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Prof. Mark Gross29/08/2026, 08:30
Broken lines, in conjunction with scattering diagrams, have been a very powerful tool for constructing regular functions on schemes obtained by gluing standard charts using the data of scattering diagrams. One could hope that broken lines could also be used to build other geometric objects on the glued schemes, e.g., vector fields. At first glance, this seems to give very poorly behaved...
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Prof. Matej Filip29/08/2026, 09:40
We prove that Gorenstein terminal toric fourfold singularities are unobstructed. We also establish vanishing results for the obstruction space for certain Gorenstein toric Fano varieties. Finally, we discuss connections with mirror symmetry and Laurent polynomials.
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Prof. Alessio Corti29/08/2026, 11:00
I discuss the structure of the deformation space of Gorenstein toric affine 3-folds following work of Filip. This is an introduction to the talk by Graefnitz.
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Dr Tim Gräfnitz29/08/2026, 13:00
I explain how Fano smoothings of Gorenstein toric varieties can be constructed using logarithmic geometry. Maximally mutable Laurent polynomials induce singular log structures on reducible toroidal crossing spaces. Conjecturally, such a space admits a log crepant resolution if and only if the Laurent polynomial is rigid. For three-dimensional examples, I construct these log resolutions...
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Dr Robert Śmiech29/08/2026, 14:10
I will report on joint work in progress with Ivan Cheltsov, Anne-Sophie Kaloghiros, and Junyan Zhao, in which we construct the $K$-moduli space of Fano varieties obtained by first blowing up a point in $\mathbb{P}^3$ and then blowing up the strict transform of a $(2,2)$ complete intersection passing through that point.
Our construction is based on the moduli continuity method, enhanced by...
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Prof. Jacopo Stoppa30/08/2026, 08:30
Thomas, Yau and Joyce made the remarkable conjecture that the existence of a special Lagrangian submanifold representing a fixed Fukaya equivalence class on a Calabi-Yau manifold should be equivalent to the stability of that class with respect to a suitable Bridgeland stability condition on the Fukaya category.
I will describe work in progress towards proving the implication from Bridgeland...
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Prof. John Christian Ottem30/08/2026, 09:30
I will explain a geometric construction of an Enriques surface fibration over $\mathbb{P}^1$ of even index. This answers a question of Colliot-Thélène and Voisin, and provides new counterexamples to the Integral Hodge conjecture. This is joint work with Fumiaki Suzuki.
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Dr Thamarai Valli Venkatachalam30/08/2026, 10:30
Fano 3-folds with terminal singularities are fundamental building blocks in birational geometry, but their classification remains an important open problem. In this talk, I will discuss my work on the classification of terminal Fano 3-fold hypersurfaces in rank 2 toric varieties, viewed as GIT quotients. By exploiting this toric structure and the Minimal Model Program, I provide a complete...
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Xianyu Hu30/08/2026, 11:20
Let $X \to S$ be a proper semistable degeneration. For the singular central fibre, the usual choices $D^b_{\mathrm{coh}}(X_0)$ and $\operatorname{Perf}(X_0)$ fail, in complementary ways, to be simultaneously smooth and proper. Inspired by the fact that the natural log structures make the degeneration log smooth, we define logarithmic coherent sheaves and the associated category of log perfect...
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Prof. Alex Küronya30/08/2026, 13:00
This is an account of an ongoing research project with Yusuf Mustopa and Jakob Stix. We study effective global generation properties of adjoint line bundles, nevertheless in a somewhat more extended setting than considered traditionally. Originally motivated by Fujita's conjecture on global generation, we investigate when adjoint line bundles coming from sums of ample ones become globally...
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Prof. Andrea Ricolfi30/08/2026, 14:10
Moduli spaces of stable sheaves on threefolds are notoriously difficult to understand and describe geometrically, especially in rank $>1$.
In this talk, I will give an explicit description, in terms of Quot schemes of reflexive sheaves, of an infinite family of moduli spaces of rank-$2$ sheaves on $\mathbb{P}^3$.
Several properties of these families will be discussed.
One of the key...
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Prof. Jørgen Vold Rennemo31/08/2026, 08:30
In recent work, Arbesfeld, Kool, and Lim, following work in physics by Nekrasov, studied the moduli space of representations of a quiver with relations called the 4D ADHM quiver. In particular, they placed Nekrasov’s partition function on a rigorous algebro-geometric footing using the fourfold counting invariants of Oh–Thomas.
In the same paper, they conjectured that the moduli space of...
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Prof. Gavin Brown31/08/2026, 09:40
Simple flops (the contraction of a single irreducible canonically trivial rational curve on a smooth 3-fold) are in bijection with their Donovan-Wemyss contraction algebras, that is particular noncommutative deformation algebras. We give an intrinsic characterisation of such algebras and classify them, and explain how to recover the flopping curves directly. Joint with Michael Wemyss.
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Prof. Timothy Logvinenko31/08/2026, 11:00
In this talk, I will explain how for any noncommutative smooth and proper variety X we can construct three actions of the Heisenberg algebra on the total Hochschild homology of its symmetric quotient stacks $[X^n/S_n]$. One is defined algebraically using the orbifold decomposition of Hochschild homology. One decategorifies the 2-categorical Heisenberg action of arXiv:2105.13334. One is defined...
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Prof. Duco van Straten31/08/2026, 13:00
I will report on work in progress joint with Mauricio Garay from Paris.
Near a critical point of a Hamiltonian function on the symplectic $p-q$ plane, the level set $H(p,q)=c$ forms a simple closed loop that encloses an area and has the dimension of an action. In quantum theory the variables no longer commute: $pq-qp=h$. We introduce the notion of quantised area, which is a formal series in...
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Prof. Jake Solomon31/08/2026, 14:10
I will discuss a version of homological mirror symmetry for Fano manifolds that incorporates the non-Archimedean norms on the morphism spaces of the Fukaya category. A Fano manifold corresponds to a Banach Landau Ginzburg model, to which is associated a category of normed matrix factorizations. This correspondence gives rise to conjectural formulas for the singular cohomology with rational...
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Mark Gross
Broken lines, in conjunction with scattering diagrams, have been a very powerful tool for constructing regular functions on schemes obtained by gluing standard charts using the data of scattering diagrams. One could hope that broken lines could also be used to build other geometric objects on the glued schemes, e.g., vector fields. At first glance, this seems to give very poorly behaved...
Go to contribution page -
Prof. Jacopo Stoppa
Thomas, Yau and Joyce made the remarkable conjecture that the existence of a special Lagrangian submanifold representing a fixed Fukaya equivalence class on a Calabi-Yau manifold should be equivalent to the stability of that class with respect to a suitable Bridgeland stability condition on the Fukaya category.
I will describe work in progress towards proving the implication from Bridgeland...
Go to contribution page
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