Non-arithmetic monodromy of higher hypergeometric functions

• John Parker (Durham University)

Room: L50 (Psychology Auditorium) A classical result of HA Schwarz (1873) relates the monodromy group of the hypergeometric equation to triangle groups in the hyperbolic plane. This was generalised by Deligne and Mostow (following earlier work of Picard) to hypergeometric functions of several variables. Among the resulting groups are some non-arithmetic lattices. In joint work with Deraux and Paupert we constructed more examples of non-arithmetic lattices. In this talk I will show these examples are monodromy groups of higherorder hypergeometric equations (in one variable).

Convergence and stability of manifolds under geometric constraints

• Lewis Tadman

Room: L50 (Psychology Auditorium) Given a sequence of closed, metric n-dimensional manifolds converging in the Gromov-Hausdorff topology, are there any relationships between terms in the tail of the sequence, or to the limit space? In this talk, we will discuss both questions under natural geometric constraints, such as a uniform contractibility function, and some of the literature surrounding this area. We will also consider when a sufficiently regular metric space (for example, topological n-manifolds with an associated distance function) can be approximated by a non-trivial sequence of spaces, and if there are any obstructions to this occurring. In particular, we verify a 1991 conjecture of Moore for finite-dimensional spaces. This is joint work with Mohammad Alattar (https://arxiv.org/abs/2507.17557).

A new metric for hyperbolic SU(2) 2-monopoles

• Thomas Galvin (University of Leeds)

Room: L50 (Psychology Auditorium) There is significant interest in the L^2 metric on the moduli space of SU(2) Euclidean monopoles, both because it is hyperkähler, and because it models monopole dynamics. No direct analogue of such a metric exists for hyperbolic monopoles, though alternatives have been suggested. I will discuss a new metric on the moduli space of parity inversion symmetric Hyperbolic SU(2) 2-monopoles based on the methods of O. Nash. This is joint work with my supervisor Derek Harland and Linden Disney-Hogg.

SL2-Tilings with Translational Symmetry

• Marie-Anne Bourgie (Université Laval)

Room: L50 (Psychology Auditorium) An SL2-tiling is a bi-infinite matrix in which all adjacent 2 × 2 minors are equal to 1. Positive integer SL2-tilings were introduced by Assem, Reutenauer and Smith as generalisations of classical Conway–Coxeter frieze patterns. We show that positive integer SL2-tilings with translational symmetry are in bijection with triangulations of annuli. We use this correspondence to study the properties of periodic positive integer SL2-tilings. This is joint work with Véronique Bazier-Matte, Anna Felikson, and Pavel Tumarkin.

Cohomogeneity one singularities of the Lagrangian Mean Curvature Flow

• Ben Lambert (University of Leeds)

Room: L50 (Psychology Auditorium) Lagrangian mean curvature flow (LMCF) is a geometric flow of n-dimenaional hypersurfaces in 2n-dimensional Calabi-Yau manifolds. As with most geometric flows, in general singularities of the flow occur. The famous Thomas--Yau--Joyce conjecture states that under certain conditions, LMCF converges to Special Lagragian manifolds, possibly after flowing through singularities. In this talk, I will describe recent results with A. Wood which classify the possible singularities of the flow in the case that the initial data is almost calibrated and cohomogeneity one under structure preserving group actions