Monday

10:00-11:00 Tom Bridgeland

Title: Boomerangs, elliptic curves and del Pezzo surfaces

Abstract: We consider boomerangs in the derived category of an elliptic curve C. These are filtrations of the zero object whose factors are polystable with ascending phase. The numerical invariants of a boomerang consist of the Chern characters of the direct summands of the factors, and define a lattice polygon. When this polygon is reflexive we show that the moduli space of boomerangs with a fixed set of polystable factors is the complement of an anti-canonical embedding of C in a del Pezzo surface Z. The proof uses exceptional collections on Z. This is joint work with Pierrick Bousseau and Luca Giovenzana.

11:30-12:30 Bernhard Keller

Title: On actions of braid groups on (ex)triangulated categories

Abstract：We will present an approach to the construction of actions of braid groups on (ex)triangulated categories arising in the (additive) construction of cluster algebras and varieties. The examples will be inspired by combinatorial braid group actions constructed by Fraser, Fock-Goncharov, Goncharov-Shen and others. The results we will present were obtained in several joint projects notably involving Chris Fraser, Yilin Wu, Miantao Liu and Haoyu Wang.

13:00-15:00 Lunch break

15:00-16:00 Paul Balmer

Title: The definition of the stable permutation category

Abstract: This is joint work in progress with Martin Gallauer. We seek a robust definition of the stable permutation category in modular representation theory of a finite group. This category is intended to be the "stable" analogue of the derived permutation category, much as the stable module category relates to the usual derived category. Our approach is guided by the tensor-triangular geometry of these categories and the insights gained from our previous study of the geometry of permutation modules, published last year. While this new "stable permutation category" is usually connected—paralleling the

classical case—it can become disconnected in specific instances. We describe the precise conditions for this phenomenon to happen in terms of the group, and we identify the resulting connected components.

16:00-16:30 Coffee break

16:30-17:30 Špela Špenko
Title: Categorical half twist

Abstract: We define half spherical objects that induce (categorical) half twists. We give examples, in the context of the topological Fukaya category of a surface, where we show that the categorical half twist coincides with the geometric half twist, and in the context of divisors in smooth quasi-projective varieties. This is joint work with Alexander Polishchuk and Michel Van den Bergh.

Tuesday

10:00-11:00 Arend Bayer

TBA

11:00-11:30 Coffee break

11:30-12:30 Emanuele Macrì

Titolo: Lagrangian subvarieties and fibrations

Abstract: A recent influential article by Liu, Liu, and Xu gave a new example of a 42-dimensional (singular) irreducible symplectic variety with a Lagrangian fibration.  This is obtained by compactifying a construction by Iliev and Manivel arising from cubic fourfolds and fivefolds, together with techniques developed recently by Saccà.  In work in progress with O’Grady and Saccà, we consider the case of Gushel-Mukai manifolds, by obtaining an example in dimension 20. The approach is similar to Liu-Liu-Xu: we compactify another construction by Iliev-Manivel, but with technical complications due to the Gushel-Mukai setting.

13:00-15:00 Lunch break

15:00-16:00 Alex Perry

Title: Inducing t-structures on semiorthogonal components

Abstract: I will discuss a new method for constructing t-structures on semiorthogonal components of triangulated categories, which leads in particular to the first examples of bounded t-structures on phantom categories. This is joint work with Alexander Kuznetsov and Shengxuan Liu.

16:00-16:30 Coffee break

16:30-17:30 Xiaolei Zhao

Title: Remarks on stability conditions on products of curves

Abstract: I will review a sequence of results starting with Yicheng Liu’s construction of stability conditions on products with curves, and my joint work with Lie Fu and Chunyi Li on characterizing geometric stability conditions in this case, to more recent joint work with Li, Macrì, Perry, Stellari on invariant stability on self-product of curves. This paves the way for Chunyi Li’s recent construction of stability conditions on all smooth projective varieties, which will be also briefly discussed.

18:00 Poster section and scientific discussion

20:00 Social dinner

Wednesday

09:30-10:30 Marco Manetti

Title: Joint deformations of coherent sheaves and sections

Abstract: Given a coherent sheaf $\mathcal{F}$ on a smooth projective manifold $X$, and a global section $\sigma\in H^0(X,\mathcal{F})$, we describe a DG-Lie algebra controlling deformations of the triple $(X,\mathcal{F},\sigma)$. Then we apply this result to deformations of pairs (manifold, divisor). Joint work with Donatella Iacono.

10:30-11:00 Coffee break

11:00-12:00 Emma Lepri

Title: Deformations of morphisms of coherent sheaves

Abstract: This talk is based on a joint work in progress with D. Iacono and E. Martinengo, where we study deformations of morphisms of coherent sheaves. Deformations of morphisms of locally free sheaves have been investigated by D. Iacono and E. Martinengo via differential graded Lie algebras and Hinich’s theorem on descent of Deligne groupoids. The difficulty in generalising this approach to morphisms of coherent sheaves lies in the fact that the semicosimplicial DGLAs attached to this deformation problem are not concentrated in non-negative degrees, and hence Hinich’s theorem needs to be extended.

