GRK-Seminar Sommersemester 2026

RTG Seminar Summer Term 2026

The Thursday morning seminar (10:15-11:45 in WSC-N-U-3.05) will be the “Research Training Group Seminar” where members of the RTG (PhD students, post-docs,…) present their results. Sometimes, we also have speakers from other places. Depending on the number of speakers and on the proposed topic, a speaker could use one or two sessions.

16.04.2026	Wieslawa Niziol	Mercator lectures.
23.04.2026	Wieslawa Niziol	Mercator lectures.
30.04.2026	Wieslawa Niziol	Mercator lectures.
07.05.2026	Wieslawa Niziol	Mercator lectures.
21.05.2026	Davide Gori	Modular Compactifications of $M_{g,n}$ via Cluster Algebras
28.05.2026	Rızacan Çiloğlu	Motivic parahoric Hecke categories in equal and mixed characteristic
11.06.2026	Davood Nejaty	Commuting Higgs bundles: mirror symmetry meets Langlands duality
02.07.2026	Hind Souly	On strong F-regularity of the zero locus of totally negative quivers moment maps and local Galois deformation rings
09.07.2026	Anna Borri	Untwisting the twisted character variety
16.07.2026	ALGANT Master Students	t.b.a.
23.07.2026	Paolo Sommaruga	t.b.a.

Abstracts

Wieslawa Niziol. Duality theorems in p-adic analytic geometry

I will discuss duality theorems for p-adic geometric pro-etale cohomology of partially proper rigid analytic varietes. The first two lectures will address the dualities on the Fargues-Fontaine curve by reducing them to coherent dualities, the remaining two — will descend these dualities to the world of Topological Vector Spaces. This is a joint work with Pierre Colmez and Sally Gilles.

Davide Gori: Modular Compactifications of $M_{g,n}$ via Cluster Algebras

We discuss the first steps of the Minimal Model Program and the Hassett-Keel program for the Deligne-Mumford compactification of $M_{g,n}$. In this context, we construct several new compactifications arising as good moduli spaces of stacks of curves with $A$-type singularities, realized as $\Theta$-semistable loci with respect to line bundles on a suitable stack. Varying the line bundle yields an involved wall-crossing picture in the space of stability conditions, which can be described combinatorially using cluster algebras.

Rızacan Çiloğlu: Motivic parahoric Hecke categories in equal and mixed characteristic

Given a split reductive group G, Katsuyuki Bando has constructed a family of affine grassmannians that interpolate between the equal characteristic and witt vector versions. Using this family and properties of universally locally acyclic sheaves, he has proven that constructible etale sheaves agree between equal and mixed characteristic.

I will report on joint work in progress with Sebastian Bartling, in which we generalize this result in 2 directions: from etale sheaves to etale motives, and from split reductive groups to parahoric models of tamely ramified reductive groups constructed by Pappas-Zhu.

Davood Nejaty: Commuting Higgs bundles: mirror symmetry meets Langlands duality

In this talk, we introduce a moduli stack of principal $G$-bundles with a pair of commuting Higgs fields on a smooth projective curve
where $G$ is a reductive algebraic group. These objects are in bijection with certain coherent sheaves on a Calabi–Yau threefold. Therefore, the moduli space of these objects admits a vanishing cycle sheaf known as Donaldson–Thomas sheaf. We propose a conjectural equality between the mixed Hodge numbers of these sheaves for Langlands dual groups $G = SL_n$ and $PGL_n$ using a torus localization on the $SL_n$-moduli space. By computing the mixed Hodge numbers of the torus fixed loci, we prove this conjecture for $n = 2$. Our result generalizes the topological mirror symmetry of Hausel and Thaddeus to a class of Calabi–Yau threefolds.

Hind Souly: On strong F-regularity of the zero locus of totally negative quivers moment maps and local Galois deformation rings

We prove that the zero fiber of the sum of commutators map for the Lie algebras $\mathfrak{gl}_n$ and $\mathfrak{sl}_n$ is strongly F-regular under certain assumptions on the number of commutators. Our results yield a positive characteristic analogue and a new proof of a theorem of Aizenbud and Avni asserting that the model of this zero locus over the complex numbers has rational singularities. Moreover, we show the strong F-regularity of the zero fiber of moment maps of totally negative quivers, assuming that the number of loops and arrows are large enough. Furthermore, we apply our results to establish the strong F-regularity of the special fibers of all irreducible components of local Galois deformation rings associated to any continuous residual representation, assuming that the base $p$-adic field is sufficiently large.

Anna Borri: Untwisting the twisted character variety

Simpson’s correspondence establishes a homeomorphism between the moduli space of degree $0$ Higgs bundles on a smooth projective complex curve $X$ and the character variety, parametrising representations of the fundamental group of $X$. For degree $d$ Higgs bundles, the character variety is replaced by a twisted version. In this talk, we explain an alternative construction of this twisted version. The key insight is that the twist appearing in the variety of representations can be thought of as monodromy around an orbifold point. This insight is formalized by adding a stacky point to the curve $X$ and then showing that the moduli space of degree $d$ Higgs bundles on $X$ can be realized as a component of the moduli space of degree $0$ Higgs bundles on the stacky curve. We then use this construction to compute the action of the correspondence on the Hodge weights in cohomology.