The GEARS seminar

Thursday 4 September 2025

12:30-13:20 Matthias Vancraeynest

Title: TBA

15:30-16:20 Tiziano Gaibisso

Title: Bow varieties: from Quivers to Branes

Abstract: Bow varieties, introduced by S. Cherkis in 2011, form a class of varieties that unify and generalize several important constructions. For instance, they include Nakajima’s quiver varieties and the Coulomb branches of affine type A quiver gauge theories (in the sense of Braverman–Finkelberg–Nakajima) as special cases.

In the first part of the talk, I will introduce bow diagrams (a generalization of quivers with dimension vectors), their representations, and the associated bow varieties, illustrating how Nakajima’s varieties fit into this broader framework. The second part will focus on bow diagrams generalizing affine (and finite) type A quivers, with emphasis on their construction via Hanany–Witten brane configurations in string theory. This perspective allows us to interpret bow varieties as Higgs and Coulomb branches in 3d N=4 supersymmetric quantum field theories. Building on this perspective, I will present a combinatorial characterization of type A bow diagrams that give rise to non-empty varieties, formulated in terms of supersymmetry for Hanany–Witten configurations. If time permits, I will also discuss further criteria: a numerical one, derived from Hanany–Witten transitions, and a representation-theoretic one, expressed in terms of weights for affine Kac–Moody algebras and arising naturally from the stratification of bow varieties.

Friday 5 September 2025

10:00-10:50 Will Cohen

Title: Artin Groups and the Tits Alternative

Abstract: In 1995 Bestvina asked which Artin groups satisfy the Tits alternative, a classical condition for group which governs the behaviour of subgroups. Since then much progress has been made in classifying particular subclasses of Artin groups with respect to this property. In this talk I will discuss the motivation for this question and more broadly the motivation for the study of Artin groups as a class, and present a recent combination theorem for the Tits alternative for Artin groups that allows us to find new examples of Artin groups satisfying the Tits alternative that do not fit into any standard subclass.

11:30-12:20 Hidde Stoffels

Title: Energy conditions and the ends of the universe

Abstract: Did the Big Bang happen? What is inside a black hole? Are wormholes real? Physicists have tried to answer these questions (and more) by formulating energy conditions: very concise and generic summaries of what we believe to be realistic properties of matter, encoding for example the idea that energy densities should be positive, or that gravity should be attractive. However, despite all their apparent sensibility, every classical energy condition is routinely violated by quantum mechanical systems, raising the question whether exotic phenomena like time travel may yet be realised through quantum effects.

In this talk, I will introduce the classical energy conditions and discuss some of their consequences and their failure in quantum field theory. Finally, I will go over some of the ways they have been generalised to quantum systems.

14:00-14:50 Stefan Roberts

Title: Stability Spaces, HRS Tilts, and Cohomological Spread

Abstract: Given a triangulated category D and a pair of bounded hearts H and K in D, there are two natural notions of distance between H and K. The first is "cohomological spread", the minimum bound on the cohomology of all objects in H with respect to K. The second is the number of Happel-Reiten-Smalø tilts necessary to get from H to K. Both notions of distance define a generalised metric on the set of bounded t-structures on D. There is no reason a priori to expect that these metrics should be equal. In this talk I will outline an argument, based on the topology of the stability space of D, that these two metrics are equal when the Grothendieck group K(D) is free of rank two.