25th anniversary of the
Gross-Siebert program
May 17-23, 2026, Cetraro

Dan Abramovich: Virtual intersection theory on the space of lines in the plane
This is joint work in progress with Rahul and Dhruv. The moduli space of stable pointed curves of genus 0 is the model moduli space par excellence, and every direction of generalization is interesting. In this talk we consider the generalization to the moduli space of configurations of lines in the plane. We provide a compactification that carries a virtual fundamental class along with an array of natural and computable tautological cycles. Two ingredients of note, moduli spaces of stable logarithmic maps and tropical degeneration, come from the Gross-Siebert program. Other ingredients are work of Alexeev, Hacking-Keel-Tevelev, and Lafforgue. 

Hülya Argüz: b-Complex Manifolds with Generalized Corners and Kato–Nakayama Spaces
Manifolds with generalized corners (g-corners), introduced by Joyce, are spaces that locally look like rational polyhedral cones. We describe the notion of b-complex manifolds with g-corners, and establish an analogue of the (formal) Newlander–Nirenberg theorem ensuring the existence of local complex coordinates on such manifolds. We also show that Kato–Nakayama spaces associated to log smooth complex analytic spaces naturally carry the structure of a b-complex manifold with g-corners. Conversely, we provide necessary and sufficient conditions characterizing which b-complex manifolds with g-corners arise as Kato–Nakayama spaces. This establishes a bridge between differential-geometric and algebro-geometric perspectives on spaces with singular boundary behavior. This is joint work with Dominic Joyce.

Denis Auroux: SYZ mirror symmetry, holomorphic discs, and corrections to the mirror geometry
This talk will focus on the geometry of SYZ mirror symmetry for Lagrangian torus fibrations on a log Calabi-Yau pair (X,D) where the divisor D is not assumed to be nef.  We will in particular explain how stable discs of negative Maslov index can cause the wall-crossing corrections to the mirror geometry to be inconsistent. We will also outline an approach to constructing the corrected mirror from the geometry of treed holomorphic discs with boundary on the Lagrangian torus fibers of the SYZ fibration, and a conjectural relation to Groman-Varolgunes' work on relative symplectic cohomology. 

Javier Bobadilla: A'Campo spaces and Lagrangian torus fibrations. (Joint work with T. Pelka)
A'Campo spaces are a hybrid geometry construction recently introduced by T. Pelka and myself. It replaces the central fibre of a normal crossings degeneration by a "radius 0 Milnor fibration" by means of a tropical blow up of the Kato-Nakayama space of the divisorial log-structure. The main advantage over other hybrid geometry constructions is that A'Campo space is a smooth manifold with boundary, with a smooth submersion to the real oriented blow up of the disc; this allows to endow them with a symplectic form. I will explain how to use this construction to produce Lagrangian torus fibrations for any maximal Calabi-Yau degenerations. This fibrations are the arquimedean analogues of the affinoid torus fibrations produced by Nicaise, Xu and Yu.

Pierrick Bousseau: Geometric helices on del Pezzo surfaces from tilting
Geometric helices on a surface S are sequences of objects in the derived category of coherent sheaves on S that provide a way to describe the derived category of coherent sheaves on the local surface K_S​ in terms of a quiver with potential.  We prove that all geometric helices in the derived category of coherent sheaves on a del Pezzo surface are related by a sequence of elementary operations: rotation, shifting, orthogonal reordering, tensoring by a line bundle, and tilting. As a consequence, any two non-commutative crepant resolutions of the affine cone over a del Pezzo surface are related by mutations. The proof relies on a geometric interpretation of tilting operations as cluster transformations acting on toric models of a log Calabi-Yau surface mirror to the del Pezzo surface.

Francesca Carocci: The Multiple cover formula for GW invariants of abelian surfaces
I will explain the  statement of the Multiple cover formula conjecture of Oberdieck for Gromov--Witten invariants of abelian surfaces, recently proved ( for many insertions) in a joint work with T. Blomme. The proof rely on the degeneration formula and thus ultimately on the study of logarithmic Gromov-Witten invariants for certain simple geometries.

