Geometry section
Invited speakers:
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Programme:
Mon 30th March, 2026
| 3:00pm – 4:00pm | Dhruv Ranganathan (Cambridge) |
| “The LMNOP Conjecture” (abstract) | |
| 4:00pm – 4:30pm | Coffee break |
| 4:30pm – 5:00pm | Contributed talk #1 |
| 5:00pm – 6:00pm | Hülya Argüz (Oxford) |
| “b-Complex Manifolds with Generalized Corners and Kato–Nakayama Spaces” (abstract) |
Tue 31st March, 2026
| 3:00pm – 4:00pm | Konstanze Rietsch (KCL) |
| 4:00pm – 4:30pm | Coffee break |
| 4:30pm – 5:00pm | Contributed talk #2 |
| 5:00pm – 6:00pm | Enrico Fatighenti (Bologna) |
| “Modular vector bundles on hyperkähler manifolds” (abstract) |
Wed 1st April, 2026
| 3:00pm – 4:00pm | Robert Hanson (Imperial) |
| “Parabolic induction for Higgs bundles” (abstract) | |
| 4:00pm – 4:30pm | Coffee break |
| 4:30pm – 5:00pm | Contributed talk #3 |
| 5:00pm – 6:00pm | Piotr Pokora (Krakow) |
| “Curves and surfaces with extreme properties” (abstract) |
Thu 2nd April, 2026
| 1:30pm – 2:30pm | Vladimir Baranovsky (UC Irvine) |
| “Geometry of curved Maurer-Cartan functors” (abstract) | |
| 3:00pm – 4:00pm | Alastair Craw (Bath) |
| “Deformations of Kleinian singularities and their Hilbert schemes” (abstract) |
Geometry section organisers:
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...with some help of:
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Abstracts:
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Hülya Argüz (Oxford): 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 in progress with Dominic Joyce.
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Vladimir Baranovsky (UC Irvine): Geometry of curved Maurer-Cartan functors
We will explain some geometric applications of Getzler's theory of Maurer-Cartan simplicial sets of curved complete \(L_{\infty}\)-algebras, in particular to the probem of lifting torsors across extensions of structure groups and construction of sheaves in commutative and noncommutative geometry.
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Alastair Craw (Bath): Deformations of Kleinian singularities and their Hilbert schemes
Every Kleinian surface singularity can be deformed to produce a flat family of symplectic surfaces, each of which is a Nakajima quiver variety, and the simultaneous resolution of these singular surfaces has been well-studied. In this talk, I'll describe work in progress with Ryo Yamagishi where we study the Hilbert schemes of points on these surfaces by investigating the relative Hilbert scheme of points on the flat family of surfaces.
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Enrico Fatighenti (Bologna): Modular vector bundles on hyperkähler manifolds
We exhibit examples of slope-stable and modular vector bundles on a hyperkähler manifold of \(K3^{[2]}\)-type. These are obtained by performing standard linear algebra constructions on the examples studied by O’Grady of (rigid) modular bundles on the Fano varieties of lines of a general cubic 4-fold and the Debarre-Voisin hyperkähler. Interestingly enough, these constructions are almost never infinitesimally rigid, and more precisely we show how to get (infinitely many) 20 and 40 dimensional families. This is a joint work with Claudio Onorati. Time permitting, I will also present a joint work with Alessandro D'Andrea and Claudio Onorati on a connection between discriminants of vector bundles on smooth and projective varieties and representation theory of \(GL(n)\).
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Robert Hanson (Imperial): Parabolic induction for Higgs bundles
Given a reductive group \(G\), a fundamental method of constructing \(G\)-bundles or \(G\)-representations is via parabolic induction, defined by a pull–push construction over the parabolic/Levi subgroups of \(G\). At the geometric, homological, or categorical level, parabolic induction decomposes several objects of interest in algebraic geometry into Levi-structured components, for instance as BPS states in cohomology or as cuspidal–Eisenstein components in the geometric Langlands program. In this talk, we describe instances of this phenomenon on the moduli stack of \(G\)-Higgs bundles over a smooth projective curve, towards potential applications to the Dolbeault geometric Langlands conjecture of Donagi–Pantev. This is based on the article arXiv:2512.24239.
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Piotr Pokora (Krakow): Curves and surfaces with extreme properties
In this talk, I will present constructions of highly singular algebraic curves exhibiting extreme homological behavior. The focus will be on free plane curves and on algebraic surfaces naturally associated with them.
As an application of these constructions, I will describe a family of surfaces in \(\mathbb{P}^3\) with only isolated singularities whose total Tjurina number admits a lower bound given by a cubic polynomial depending solely on the degree of the surface.
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Dhruv Ranganathan (Cambridge): The LMNOP Conjecture
The Gromov-Witten/Donaldson-Thomas correspondence, proposed by Maulik-Nekrasov-Okounkov-Pandharipande (MNOP) in 2003, is a series of conjectures relating two theories of enumerative geometric origin on projective threefolds. The correspondence reflects a mysterious relationship between two ways to study curves: via equations and via parameterizations. I will outline an extension of the conjecture to logarithmic targets, the “LMNOP” conjecture, and then how this helps study the original correspondence. In particular, I will outline a proof of the full descendent GW/PT conjecture for Fano threefolds. Joint work with Davesh Maulik.
Contact:
All further questions and inquiries can be addressed to Timothy Logvinenko at:
- LogvinenkoT at cardiff dot ac dot uk