Yorkshire Durham Geometry Days

Upcoming Meeting

Date: 31st March 2026.
Location: University of York

Lecture room: Alcuin Seebohm Rowntree Building (Dept. of Health Sciences) room ATB/042 (D2 on campus map).

Lunch: We will meet for lunch at 12:30 at the Link Café, Church Lane Building, Church Lane (F2 on campus map).
Organisers: Ian McIntosh

Travel

By train: the nearest bus-stop is University Library. The U1/U2 bus runs from the opposite side of the road from the station, to Merchantgate and then to the

University.

By car: the nearest pay-and-display car-park is opposite the library, off University Road (called Campus Central on Google Maps).

Travel support for ECRs: contact Derek Harland if you would like to apply for support

Programme.

12:30-13:25 Lunch.

13:30-14:30 Georgios Kydonakis (Patras, Greece), Symplectic groups over involutive algebras and Higgs bundles.

14:35-15:35 Fernando Galaz-Garcia (Durham), A Myers-Steenrod Theorem for Singular Riemannian Foliations.

15:35-16:00 Afternoon Tea.

16:00-16:35 Nora Gavrea (Leeds), Shape modes of CP 1 vortices.

16:40-17:40 Johannes Nordstrom (Bath), Rational homotopy of 7- and 8-manifolds.

We will have dinner in York centre afterwards, probably at 18:30.

Abstracts.

Georgios Kydonakis (Patras, Greece) Symplectic groups over involutive algebras and Higgs bundles.

For a possibly noncommutative algebra A with an anti-involution σ, many classical Lie groups

can be realized as certain symplectic or orthogonal Lie groups over the pair (A, σ). When the

involutive algebra (A, σ) is Hermitian, one can define and study the associated Riemannian

symmetric space of such Lie groups. We will describe different geometric interpretations of

such symmetric spaces that generalize the various models of the hyperbolic plane viewed as

the symmetric space associated to the group SL 2 (R) = Sp 2 (R). Moreover, we will explore

implications of this theory in the realm of non-abelian Hodge theory using these new geometric

models of the symmetric space. This is joint work with Pengfei Huang, Eugen Rogozinnikov

and Anna Wienhard.

Fernando Galaz-Garcia (Durham), A Myers-Steenrod Theorem for Singular Riemannian Foliations.

The Myers–Steenrod theorem states that the isometry group of a Riemannian n-manifold is a

Lie group of dimension at most n(n+1)/2. If the manifold is compact, then its isometry group

is compact as well, by a theorem of van Dantzig and van der Waerden. These results underpin

the role of symmetry in Riemannian geometry and admit analogues in broader metric settings

such as Alexandrov and RCD spaces. Singular Riemannian foliations generalise both isometric

actions of compact Lie groups and Riemannian submersions, which induce decompositions into

embedded submanifolds of lower dimension. Although such foliations need not come from group

actions, one can still consider isometries of the ambient manifold that preserve the leaves of

the foliation, hence inducing isometries of the leaf space. In this talk I will present an analogue

of the Myers–Steenrod theorem for the group of foliated isometries of a Riemannian manifold

with a singular Riemannian foliation and discuss extensions to Alexandrov spaces. Joint work

with Diego Corro (Cardiff University).

Nora Gavrea (Leeds) Shape modes of CP 1 vortices.

In this talk, I will introduce the gauged sigma model with target CP 1 defined on a Rieman-

nian surface Σ, concentrating on the case Σ = R 2 . This model admits topological solitons

called vortices which attain a topological lower energy bound characterized by a pair of degrees

(k + , k − ). They come in two different species, which may coexist, and can be thought of as

two-dimensional analogues of magnetic monopoles. I will present a geometric formalism to

compute the second variation of the energy functional around a general (k + , k − )-vortex. On

a non-compact domain, such as R 2 , it is a nontrivial question whether the associated Jacobi

operator has any L 2 normalizable eigensections. Such eigensections are called ”shape modes”

in the physics literature, and, if present, they have a strong effect on the low energy scattering

behaviour of vortices. I will prove (on R 2 ) that all vortices have at least one shape mode,

and that such shape modes can be constructed by solving a simple scalar Schroedinger-type

eigenvalue problem. The formalism rests on deep structural properties of the model (its so

called Bogomolny decomposition), leading one to expect that it can be adapted to a wide class

2of structurally similar field theories. This is based on joint work with Derek Harland and Martin

Speight.

Johannes Nordstrom (Bath) Rational homotopy of 7- and 8-manifolds.

Rational homotopy equivalence is a weakening of the usual notion of homotopy equivalence,

that is easier to study algebraically in terms of commutative differential graded algebras (like

the de Rham complex of a smooth manifold). The simplest rational homotopy invariant is the

rational cohomology algebra, but there can in addition be so-called Massey products between

triples or higher tuples of classes that can also distinguish rational homotopy types.

Defining tensors on the cohomology of a space by multiplying triple or fourfold Massey

products by a further cohomology class gives an object that has less dependence on choices

than the Massey products themselves, making them easier to work with. On the other hand,

for a closed oriented manifold, Poincare duality allows all Massey products to be recovered

from these tensors. Moreover, suitable interpretations of these tensors can capture information

about the rational homotopy type even when the Massey products are undefined, and they

have nice functoriality properties. For closed k-connected manifolds of dimension up to 6k + 2

(k > 0), these tensors (along with the cohomology algebra itself) suffice to determine the

rational homotopy type. This is based on joint work with Diarmuid Crowley and Csaba Nagy.