Upcoming Meetings

Leeds, Tuesday 2nd June 2026

Programme

Talks are in the MALL in Leeds School of Maths in building 84 on the campus map.

Coffee breaks are in the Maths Research Deck in building 74 on the campus map. This is directly opposite the main maths entrance.

11:30 Coffee and welcome in Maths Research Deck

12:00 Francesca Tripaldi (Leeds) Extracting subcomplexes on Carnot groups

Differential complexes are fundamental tools in geometry and analysis, encoding geometric structures through differential operators and cohomological invariants. In subRiemannian geometry, the classical de Rham complex is often replaced by more intrinsic subcomplexes, such as the Rumin complex, which better reflect the underlying graded structure. In this talk, I will discuss the problem of extracting differential subcomplexes adapted to Carnot groups and introduce a new family of complexes, called spectral complexes, arising from spectral sequence methods. I will present the construction of these complexes and outline some applications.

13:00 Lunch in the refectory

14:00 Joel Fine (Brussels) What does the Alexander polynomial know about minimal surfaces?

Let L be an oriented link in the 3-sphere. We will think of the 3-sphere as the ideal boundary of hyperbolic 4-space H^4. My talk will be about trying to count the number of oriented minimal surfaces in H^4 which have L as their ideal boundary. Firstly, I conjecture that this is a topological invariant of the link L. In other words, the number of minimal fillings doesn’t change under isotopies of the ideal boundary. Secondly, I conjecture that the number of genus g fillings of a link with k components gives the coefficient of z^{2g-1+k} in the Alexander polynomial of L. It turns out that these conjectures are related to the study of J-holomorphic curves in a certain symplectic 6-manifold. I will explain why I believe these conjectures, why I find them exciting, what has been proved so far, and what remains to be done. 

15:00 Zhengyao Huang (Durham) Smirnov Decomposition of a Horizontal Vector Charge in the Heisenberg Group

Joint work of Zhengyao Huang and Wilhelm Klingenberg. A divergence-free horizontal vector current in Heisenberg space may be viewed as an element of the dual space of horizontal test vector fields. By applying a horizontal Liouville theorem in this setting, the flow lines of such a vector field generate a family of horizontal curves and an associated measure on this collection. In this paper, we provide a direct proof of the Smirnov decomposition for a Federer-Fleming current within the horizontal distribution.

15:30 Tea and coffee break in Maths Research Deck

16:00 Prachi Sahjwani (Cardiff) When Does a Shape Know It's Almost a Sphere?

A recurring theme in geometry is that equality in a sharp inequality forces a shape to be perfectly round. But what happens near equality? If a domain nearly optimises the isoperimetric ratio, or the quermassintegral deficit, does it have to nearly look like a ball? I will discuss recent quantitative stability results for quermassintegral inequalities in hyperbolic space and Minkowski-type inequalities in warped product spaces, explaining how geometric flows give a natural route to such estimates and what new difficulties arise in curved settings.

17:00 Matthew Dales (Leicester) Flat space limits of symmetric Taub-NUT instantons

The Taub-NUT space is the prototypical example of an asymptotically locally flat (ALF) gravitational instanton. It is a Ricci-flat 4-manifold asymptotic to a circle bundle over R3 and interpolates between flat R4 and R3 × S1 by taking various limits of the metric. Yang-Mills instantons (anti-self-dual connections) on the Taub-NUT space may be constructed via a non-linear transform which identifies them with a set of ‘bow data’ solving an integrable ODE (Nahm’s equations) and a set of algebraic relations on an interval. In this talk we will discuss a classification of the moduli spaces of bow data corresponding to U(1)-symmetric SU (2) multi-instantons on the Taub-NUT space, and show how the bow data recovers the data for corresponding U(1)-symmetric instantons on flat R4 and calorons on R3 × S1 in various limits.

17:30 Leave for dinner in city centre

Directions and financial support

Financial support is available for the participation of PhD students and early career researchers.  Contact Derek Harland d.g.harland@leeds.ac.uk if you would like to request this.

The University of Leeds campus is about a 20 minute walk from Leeds train station.

The campus map can be downloaded here .

If you plan to travel by car please contact Derek Harland d.g.harland@leeds.ac.uk to arrange a parking space on campus.