Autumn 2025
The Seminar runs on Tuesdays at STRAND BLDG S5.20. This term, some talks will run from 15:00 to 16:00, and others will be in two parts – an introductory talk from 15:00 to 15:40 and a research talk from 15:45 to 16:30.
14 October, 15:00-16:00, STRAND BLDG S5.20
Speaker: Luca Tasin (Univeristy of Milan)
Title: Sasaki–Einstein metrics on spheres
Abstract: The differential geometry of spheres has long been a source of central problems in mathematics, and Sasaki–Einstein metrics—odd-dimensional analogues of Kähler–Einstein metrics—offer a particularly rich perspective, with significance both in geometry and in theoretical physics. In joint work with Yuchen Liu and Taro Sano, we construct infinitely many Sasaki–Einstein metrics on odd-dimensional spheres that bound parallelizable manifolds, thereby confirming conjectures of Boyer–Galicki–Kollár and Collins–Székelyhidi. Our approach is based on establishing the K-stability of certain Fano weighted hypersurfaces.
21 October, 15:00-16:00, STRAND BLDG S5.20
Speaker: Hannah Tillmann-Morris (KCL)
Title: Birational mirrors to pairs of Laurent polynomials
Abstract: Under mirror symmetry, deformation classes of Fano varieties are associated to mutation classes of maximally mutable Laurent polynomials (MMLPs). We expect birational relationships between the general members of two deformation classes to be reflected, in the pair of mirror mutation classes, as combinatorial relationships between two MMLPs.
I will present an alternative construction of a Fano variety that is mirror to a given MMLP, which uses mirror theorems of the Gross-Siebert program. The resulting Fano variety is difficult to describe explicitly. However, when two given MMLPs are related by certain combinatorial conditions, the construction can be extended to include the construction of a birational map between the two Fano varieties produced.
Applying all this to rigid MMLPs in two variables recovers all but one of the blow-ups in the chain of smooth del Pezzo surfaces.
28 October, 15:00-16:00, STRAND BLDG S5.20
Speaker: Sasha Veselov (Loughborough)
Title: Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$
Abstract: We show that the Markov fractions introduced recently by Boris Springborn are precisely the slopes of the exceptional vector bundles on $\mathbb P^2$ studied in 1980s by Dr`ezet and Le Potier and by Rudakov. In particular, we provide a simpler proof of Rudakov’s result claiming that the ranks of the exceptional bundles on $\mathbb P^2$ are Markov numbers.
4 November, 15:00-16:00, STRAND BLDG S5.20
Speaker: Roney Santos (King’s College London)
Title: Stability of minimal submanifolds
Abstract: We aim to introduce and discuss some concepts and results on the stability of minimal submanifolds, mainly when the ambient manifold is conformal either to a round sphere or to a convex domain of the Euclidean space. In particular, we will talk about a joint work with Alcides de Carvalho and Federico Trinca, in which we showed that a conformally Euclidean manifold with convex boundary does not admit volume-minimizing free boundary minimal submanifolds.
11 November, Part I: 15:00-15:40, Part II: 15:45-16:30, STRAND BLDG S5.20
Speaker: Cameron Gates Rudd (Oxford)
Title: TBD
Abstract: TBD
18 November, Part I: 15:00-15:40, Part II: 15:45-16:30, STRAND BLDG S5.20
Speaker: Dima Panov (KCL)
Title: TBD
Abstract: TBD
25 November, Part I: 15:00-15:40, Part II: 15:45-16:30, STRAND BLDG S5.20
Speaker: TBD (TBD)
Title: TBD
Abstract: TBD
2 December, Part I: 15:00-15:40, Part II: 15:45-16:30, STRAND BLDG S5.20
Speaker: Dan Ciubotaru (Oxford)
Title: TBD
Abstract: TBD
9 December, Part I: 15:00-15:40, Part II: 15:45-16:30, STRAND BLDG S5.20
Speaker: Jason Lotay (Oxford)
Title: TBD
Abstract: TBD