in the category of graded manifolds asso-
ciated with the nontrivial homomorphism ℤ → ℤ₂. Furthermore, the space of
infinite jets can also be viewed as a covering of a (super)manifold in the cate-
gory of graded manifolds corresponding to the homomorphism ℤ × ℤ₂ → ℤ₂,
given by (m, n¯ ) ↦ n¯. (For ordinary manifolds, this homomorphism reduces
to the trivial map ℤ → 0.)
Our talk is devoted to the current state of the theory of graded coverings,
including the general framework, key examples, and a presentation of our
recent results.

Speaker: Prof. Elizaveta Vishnyakova (UFMG)

12:30 PM → 2:30 PM LUNCH: Lunch

2:30 PM → 3:30 PM Cotangent complexes and obstruction theories in supergeometry

One of the most celebrated and far-reaching achievements in algebraic geometry is the concept of (perfect) obstruction theory introduced by Behrend and Fantechi. Roughly, this amounts to replacing unbounded cotangent complexes of (very singular) stacks with smaller complexes in order to produce and compute numerical invariants.
In this talk, we describe how this machinery can be generalized to the supergeometric setting, thanks to the powerful formalism of homotopical algebra. As a possible application, we hint at the construction of an obstruction theory for the moduli superstack of stable supermaps.
This is based on joint work in progress with U. Bruzzo, D. Hernández Ruipérez, and A. Ricolfi.

Speaker: Dr Emanuele Pavia (University of Luxembourg)

3:30 PM → 4:00 PM Coffee Break

4:00 PM → 5:00 PM Poincaré duality and supergravity

In this talk I will discuss how Verdier–Poincaré duality specializes to families of supermanifolds in a relative setting. I will then show how this framework yields a genuinely supergeometric (and mathematically rigorous) formulation of supergravity. In particular, it provides a conceptual bridge between the component, geometric, and superspace approaches, clarifying their equivalence as different presentations of the same underlying structure.

Speaker: Dr Simone Noja (Univ. Bari)

Saturday, February 14

10:00 AM → 11:00 AM The superstack of coherent sheaves

We introduce superstacks and describe some of their basic features. As an example the superstack of coherent sheaves on a superprojective superscheme is constructed. A description of its bosonic reduction is given

Speaker: Prof. Daniel Hernández Ruipérez (Univ. Salamanca)

11:00 AM → 11:30 AM Coffee Break

11:30 AM → 12:30 PM Super Geometry, a classical viewpoint

In a joint ongoing project with Ugo Bruzzo and Charles Almeida, we are working on a generalisation of classical notions from algebraic geometry to the super setting. In my talk I will present some of this ideas through a series of examples.

Speaker: Michele Graffeo (SISSA)

12:30 PM → 2:30 PM LUNCH: Lunch

2:30 PM → 3:30 PM Super Mumford form as a string measure

According to a proposal by Yuri Manin, we want to show that the super Mumford form is the natural measure for the perturbative computation of the string scattering amplitudes.
Starting from a formula provided by A. Voronov in 1988, we show how to get an expression for it in super-coordinates, which correctly reproduces the tree-level amplitudes for Neveau-Schwarz states, without the need to introduce ghosts and picture changing operators. We will also give some hints on how it works for Ramond states.

Speaker: Prof. Sergio Cacciatori (Univ. Insubria, Como)

3:30 PM → 4:00 PM Coffee Break

4:00 PM → 5:00 PM Stable supermaps

I will introduce the notion stable map from a SUSY curve to a fixed target superscheme and study their moduli space, which is a Deligne-Mumford superstack.

Speaker: Prof. Ugo Bruzzo (UFMG & IGAP)