Schedule

Location

The workshop takes place in room 6.11 in the Hans Freudenthal building, on the Utrecht Science Park campus.

November 6, 2026

10:00–11:00: Moduli of parahoric Higgs bundles and symplectic resolutions; Johan Martens (University of Edinburgh)
11:00–11:30: coffee break
11:30–12:30: Diagrammatic algebras and Hermitian symmetric pairs; Emily Norton (University of Kent)
12:30–14:00: lunch
14:00–15:00: Cubic surfaces and the Petersen graph; Eduard Looijenga (Utrecht University)
15:00–15:30: coffee break
15:30–16:30: From Springer to Langlands: a geometric view on the representations of Weyl groups and reductive groups; Maarten Solleveld (Radboud University)

Abstracts

Eduard Looijenga: Cubic surfaces and the Petersen graph
Emily Norton: Diagrammatic algebras and Hermitian symmetric pairs
Johan Martens: Moduli of parahoric Higgs bundles and symplectic resolutions
Maarten Solleveld: From Springer to Langlands: a geometric view on the representations of Weyl groups and reductive groups

Cubic surfaces and the Petersen graph

Eduard Looijenga (Utrecht University)

Ever since Cayley and Salmon found in 1849 that a smooth cubic surface contains exactly 27 lines, algebraic geometers have been fascinated by that discovery. Perhaps the most symmetric cubic surface is the one named after Clebsch, who studied it in detail (1871) (and of which Klein had a plaster model made that was shown at the World Fair in Chicago in 1894).
The Clebsch surface has the same symmetry group as the Petersen graph, namely the alternating group of degree 5. I will explain that this is more than a mere coincidence, for this leads to a presentation of the (orbifold) fundamental group of the moduli space of cubic surfaces in terms of a generalized braid group defined by the Petersen graph. This is based on joint work with Allcock and Basak.

Diagrammatic algebras and Hermitian symmetric pairs

Emily Norton (University of Kent)

Some 10-20 years ago, Brundan-Stroppel and Ehrig-Stroppel introduced diagrammatic algebras that realise the basic algebras of the parabolic BGG category O for maximal parabolics of Dynkin types (A,A) and (D,A), respectively. I will discuss another approach using diagrammatic anti-spherical Hecke categories (joint work with Chris Bowman, Maud de Visscher, Niamh Farrell and Amit Hazi), as well as a recent result on the diagrammatic algebra of type (D,A) by my master’s student Eliot Grimont.

Moduli of parahoric Higgs bundles and symplectic resolutions

Johan Martens (University of Edinburgh)

We will discuss moduli spaces of parahoric Higgs bundles, and use them to describe natural (partial) symplectic resolutions that provide global analogues of Springer resolutions. This talk is based on joint work with Logares, Pym, Roth and Wong.

From Springer to Langlands: a geometric view on the representations of Weyl groups and reductive groups

Maarten Solleveld (Radboud University)

Springer’s best-known achievement is his correspondence, about representations of Weyl groups. We discuss how the generalized Springer correspondence (due to Lusztig) appears in the representation theory of reductive groups over finite fields. We will explain how this leads to the Langlands correspondence for a finite reductive group $G$, as formulated recently by Imai-Vogan. It relates $G$-representations to sheaves on Langlands parameters, like modern versions of the local Langlands program.