## Schedule

### Tuesday, November 26

- 08:30–09:30
- registration
- 09:30–10:30
*to be determined*- 10:30–11:00
- break
- 11:00–12:00
*to be determined*- 12:00–14:00
- lunch
- 14:00–15:00
*to be determined*- 15:15–16:15
*to be determined*- 16:15–16:45
- break
- 16:45–17:45
*to be determined*

### Wednesday, November 27

- 09:30–10:30
*to be determined*- 10:30–11:00
- break
- 11:00–12:00
*to be determined*- 12:00–14:00
- lunch
- 14:00–15:00
*to be determined*- 15:15–16:15
*to be determined*- 16:15–16:45
- break
- 16:45–17:45
*to be determined*

### Thursday, November 28

- 09:30–10:30
*to be determined*- 10:30–11:00
- break
- 11:00–12:00
*to be determined*- 12:00–14:00
- lunch
- 14:00–15:00
*to be determined*- 15:15–16:15
*to be determined*- 16:15–17:00
- closing

### Abstracts

- Johannes Krah: On proper splinters in positive characteristic
- Markus Reineke: Motives of Kronecker moduli
- Andrea Ricolfi: The motive of the Hilbert scheme of points in all dimensions
- Tudor Padurariu: Hall algebras of Higgs bundles on a curve
- Martijn Kool: Nekrasov’s gauge origami and Oh-Thomas’s virtual cycles
- Yifei Zhao: The local Langlands correspondence for covering groups

##### On proper splinters in positive characteristic

Johannes Krah (Bielefeld University)

A scheme $X$ is a splinter if for any finite surjective morphism $f\colon Y \to X$ the pullback map $\mathcal{O}_X \to f_* \mathcal{O}_Y$ splits as $\mathcal{O}_X$-modules. By the direct summand conjecture, now a theorem due to André, every regular Noetherian ring is a splinter. Whilst for affine schemes the splinter property can be viewed as a local measure of singularity, the splinter property imposes strong constraints on the global geometry of proper schemes over a field of positive characteristic. For instance, the structure sheaf of a proper splinter in positive characteristic has vanishing positive-degree cohomology. I will report on joint work with Charles Vial concerning further obstructions on the global geometry of proper splinters in positive characteristic. Further, I will address the derived-invariance of the (derived-)splinter property.

##### Motives of Kronecker moduli

Markus Reineke (Bochum University)

Kronecker moduli are algebraic varieties parametrizing linear algebra data up to base change. We consider generating series of their motives, and discuss results characterizing these series by functional and differential equations.

##### The motive of the Hilbert scheme of points in all dimensions

Andrea Ricolfi (SISSA)

The geometry of Hilbert schemes of points is largely unknown, or known to be pathological in a precise sense. This should in principle make most Hilbert scheme invariants essentially inaccessible. We present a closed formula for the generating function of the motives (classes in the Grothendieck ring of varieties) of Hilbert schemes of points $\mathrm{Hilb}(\mathbb{C}^n,d)$, varying the ambient dimension $n$ and having fixed the number of points $d$. Joint work with M. Graffeo, S. Monavari and R. Moschetti.

##### Hall algebras of Higgs bundles on a curve

Tudor Padurariu (Sorbonne Université)

I will report on joint work with Yukinobu Toda (partially in progress) about the (categorical) Hall algebra of Higgs bundles on a curve. These categories have semiorthogonal decompositions in certain categories, called quasi-BPS, whose construction is inspired by the enumerative geometry of Calabi-Yau threefolds.

I will focus on two conjectural dualitities. The first is between the Hall algebra of semistable Higgs bundles of degree zero and a "limit" category. This equivalence aims to make precise the proposal of Donagi-Pantev of considering the classical limit of the de Rham Langlands equivalence. The second is a primitive (or BPS) version of the first, and it relates categories of sheaves on moduli of semistable Higgs bundles (for various degrees). This equivalence may be regarded as a version of the D-equivalence conjecture / SYZ mirror symmetry. We can prove (partial) versions of these conjectures for topological K-theory of these categories.

##### Nekrasov’s gauge origami and Oh-Thomas’s virtual cycles

Martijn Kool (Utrecht University)

Nekrasov's 4D ADHM quiver is a generalisation of the 2D and 3D ADHM quivers. I will give a mathematical definition of the corresponding "gauge origami" partition function in terms of certain torus localized Oh-Thomas virtual cycles. I will relate the orientation problem of gauge origami to the one of Hilbert schemes of points on affine 4-space, which was previously analysed in physics by Nekrasov-Piazzalunga ("Magnificent Four") and in algebraic geometry in a joint work with J. Rennemo. I will provide a conjectural sheaf-theoretic interpretation of gauge origami in terms of certain moduli of 2-dimensional framed sheaves on $(\mathbb{P}^1)^4$. Joint work in progress with N. Arbesfeld and W. Lim.

##### The local Langlands correspondence for covering groups

Yifei Zhao (University of Münster)

The local Langlands correspondence (LLC) for covering groups is a conjectural parametrization of genuine smooth representations of (non-algebraic) covers of $p$-adic reductive groups by L-parameters. In this talk, I will explain how covering groups arise from transgressions of degree-4 characteristic classes, and why this perspective leads to a construction of the LLC whenever the covering degree is coprime to p. This is joint work with T. Feng, I. Gaisin, N. Imai, and T. Koshikawa.