Winter 2025
The Seminar runs on Tuesdays at STRAND BLDG S4.29. 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.
21 January, 15:00-16:00, STRAND BLDG S4.29
Speaker: Konstanze Rietsch (King’s College London)
Title: Generalising Euler’s Tonnetz
Abstract: Euler in 1739 wrote about a way to visualise harmonic relationships in music thus creating what is now called `Euler’s Tonnetz’. This talk is about Euler’s tonnetz from a modern point of view, and how to generalise it. Our ‘Tonnetze’ will take place on triangulated surfaces. We will, in particular, consider a set of examples that live on triangulations of tori and are related to crystallographic reflection groups, and a diatonic example related to a famous finite geometry.
28 January, Part I: 15:00-15:40, Part II: 15:45-16:30, STRAND BLDG S4.29
Speaker: Jeehoon Park (Seoul National Univeristy)
Title: Flat F-manifolds for Calabi-Yau smooth projective complete intersection varieties
Abstract: In this talk, I will explain how to construct formal flat F-manifold structures on the primitive cohomology H of a Calabi-Yau smooth projective complete intersection variety X. My strategy is to convert an analysis on H to study on non-isolated hypersurface singularities using the Cayley trick; we associate a dGBV (differential Gerstenhaber-Batalin-Vilkovisky) algebra A to H, and find a special solution to Maurer-Cartan equation in order to construct formal flat F-manifolds.
4 February, Part I: 15:00-15:40, Part II: 15:45-16:30, STRAND BLDG S4.29
Speaker: Yanki Lekili (Imperial College London)
Title: Deformations of cyclic quotient surface singularities via mirror symmetry
Abstract: Let $X_0$ be a rational surface with a cyclic quotient singularity $(1,a)/r$. Kawamata constructed a remarkable vector bundle $K_0$ on $X_0$ such that the finite-dimensional algebra $End(K_0)$, called the Kalck-Karmazyn algebra, “absorbs’’ the singularity of $X_0$ in a categorical sense. If we deform over an irreducible component of the versal deformation space of $X_0$ (as described by Kollár and Shepherd-Barron), the bundle $K_0$ also deforms to a vector bundle $K$. These results were established using abstract methods of birational geometry, making the explicit computation of the family of algebras challenging. We will utilise homological mirror symmetry to compute $End(K)$ explicitly. In the case of a Q-Gorenstein smoothing, this algebra $End(K)$ is a matrix order deforming the Kalck-Karmazyn algebra, and “absorbs” the singularity of the corresponding terminal 3-fold singularity. I will also discuss a conjecture describing irreducible components of the deformation space of $X_0$ in terms of the finite-dimensional algebra $End(K_0)$.
This is based on our joint work (on arXiv) with Jenia Tevelev.
11 February, Part I: 15:00-15:40, Part II: 15:45-16:30, STRAND BLDG S4.29
Speaker: Tyler Kelly (Queen Mary University London)
Title: Applying Exoflops to Calabi-Yau Complete Intersections in Toric Varieties
Abstract: Landau-Ginzburg (LG) models consist of the data of a quotient stack X and a regular complex-valued function W on X. Here, geometry is encapsulated in the singularity theory of W. One can find that LG models are deformations of Calabi-Yau complete intersections in some sense. Exoflops essentially create new GIT problems of partial compactifications of X, expanding the tractable birational geometries related to a given Calabi-Yau complete intersection. We will explain this technique, provide some foundational results about this and then some new applications proven recently for Calabi-Yau orbifolds. This talk contains results from a series of joint works with D. Favero (UMinn) and A. Malter (BIMSA).
18 February, Part I: 15:00-15:40, Part II: 15:45-16:30, STRAND BLDG S4.29
Speaker: Henry Wilton (University of Cambridge)
Title: On the congruence subgroup property for mapping class groups of surfaces
Abstract: I will relate two notorious open questions in low-dimensional topology. The first asks whether every hyperbolic group is residually finite. The second, the congruence subgroup property, relates the finite-index subgroups of mapping class groups of surfaces to the topology of the underlying surface. I will explain why, if every hyperbolic group is residually finite, then mapping class groups enjoy the congruence subgroup property. If there’s time, I may give some further applications to the question of whether hyperbolic 3-manifolds are determined by the finite quotients of their fundamental groups.
25 February, Part I: 15:00-15:40, Part II: 15:45-16:30, STRAND BLDG S4.29
Speaker: Samuel Johnston (Imperial College London)
Title: TBA
Abstract: TBA
4 March, Part I: 15:00-15:40, Part II: 15:45-16:30, STRAND BLDG S4.29
Speaker: Ximena Fernández (City St George’s, University of London)
Title: TBA
Abstract: TBA
11 March, Part I: 15:00-15:40, Part II: 15:45-16:30, STRAND BLDG S4.29
Speaker: TBA
Title: TBA
Abstract: TBA
18 March, Part I: 15:00-15:40, Part II: 15:45-16:30, STRAND BLDG S4.29
Speaker: Monika Kudlinska (University of Cambridge)
Title: TBA
Abstract: TBA
25 March, Part I: 15:00-15:40, Part II: 15:45-16:30, STRAND BLDG S4.29
Speaker: Andras Juhasz (University of Oxford)
Title: TBA
Abstract: TBA