The King's College London geometry seminar runs weekly during term time inperson. Currently no hybrid option is offered. Talks take one hour, directly after we go for a coffee break in the common room S5.21 in the Strand building. The seminar is organised by Martin de Borbon, Daniel Platt, and Mehdi Yazdi. If you want to receive regular seminar announcements, please subscribe to the seminar ling list at mailman.kcl.ac.uk/mailman/listinfo/kclgeometryseminar. Seminars take place in Bush House South Wing, SouthEast Wing, and the King's Building. You can find a campus map here: strandmap.pdf. If you do not have a King's ID card, please email me, so that I can ask security to let you into the building in advance.
Time: 19 Apr 2022, 15.3016.30  Room: KINGS BLDG K1.26 
Speaker: Nikon Kurnosov (UCL) Title: Automorphisms of BGmanifolds Abstract: The goal of a talk is to shed some light on the geometry of a partial class of nonKahler manifolds, described in the works of Bogomolov and Guan, which we call BGmanifolds. In particular, we establish some properties of groups of biholomorphic and bimero morphic automorphisms of BGmanifolds. I will study the degenerate fibers of an algebraic reduction of a BGmanifold and use is to prove the Jordan property of the group of biholomorphic automorphisms of a BGmanifold. 

Time: 26 Apr 2022, 15.3016.30  Room: Bush House (SE) 2.01 
Speaker: Daniel Platt (KCL) Title: Associatives in the generalised Kummer construction Abstract: Associative submanifolds are certain 3dimensional manifolds in 7dimensional manifolds. They are calibrated, and therefore minimal surfaces, and there is a research programme that attempts to count them in order to define numerical invariants of manifolds, similar to GromovWitten invariants. However, not many examples of associative submanifolds are known, which is one of the difficulties in working out the details of this programme. In the talk I will explain how to construct some dozens of associatives whose existence had previously been predicted by physicists. 

Time: 3 May 2022, 15.3016.30  Room: Bush House (SE) 2.01 
Speaker: Ragini Singhal (KCL) Title: Deformation theory of nearly G_2 manifolds Abstract: We study the deformation theory of nearly G_2 manifolds. These are seven dimensional manifolds admitting real Killing spinors. We show that the infinitesimal deformations of nearly G_2 structures are obstructed in general. Explicitly, we prove that the infinitesimal deformations of the homogeneous nearly G_2 structure on the AloffWallach space are all obstructed to second order. We also completely describe the cohomology of nearly G_2 manifolds. The talk is based on a joint work with Shubham Dwivedi (HU, Berlin). 

Time: 10 May 2022, 15.3016.30  Room: Bush House (SE) 2.01 
Speaker: Nicholas SheperdBarron (KCL) Title: Periods of elliptic surfaces Abstract: Elliptic surfaces are one of the classes of complex algebraic surfaces picked out in the EnriquesKodaira classification of surfaces. In this talk we shall explain how, given a generic such surface X, the primitive part of H^{1,1}(X) has a natural orthonormal basis defined by certain meromorphic 2forms of the 2nd kind. We shall also describe the variational approach that leads to this result and that underlies other aspects of these surfaces, their moduli and their periods. The primary aim, however, is to convey some of these ideas to a general geometricallyminded audience. 

Time: 17 May 2022, 15.3016.30  Room: Bush House (SE) 2.01 
Speaker: seminar cancelled Title: seminar cancelled Abstract: seminar cancelled 

Time: 24 May 2022, 15.3016.30  Room: Bush House (SE) 2.01 
Speaker: Giuseppe Tinaglia (KCL) Title: A structure theorem for properly embedded CMC surfaces of finite genus and applications Abstract: I will discuss the geometry of CMC surfaces embedded in Euclidean space with finite genus and, among other things, prove a local area estimate for such surfaces. This is joint work with Bill Meeks. 

Time: 31 May 2022, 15.3016.30  Room: Bush House (SE) 2.01 
Speaker: Simon Salamon (KCL) Title: The Horrocks bundle as an instanton Abstract: The Horrocks bundle (not to be confused with the HorrocksMumford bundle) is an indecomposable holomorphic rank 3 bundle over CP^5 with c_2=3. It can be interpreted as a solution of the YangMills equations on the quaternionic projective plane HP^2, via a Penrose transform and twistor equation. In joint work with Udhav Fowdar, this realization leads to the existence of nowherevanishing spinors on HP^2 invariant by SU(3). I shall use this example to introduce instantons associated with Gstructures in higher dimensions, cohomogeneityone actions by SU(3), and Spin(7) structures on 8manifolds. 

