Hello! This is the website for the London Low Dimensional Topology Seminar, a seminar for low-dimensional topologists at any career stage! We are big proponents of a vertical approach, and our regular attendees range from senior academics to masters' students and final year undergraduates.
We currently meet on Wednesdays at 14:00, with (optional) lunch together beforehand. Rooms and other details will be communicated via email, as these vary week to week.
To be added to the email list, please email one of the organisers :)
Organisers: Alessandro Cigna, KCL (firstname.surname@kcl.ac.uk), Xander Povey, Imperial (firstname.surname23@imperial.ac.uk) and Maartje Wisse, LSGNT (firstname.surname@kcl.ac.uk)
21st January: Ayodeji Lindblad, MIT
Title: Boundary Dehn twists after abelianization
Abstract: Work of Kronheimer-Mrowka, Jianfeng Lin, Baraglia-Konno, and Tilton shows that the boundary Dehn twist on punctured X is non-trivial in the smooth relative mapping class group for X the K3 surface, the once-stabilized K3 surface, a connected sum of two K3 surfaces, and any one of the infinitely many complete intersections with first Chern class divisible by 32 and signature 16 modulo 32. For X any of these spaces (or any other finite connected sum and stabilization of an important class of complex surfaces including the elliptic surfaces E(n)), we build a smooth X-bundle over the torus whose total space has non-vanishing w_2 to prove that the boundary Dehn twist on punctured X is trivial after abelianization. This generalizes work of Lin, which applied the global Torelli theorem and an obstruction of Baraglia-Konno to prove the corresponding statement for X the K3 surface.
28th January: Monika Kudlinska, University of Cambridge
Title: Geometry of mapping tori
Abstract: The geometry of a mapping torus of a surface diffeomorphism is determined by the dynamics of the monodromy map. In particular, Thurston showed that such a mapping torus is hyperbolic exactly when the monodromy is pseudo-Anosov. In this talk, we will consider mapping tori of homotopy equivalences of graphs. Parallel to the 3-manifold setting, such mapping tori are Gromov-hyperbolic precisely when the monodromy map does not periodically on conjugacy classes of closed curves in the graph. Moreover, as in the case of closed hyperbolic 3-manifolds, hyperbolic mapping tori are virtually modelled by CAT(0) cube complexes. On the other hand, the geometry of non-hyperbolic mapping tori has remained largely mysterious. I will discuss recent joint work with Harry Petyt in which we resolve several open questions on the geometry of such spaces by constructing natural Gromov-hyperbolic quotients that detect Morse geodesic of the original spaces.
4th February: Giovanni Italiano, University of Oxford
Title: Improved virtual algebraic fibrations of high dimensional hyperbolic Coxeter groups
Abstract: In a recent paper, Lafont, Minemyer, Sorcar, Stover, and Wells built hyperbolic right-angled Coxeter groups that virtually algebraically fibre in any virtual cohomological dimension.
We provide a new construction that allows us to construct groups that virtually fibre with finitely presented kernel.
Obtaining finite presentability is usually a big step forward, since it allows to use homological methods (due to Kielak and Fisher) to leverage even stronger finiteness properties. However, our technique is quite in dissonance with this, so these particular examples do not seem to be upgradable in general.
This is joint work with Matteo Migliorini and Andrew Ng.
11th February: Ananya Satsokar, KCL
Title: Algebraic Structure of the Torelli Group
Abstract: The mapping class group is the group of all orientation-preserving self-homeomorphisms of a surface (up to isotopy). Mapping classes define a natural action on the first homology of the surface through diffeomorphisms, which also preserve the algebraic intersection number associated to homology cycles; this gives us a representation from the mapping class group into the symplectic group. The kernel of this representation, the Torelli group, is the subgroup of the mapping class group whose action on homology is trivial. This is a rich and mysterious group whose algebraic structure is not yet well understood. In this talk I will first discuss why existing methods in the area do not work for the Torelli group, then construct two relations in the Torelli group and discuss some work in progress aimed at studying its algebraic structure by combining work by Birman, Johnson and Putman. There will be many pictures!
18th February: Xander Povey, Imperial College London
Title: Overview of the inscribed square problem
Abstract: In 1911, Otto Toeplitz conjectured that every Jordan curve in the plane inscribes a square. In the following hundred years, much progress has been made, however a solution to Toeplitz's original problem remains elusive. In this talk, we will cover the last century's worth of attempts to prove the conjecture, culminating with recent work of Greene and Lobb, which shows the existence of rectangles of any ratio inscribed within a smooth curve. Their method uses a non-existence result for symplectic embeddings of Klein bottles in Euclidean four-space.
25th February: Susanna Terron, University of Glasgow
Title: Thompson representatives and connected sum
Abstract: In 2017 Vaughan Jones introduced a construction associating links to elements of Thompson’s group F and its generalisation F3. He then proved that all links can be obtained in such a way, opening the way to new possible connections between these objects.
In this talk I will present Jones’ construction and extend it to obtain a surjective map into the set of pointed links. I’ll then define a new algebraic structure by endowing F3 with a monoid operation, which turns our map into a surjective monoid homomorphism, with image the monoid of pointed links with operation connected sum. As a consequence, we obtain a standard form for connected sum representatives, which can then be extended to obtain representatives for a certain family of links that we will refer to as tree links.