Alessio Corti: Symbol-preserving birational maps of the torus and mirrors of Fanos
I introduce the concept of symbol-preserving birational maps of the torus. I show some examples and nonexamples. I show some consequences for (generalised) cluster varieties built from a seed made of symbol-preserving maps. This is joint work with Matt Kerr and John E McCarthy of WashU

Qile Chen: A geometric polynomiality of Gromov-Witten generating functions
Introduced by Witten in the 1990s, Gauged Linear Sigma Models (GLSM) provide a framework for interpolating between Gromov-Witten theory and Landau–Ginzburg models. Mathematically, they are realized as a family of theories that count curves in the critical loci of holomorphic functions known as superpotentials. In this talk, I will report on a joint project in progress with Felix Janda and Yongbin Ruan on computing Gauged Linear Sigma Models via logarithmic compactifications. On the Gromov-Witten side, our method yields all-genus quantum Lefschetz formulas that relate Gromov-Witten invariants of complete intersections to the enumerative geometry of their ambient spaces. These formulas can be further lifted to reveal an underlying polynomial structure of Gromov-Witten generating functions in any genus. 

Suraj Dash: GIT Wall Crossing in the Hilbert Scheme of an Expanded Degeneration
We study the Hilbert schemes of points on expanded degenerations of simple normal crossings pairs via Variation in Geometric Invariant Theory. The main tool is an Altmann–Hausen-inspired polyhedral-divisor package, built from invariant divisorial valuations recording boundary degenerations, which replaces stratum-by-stratum Hilbert–Mumford computations. For a smooth pointed curve, this gives an explicit wall-crossing picture from the logarithmic Hilbert chamber to the absolute Hilbert scheme, with bubbling and discriminant walls realized respectively by non-crepant weighted blow-ups and Thaddeus flips for punctual Hilbert schemes at nodes.

Philip Engel: Matroids and the integral Hodge conjecture
Associated to any regular matroid of rank g on k elements, one can associate a multivariable semistable degeneration of principally polarized abelian g-folds over a k-dimensional base. I will discuss joint work with de Gaay Fortman and Schreieder, proving that a combinatorial invariant of the matroid obstructs the algebraicity of the minimal curve class, on the very general fiber of the associated degeneration. Corollaries include the failure of the integral Hodge conjecture for abelian varieties of dimension ≥ 4 and the stably irrationality of very general cubic threefolds.

Michel van Garrel: A-model Fano correspondences as integral transforms of the intrinsic B-model
Given a Fano variety X with smooth anticanonical divisor D, one may consider the enumerative geometry of X, of the pair (X,D) or of D. The study of how to go from counting genus 0 curves in X to genus 0 curves in (X,D) to genus 0 curves in D goes back to Gathmann. While the A-model statements are fairly involved, they become standard integral transforms when formulated as B-model correspondences within the Intrinsic Mirror Construction. I will explain how this works.

Tim Gräfnitz: Toric degenerations of Fano 3-folds
A central tool in the original Gross-Siebert mirror construction are degenerations to a union of toric varieties with transversely intersecting log singular locus. I explain recent and ongoing work (joint with Alessio Corti and Helge Ruddat) on how more intricate intersections of the log singular locus appear naturally from smooth Fano 3-folds and their mirror dual Laurent polynomials.

Paul Hacking: Moduli of Calabi--Yau 3-folds and mirror symmetry
Recent work of Bakker-Filipazzi-Mauri-Tsimerman constructs compactifications of moduli spaces of polarized Calabi--Yau manifolds generalizing the Baily-Borel compactification for K3 surfaces, proving conjectures of Green-Griffiths-Laza-Robles. We conjecture that the BFMT compactification for Calabi Yau 3-folds coincides with the compactification proposed by Morrison in 1993 based on mirror symmetry in a neighborhood of a large complex structure limit point. In particular, the boundary strata near the limit can be understood in terms of the birational geometry of the mirror.  We will present a dictionary relating degenerations and contractions of the mirror supporting our conjecture.

