Geometry and Topology
Please contact , Davide Spriano, or if you would like to speak or to suggest a speaker.
We will also attempt to maintain an up-to-date listing at .
The seminar will be hybrid, and will be run weekly in term. The talks are physically in B3.02 Zeeman Building on Thursdays, with times as listed below. We will open the approximately five minutes before the talk starts.
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29 October 2026 at 13:30 in B3.02
Speaker: Dawid Kielak (University of Oxford)
Title: Fibring of Poincare-duality groups
Abstract: I will introduce Poincare-duality groups, and talk about what we know about their virtual fibring properties.
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05 November 2026 at 13:30 in B3.02
Speaker: Danielle West (Tel Aviv University)
Title: Cores of modules over free group algebras
Abstract: Stallings core graphs are a powerful graphical representation of the finitely generated subgroups of a free group. They bring geometric insight to the study of free groups, make many properties and algorithmic tasks transparent, and are a ubiquitous tool in combinatorial and geometric group theory.
Free group algebras are strikingly analogous to free groups. Most notably, just as the Nielsen-Schreier theorem says that every subgroup of a free group is free, the Cohn-Lewin theorem says that every right (or left) ideal of a free group algebra is free. Yet free group algebras have had no counterpart to core graphs.
In this talk I will present one. We define the core of a module over a free group algebra, and show that it is unique whenever the module is algebraic (also known as bound). Many of the concepts of Stallings' theory, such as folding and pullbacks, generalize to these new objects, and this yields simple proofs and algorithms for many natural problems about free group algebras. For example, I will present an algorithm for testing primitivity in free modules which generalizes (Wilton's simplification of) Whitehead's classical algorithm for testing primitivity in free groups.
This is joint work with Doron Puder. -
12 November 2026 at 13:30 in B3.02
Speaker: Koji Fujiwara (Kyoto University)
Title: TBA
Abstract: TBA
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19 November 2026 at 13:30 in B3.02
Speaker: Giovanni Sartori (Heriot-Watt University)
Title: TBA
Abstract: TBA
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26 November 2026 at 13:30 in B3.02
Speaker: Antoine Poulin (University of 糖心TV)
Title: TBA
Abstract: TBA
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03 December 2026 at 13:30 in B3.02
Speaker: Alexander Nolte (Institut des Hautes Études Scientifiques)
Title: TBA
Abstract: TBA
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22 October 2026 at 13:30 in B3.02
Speaker: Laura Wakelin (King's College London)
Title: Constructing Lagrangians in symplectic toric 4-manifolds from multi-grid diagrams
Abstract: Triple grid diagrams were introduced by Blackwell, Gay and Lambert-Cole as a way to construct Lagrangians in CP2 through the lens of an underlying trisection. We generalise this to multi-grid diagrams, which can be used to construct Lagrangians in all symplectic toric 4-manifolds. We give examples of multi-grid diagrams for a range of Lagrangians in S2 x S2, including Evans’ recent non-squeezable Klein bottle. This is joint work with Shintaro Fushida-Hardy.
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15 October 2026 at 13:30 in B3.02
Speaker: Thomas Hill (University of 糖心TV)
Title: Mapping class groups of infinite graphs
Abstract: The group of topological symmetries of a surface, known as the mapping class group, provides a powerful lens for studying the geometry and topology of surfaces. The outer automorphism groups of a free group, Out(\(F_n\)), can be thought of as a graph-theoretic analog of the mapping class group. Although results do not translate directly between the surface and graph settings, their structural parallels inspire questions and techniques between these areas. Over the past decade, there has been a growing interest in studying big mapping class groups, namely those of infinite-type surfaces. In this talk, I will discuss recent progress on the analog of Out(\(F_n\)) for infinite graphs, including a rigidity theorem, results about the algebraic properties of their asymptotically rigid subgroups, and recent work on actions of these groups on hyperbolic spaces, particularly obstructions to general-type actions.
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08 October 2026 at 13:30 in B3.02
Speaker: Ana Isakovic (University of Cambridge)
Title: Top-dimensional \(l^2\)-homology of hyperbolic groups
Abstract: Computing \(l^2\)-homology can be a demanding task especially if one attempts to follow the definition directly. In this talk, I will speak about using automatic structures to construct top-dimensional \(l^2\)-cycles and how they can further be used to compute \(l^2\)-homology of certain hyperbolic groups.
Click on a title to view the abstract!