12:00-13:00 Jan Štovíček
Title: The Matlis-Greenlees-May equivalence for non-affine schemes

Abstract: In the 1990's, Greenlees and May studied the total left derived functor of the I-adic completion, where R is a commutative ring and I is a finitely generated ideal. One interpretation of their results, in view of work of other authors, is that this functor under a suprisingly mild condition provide a derived equivalence of the abealian categories of R-modules supported in V(I) on the one hand, and the category of so-called derived I-adically complete (also known as L-complete) modules. The condition is the so-called weak proregularity of I and it is always satisfied when R is noetherian, but also in other

situations in homotopy theory, which was the original motivation. In this talk, I will present a non-affine version of this result for

quasi-compact semi-separated schemes. The is joint work with Leonid Positselski and is based on the idea to consider cosheaves instead of sheaves on the adically complete side, since the completion interacts much better with colocalization than localization. The approach is rather different from the previous work of Alonso, Jeremías and Lipman on this problem.

Thursday

10:00-11:00 Gabriele Vezzosi

Title: Affine Grassmannians for surfaces

Abstract: The affine Grassmannian (and its Beilinson-Drinfeld version) for a curve and an algebraic group  is a very useful classical tool in geometric representation theory and Geometric Langlands. The situation in higher dimensions is, so far, unexplored. I will propose some geometric versions of affine Grassmannians for surfaces (and an algebraic group), describe them as quotients, and prove representability results.

11:00-11:30 Coffee break

11:30-12:30 Mauro Porta

Title : Variations of CoHAs and Schiffmann's positivity conjecture

Abstract : In one of his seminal papers, Schiffmann introduced an analogue for algebraic curves of Kac's counting polynomial (defined for quivers) and formulated several positivity conjectures. In this talk I will address the strong version of such conjecture, predicting the existence of a certain representation of the general symplectic group. In joint, ongoing work with L. Hennecart, F. Sala and O. Schiffmann we are solving this conjecture. Our method relies on studying the variation of the cohomological Hall algebra of Higgs bundles over the moduli space of curves. If time permits, I will discuss some natural questions that originate from this perspective.

13:00-15:00 Lunch break

15:00-16:00 Yukinobu Toda

Title: The Dolbeault geometric Langlands conjecture via limit categories  

Abstract: I will propose a precise formulation of the Dolbeault geometric Langlands conjecture, introduced by Donagi–Pantev 

as the classical limit of the (de Rham) geometric Langlands correspondence. It asserts an equivalence between certain  derived categories of coherent sheaves on moduli stacks of Higgs bundles on a smooth projective curve. On the automorphic side, I introduce limit categories, which may be viewed as classical limits of categories of D-modules  on moduli stacks of bundles over curves. Their definition is based on noncommutative resolutions due to Špenko–Van den Bergh  and on magic windows in the sense of Halpern-Leistner–Sam. Our formulation states an equivalence between the derived categories  of moduli stacks of semistable Higgs bundles and the limit categories associated with moduli stacks of all Higgs bundles.  I show that the (ind-)limit categories are compactly generated, admit Hecke operators, and carry semiorthogonal decompositions 

into quasi-BPS categories, categorifying BPS invariants in Donaldson–Thomas theory (joint work woth Tudor Pădurariu, arXiv:2508.19624). Finally, I will explain a proof of this equivalence for GL_2 over the locus of the Hitchin base where spectral curves are reduced. This provides the first nontrivial case in which the relevant moduli stacks are not quasi-compact, and the use of limit categories is  essential both for the formulation and for the proof.

16:00-16:30 Coffee break

16:30-17:30 Evgeny Shinder
Title: Canonical decompositions for derived categories of G-surfaces

Abstract: We study semiorthogonal decompositions of derived categories of smooth projective varieties and their behavior under birational transformations. Motivated by Kuznetsov’s conjecture on cubic fourfolds and Kontsevich’s vision of canonical decompositions, we introduce the notion of G-atomic theory: canonical, mutation-equivalence classes of G-invariant semiorthogonal decompositions compatible with derived contractions with respect to a group G-action. We prove the existence of such a theory in dimension ≤ 2 for any group G, thereby establishing Kontsevich’s conjecture in this case. This framework refines and extends previous work by Auel–Bernardara and yields a complete birational classification of geometrically rational surfaces over perfect fields in terms of their atoms (canonical building blocks of the derived category). Connections are drawn to the atomic decompositions of quantum cohomology by Katzarkov–Kontsevich–Pantev–Yu. This is joint work with Alexey Elagin and Julia Schneider.

Friday

10:00-11:00 Fernando Muro

TBA

11:00-11:30 Coffee break

11:30-12:30 Soheyla Feyzbakhsh
Title: Stability conditions on Calabi-Yau threefolds via Brill-Noether theory of curves

Abstract: I will explain how classical Brill–Noether theory for vector bundles on curves, which studies the number of sections of stable vector bundles, can be used to prove the Bayer–Macrì–Toda conjecture for Calabi–Yau threefolds, which guarantees the existence of Bridgeland stability conditions on them. This is joint work with Zhiyu Liu, Naoki Koseki, and Nick Rekuski.