Ilia Itenberg: Refined invariants for real curves
The talk is devoted to several real and tropical enumerative problems. We suggest new invariants of the projective plane (and, more generally, of certain toric surfaces) that arise from appropriate signed enumeration of real algebraic curves of genus 1 and 2.  These invariants admit a refinement (according to the quantum index) similar to the one introduced by Grigory Mikhalkin in the genus zero case. We also suggest an extension of the invariants under consideration to a non-toric setting. This is a joint work with Eugenii Shustin.

Samuel Johnston: Punctured log Gromov-Witten theory of log modifications and double ramification cycles with target log variety
We outline upcoming work which reduces the punctured log Gromov-Witten theory of any logarithmic modification of a log smooth scheme X to the punctured log Gromov-Witten theory of X. We will describe an application which expresses any punctured log GW class of a toric bundle over a log smooth base B in terms of punctured log GW classes of B. An intermediate step in establishing this expression is the introduction and study of the double ramification cycle with target log variety, a generalization of the double ramification cycle with target variety which admits a natural construction via punctured log maps.

Dominic Joyce: The Pandharipande-Thomas rationality conjecture for superpositive curve classes
In https://arxiv.org/abs/2111.04694 I developed a theory of enumerative invariants in homology counting semistable objects in abelian categories, with wall-crossing formulae under change of stability condition. In joint work with Reginald Anderson https://arxiv.org/abs/2604.05664, I apply this to prove the rationality conjecture for generating functions of Pandharipande-Thomas invariants of smooth projective complex 3-folds $X$, for superpositive curve classes $\beta$, that is, curve classes $\beta$ all of whose effective summands $\gamma$ have $c_1(X) \cdot \gamma > 0$. If $X$ is a Fano 3-fold then every curve class is superpositive. The proof uses a wall-crossing formulae relating Pandharipande-Thomas virtual classes to Donaldson-Thomas type invariants counting 1-dimensional sheaves in superpositive curve classes $\gamma$ on $X$.

Ludmil Katzarkov: New birational invariants
In this talk we will introduce the theory of atoms and outline a road map - how to apply the theory to the question of nonrationality.

Ailsa Keating: Homological mirror symmetry for K3 surfaces
Joint work in progress with Paul Hacking. We outline a proof of the homological mirror symmetry conjecture of Kontsevich for K3 surfaces in the following form. Let X be a K3 surface equipped with a Kähler form ω such that the lattice L := [ω]^⊥ ∩ H²(X, ℤ) has signature (2, r-2) and contains a copy of the hyperbolic plane U = (0 1 ; 1 0). Then there is a projective K3 surface Y defined over a Novikov field and a quasi-equivalence of A^∞ categories between the Fukaya category of (X, ω) and the derived category of coherent sheaves on Y. (Note that the condition on the lattice L is necessary, e.g. by considering numerical K-theory.) Our work builds on prior work of Seidel, Gross–Siebert, Sheridan, Lekili–Ueda, and Ganatra–Pardon–Shende, among others.

Xuanchun Lu: Enumerativity of bulk-deformed LG models for toric del Pezzo surfaces
The mirror to a toric variety is given by a Landau--Ginzburg model. In the Fano case, the Jacobian ring of the superpotential recovers the small quantum cohomology of the original toric variety. I will discuss how this story generalises to the big quantum cohomology, at least in the case of nonsingular toric del Pezzo surfaces, and provide a purely algebraic proof of the analogous statement by FOOO.

Daniel Pomerleano: The noncommutative Landau-Ginzburg model
Given an anticanonical divisor D in a Fano variety M, the Fukaya category and symplectic cohomology of M/D give rise to a kind of ``noncommutative Landau-Ginzburg model." I will describe what is known about this framework and outline some applications to studying the quantum connection of M. This is based on joint work with P. Seidel. 