This is based on the following paper: https://arxiv.org/abs/2511.21259
4th March: Raphael Zentner, Durham University
Title: TBA
Abstract: TBA
11th March: TBA, TBA
Title: TBA
Abstract: TBA
15th October: Steven Sivek, Imperial College London
Title: Ribbon concordance and fibered predecessors
Abstract: Ribbon concordance defines an interesting relation on knots. In his initial work on the topic, Gordon asked whether it is a partial order, and this question was open for over 40 years until Agol answered it affirmatively in 2022. However, we still don’t know many basic facts about this partial order: for example, does any infinite chain of ribbon concordances eventually stabilize? Even better, if we fix a knot in the 3-sphere, are there only finitely many knots that are ribbon concordant to ? I’ll talk about joint work with John Baldwin toward these questions, in which we use tools from both Heegaard Floer homology and hyperbolic geometry to say that at the very least, there are only finitely many fibered hyperbolic knots ribbon concordant to.
22nd October: Misha Schmalian, Oxford University
Title: Uniqueness of Dehn Surgery
Abstract: Dehn Surgery is an operation that allows us to describe any three-manifold via a framed link in the three-sphere. How unique is such a description? Recently, there has been substantial progress and attention on questions of this nature. In this talk I will:
Give an introduction to Dehn surgery problems and how tackle them using Geometrization;
Discuss some recent and some upcoming work with Marc Kegel on this topic;
Give a longer exposition of open questions in the area (not all of which look impossible).
29th October: Maartje Wisse, LSGNT/King's College London
Title: The Dowlin Spectral Sequence for Dummies
Abstract: Rasmussen's 2005 conjecture that there should be a spectral sequence from Khovanov Homology to Knot Floer Homology was fully proved by Dowlin in 2018, following on from various similar earlier results. In this talk I will cover the motivation to build such an object, as well as an outline of the arguments used in Dowlin's construction. If time allows I will lay out the work I am doing with this. This is intended to be an overview talk and will be as light on the details as is possible!
5th November: No seminar for KCL Reading Week!
12th November: Gheehyun Nahm, Princeton University
Title: Barbells and Knotted things
Abstract: In 2019, Budney and Gabai defined barbell diffeomorphisms and used them to construct knotted 3-balls in S^4. Barbell diffeomorphisms provide a concise and hands-on method to produce interesting diffeomorphisms of 4-manifolds. After introducing barbell diffeomorphisms, we explore further applications of them: first, we construct knotted S^3’s in S^5 with four critical points with respect to the standard height function. This, in particular, produces knotted solid tori in S^4, proving the remaining case of a conjecture of Budney and Gabai. Time permitting, we also use barbell diffeomorphisms to construct Brunnian links of 3-balls in S^4. This is joint work with Seungwon Kim and Alison Tatsuoka.
19th November: Selim Ghazouani, UCL
Title: Dynamical systems, surface homeomorphisms and 3-manifolds
Abstract: I will try to explain how Thurston's introduction of dynamical systems in low-dimensional topology revolutionised the field in the 70s.
26th November: Soheil Azarpendar, University of Oxford
Title: On Fox’s trapezoidal conjecture
Abstract: An old and challenging conjecture proposed by R. H. Fox in 1962 states that the absolute values of the coefficients of the Alexander polynomial of an alternating knot are trapezoidal, i.e. they strictly increase, possibly plateau, then strictly decrease. In this talk, I will describe a recent development on the conjecture, based on joint work with András Juhász and Tamás Kálmán, where we prove it for diagrammatic plumbings of special alternating links and obtain partial results for alternating three-braid closures.
3rd December: Alessandro Cigna, King's College London
Title: Constructing Taut Foliations: Ideas from Gabai’s Theory
Abstract: Taut foliations provide powerful insight into the topology of 3-manifolds, yet determining which manifolds admit such structures remains a central question in low-dimensional topology. In 1980, Gabai introduced the framework of sutured manifolds, offering a systematic way to construct taut foliations and to analyse their behaviour under topological operations. Using this machinery, he proved that every oriented, compact, irreducible 3-manifold with torus boundary and positive first Betti number admits a taut foliation. He also applied similar techniques to knot theory, showing that the Seifert algorithm produces minimal-genus Seifert surfaces for alternating links.
In this talk, I will introduce the sutured manifold theory developed by Gabai and outline the ideas behind these influential results.
10th December: Abigail Hollingsworth, University of Warwick
Title: From the boundary of Dehn surgery space to the real locus of the shape variety.
Abstract: The complement of the 5_2 knot is a hyperbolic three-manifold. We will take its ideal triangulation and define its shape variety from the edge gluings of the triangulation. Defining the Dehn filling equation for three-manifolds, we will build the Dehn surgery space of the 5_2 knot complement.
In many pictures of Dehn surgery space, we see the real representations corresponding to straight lines on the boundary of Dehn surgery space. Is this always true?
A 'nice' type of flattening of tetrahedra shapes is a called a taut flattening. Given a path of positive volume tetrahedra to a flattening, that flattening is always taut.
Is it possible for a taut flattening to be approached by a path of tetrahedra that contain some negative volume tetrahedra?
What other questions can we ask about the relationships between real shapes on the shape variety and the boundary of Dehn surgery space?
17th December: Laura Wakelin, UT Austin
Title: Dehn surgery functions are never injective
Abstract: For any fixed rational number p/q, Dehn surgery gives a map from the set of knots in the 3-sphere to the set of closed orientable 3-manifolds. In 1978, Gordon conjectured that these maps are never injective. I will discuss some results which demonstrate non-injectivity for some special cases of p/q, before going on to discuss joint work with Kyle Hayden and Lisa Piccirillo in which we prove the conjecture using rational RBG links and the zeroth HOMFLYPT polynomial.
For the seminar's 2024-2025 program, please click here (full credit and thanks to Laura Wakelin!)