## In Luxembourg

Below is the current schedule for the algebraic geometry seminar. Talks take place in MNO 1.020, from 16 to 17.

- November 30, 2022
- Raf Bocklandt
*Local systems of derived categories of gentle algebras*- We will show how you can construct local systems of derived categories of gentle algebras by viewing them as Fukaya categories of surfaces and explore the connection with the work of Spenko and Van den Bergh on perverse schobers coming from noncommutative crepant resolutions of toric quotients.
- November 9, 2022
- Shengxuan Liu
*Kernels of categorical resolutions of nodal singularities*- Resolution of singularities is a central topic of algebraic geometry. Hironaka showed that the resolution of singularities exists over $\mathbb{C}$. An analogous definition in derived categories was proposed by Lunts and the existence of categorical resolutions was shown by Kuznetsov and Lunts. One thus considers whether there is a link between categorical resolutions and classical resolutions of singularities. In this talk, I will discuss the case of nodal singularities. I will start with basic definitions and notations in derived categories and singularities. Then I will show how to use the Lefschetz decomposition of a quadric to give a categorical resolution of a nodal variety and the property of the kernel generator of this categorical resolution. If time permits, I will describe a categorical resolution of the Kuznetsov component of a nodal cubic fourfold. This is joint work with W. Cattani, F. Giovenzana, P. Magni, L. Martinelli, L. Pertusi, and J. Song.
- October 26, 2022
- Fei Xie
*Residual categories of quadric surface bundles*- I will discuss the relation between the relative Hilbert scheme of lines of a quadric surface bundle and its residual category, the non-trivial semiorthogonal component in its derived category. For a smooth 4-fold with the structure of a quadric surface bundle over a smooth surface, there is a finite number of fibres that are quadrics of corank 2 (unions of two projective planes). This relation can be used to give a nice description of the derived category of the smooth 4-fold. This result applies to cubic 4-folds containing a plane and even-dimensional Fano varieties of dimension at most 10 that are smooth complete intersections of three quadrics. Time permitting, I will also discuss how this result can be generalised to quadric surface bundles over a general base.
- October 5, 2022
- Andreas Krug
*Compactified Jacobians of non-integral curves and Lagrangian fibrations*- I report on joint work with Adam Czaplinski, Manfred Lehn, and SÃ¶nke Rollenske. We describe moduli spaces of stable sheaves, which are generically line bundles, on a certain class of non-integral curves, which we call extended ADE curves. This class of curves generalises the non-integral fibres of elliptic fibrations. The main motivation is that our moduli spaces occur as general singular fibres of Lagrangian fibrations.
- September 28, 2022
- Maxim Smirnov
*Quantum cohomology and derived categories of coadjoint varieties*- We will discuss properties of quantum cohomology, both small and big, of coadjoint varieties of simple algebraic groups and how they relate to the structure of Lefschetz collections in the derived categories of these varieties. Some general conjectures pertaining to this will be formulated. The talk is based on the joint works with Alexander Kuznetsov and Nicolas Perrin.
- November 4, 2021
- Hans Franzen
*Positivity properties of moduli spaces of quiver representations*- I will report on joint work in progress with P. Belmans, C. Damiolini, V. Hoskins, S. Makarova, and T. Tajakka.
The talk will be about (parts of) a geometric proof, using dimension estimates, that a certain line bundle on a moduli space of semi-stable quiver representations is ample, provided that the quiver is acyclic. This re-proves a known result on semi-invariants of quivers. We believe that our approach can be used to provide estimates for the lowest degree in which semi-invariant functions exist.

In weeks without an external speaker we will sometimes set up internal events, besides the ongoing reading groups.

- October 12, 2022
- Gianni Petrella
*Models of trigonal elliptic K3 surfaces*- September 21, 2022
- group afternoon, with expository talks or talks on what currently interests us
- Thilo Baumann: Semiorthogonal decompositions of Brauer–Severi schemes
- Pieter Belmans: 3-dimensional Sklyanin algebras
- David Fernandez Alvarez: Double derivations and Cartan identities
- Nina Morishige: Conjectures on genus-zero Gopakumar–Vafa invariants
- Alessandro Nobile: LCI morphisms for adic morphisms
- Okke van Garderen: GV invariants and root systems

## In Bonn

I co-organised the Representation Theory Oberseminar at the University of Bonn. For other seminars related to the algebras and representation theory group, see the group's website.

I also organised several graduate student seminars.

## In Antwerp

I co-organised the weekly departmental seminar, for which there is a mailing list.

I also organised ANAGRAMS, a graduate student seminar, centered around the topics of (noncommutative) algebra and algebraic geometry.