Konstanze Rietsch: On mirror symmetry for Schubert varieties
I will report on two recent works about the construction of mirror superpotentials for Schubert varieties: one with L. Williams and one with C. Li and M. Yang. The first work concerns Grassmannian Schubert varieties X, where (with L. Williams) we construct a superpotential that is given in terms of Pluecker coordinates and Young diagram combinatorics and that encodes Newton-Okounkov bodies and toric degenerations of X. Our formula generalises a formula for the full Grassmannian superpotential from earlier work with B. Marsh. In the second work, with Li and Yang, these Grassmannian Schubert superpotentials are then given a Lie-theoretic reinterpretation, and we obtain a conjectural superpotential for a general G/P-Schubert variety. This work also provides a generalisation of the (Dale) Peterson variety that governs the quantum cohomology rings of the homogeneous spaces G/P, and we state a conjecture about the quantum cohomology rings of smooth Fano Schubert varieties.

Jacopo Stoppa: A toric case of the Thomas-Yau conjecture
We consider a class of Lagrangian sections L contained in certain Calabi-Yau Lagrangian fibrations (mirrors of toric weak Fano manifolds). We prove that a form of the Thomas-Yau conjecture holds in this case: L is isomorphic to a special Lagrangian section in this class if and only if a stability condition holds, in the sense of a slope inequality on objects in a set of exact triangles in the Fukaya-Seidel category. This agrees with general proposals by Li. On surfaces and threefolds, under more restrictive assumptions, this result can be used to show a precise relation with Bridgeland stability, as predicted by Joyce. These results should fit well with mirror symmetry at a large complex structure limit, a topic closely related to the Gross-Siebert program.  

Wang Yao: Quantum Mirror Symmetry via Gross-Siebert Program
In this talk, I will present the first mathematical proof of the quantum mirror symmetry conjecture proposed by Aganagic-Cheng-Dijkgraaf-Krefl-Vafa about the NS-limit of closed refined topological string theory in the case of local P^2. The NS-limit of the refined topological string A-model is in fact the same as the higher genus logarithmic Gromov-Witten invariants of (P^2,E) by Bousseau’s work, while the mirror B-model is predicted to be the quantum curve and its WKB approximation, which will give the quantum correction of the classical period integrals, i.e. the quantum periods. The two key ingredients of the proof are the intrinsic definition of the quantum periods given by the deformation quantization theory and the Gross-Siebert construction of the proper Landau-Ginzburg model together with its deformation quantization by Bousseau. Due to the generality of those theories, our method could be easily generalized to all local (toric) del Pezzo surfaces. If time permits, I will make some remarks on how to use the Gross-Siebert program to explore the open string case. This talk is based on a joint work with Pierrick Bousseau and Bernd Siebert.

Peter Zaika: On Birational Invariance of the Canonical Wall Structure
The canonical wall structure is a combinatorial object associated with certain log Calabi-Yau pairs (X,D), which allows one to calculate the associated intrinsic mirror ring and its basis of theta functions. It is constructed via counts of curves meeting the boundary D at a single point with maximal tangency. A natural question that arises in this construction is the dependence on the boundary divisor. In this work I will go over results showing that under certain positivity assumptions on D, the construction is birationally invariant. 

Ilia Zharkov: Lagrangian torus fibrations of anti-canonical toric hypersurfaces
Based an idea of Evans-Mauri of using Liouville flows for local models. I will show how to build Lagrangian torus fibrations of symplectic hypersurfaces in toric varieties associated with reflexive polytopes. The key feature of the fibration is that the discriminant is in codimension 2. Also, there are two sections of the fibration whose difference generates symplectic monodromy of certain 1-parameter families of such hypersurfaces. This is a joint work with C.Y. Mak, D. Matessi and H. Ruddat.