Time: 15 June 2022 (Wednesday!), 15.3016.30  Room: Bush House (NE) 2.01 (Unusual room!) 
Speaker: Guillaume Tahar (Weizmann) Title: Quadratic differentials and applications to spherical geometry (joint work with Quentin Gendron) Abstract: Up to biholomorphic change of variable, local invariants of a quadratic differential at some point of a Riemann surface are the order and the residue if the point is a pole of even order. Using the geometric interpretation in terms of flat surfaces, we solve the RiemannHilbert type problem of characterizing the sets of local invariants that can be realized by a pair (X,q) where X is a compact Riemann surface and q is a meromorphic quadratic differential. As an application to geometry of surfaces with positive curvature, we give a complete characterization of the distributions of conical angles that can be realized by a cone spherical metric with dihedral monodromy. 
Time: 1 Mar 2022, 15.3016.30  Room: Bush House South Wing 2.02 
Speaker: Martin de Borbon (KCL) Title: Polyhedral Kahler cone metrics on C^n Abstract: I will discuss a particular class of flat torsion free meromorphic connections on Cn with simple poles at hyperplane arrangements. The main result is that, if the holonomy is unitary, then the metric completion (of the flat Kahler metric on the arrangement complement) is polyhedral. Taking the quotient by scalar multiplication leads to new interesting FubiniStudy metrics with cone singularities. In the case of the braid arrangement, our result extends to higher dimensions the wellknown existence criterion for spherical metrics on the projective line with three cone points (which goes back to Klein's work on the monodromy of Gauss' hypergeometric equation). This is joint work with Dmitri Panov. 

Time: 8 Mar 2022, 15.3016.30  Room: KINGS BLDG K0.19 
Speaker: Tim Magee Title: Cluster varieties building a new playground for toric geometers Abstract: Toric varieties are some of the simplest and beststudied objects in algebraic geometry. Many geometric notions have elegant pictorial and combinatorial descriptions in the toric world. I'll describe compactified cluster varieties as a generalization of toric varieties and explain how some of the pictorial and combinatorial gadgets of toric geometry can extend to the cluster setting. In particular, I plan to discuss extensions of following toric geometry topics: fans, polyhedra, convexity, Minkowski sums, and the Batyrev/ BatyrevBorisov mirror constructions for CalabiYau subvarieties of Gorenstein toric Fanos. Some parts of this are worked out while others are still in the naïve guess stage. I'll indicate what we know, what we hope, and what causes complications. Based on collaborations with Lara Bossinger, Mandy Cheung, Juan Bosco Frías Medina, and Alfredo Nájera Chávez. 

Time: 15 Mar 2022, 15.3016.30  Room: 
No seminar  
Time: 22 Mar 2022, 15.3016.30  Room: Bush House SouthEast Wing 1.02 
Speaker: Calum Spicer (KCL) Title: Boundedness of surface foliations Abstract: I will explain some work relating to the boundedness of holomorphic foliations on algebraic surfaces using techniques from birational geometry and the minimal model program. I will then explain some applications of these ideas to some classical problems in foliation theory (e.g., can we bound the degree of an algebraic orbit of a polynomial vector field on the plane), as well as some applications to more modern problems (e.g., moduli spaces of holomorphic foliations). 

Time: 29 Mar 2022, 15.3016.30  Room: KINGS BLDG K0.19 
Speaker: Mehdi Yazdi (KCL) Title: The fully marked surface theorem Abstract: In his seminal 1976 paper, Bill Thurston observed that a closed leaf S of a codimension1 foliation of a compact 3manifold has Euler characteristic equal, up to sign, to the Euler class of the foliation evaluated on [S], the homology class represented by S. We give a converse for taut foliations: if the Euler class of a taut foliation F evaluated on [S] equals up to sign the Euler characteristic of S and the underlying manifold is hyperbolic, then there exists another taut foliation G such that S is homologous to a union of compact leaves and such that the plane field of G is homotopic to that of F. In particular, F and G have the same Euler class. In the same paper Thurston proved that taut foliations on closed hyperbolic 3manifolds have Euler class of norm at most one, and conjectured that, conversely, any integral cohomology class with norm equal to one is the Euler class of a taut foliation. My previous work, together with our main result, gives a negative answer to Thurston's conjecture. We mention how Thurston's conjecture leads to natural open questions on contact structures, flows, as well as representations into the group of homeomorphisms of the circle. This is joint work with David Gabai. 