Mon, 04 May 2026
15:30
15:30
L5
The prime decomposition fibre sequence for moduli spaces of 3-manifolds
Jan Steinebrunner
(Cambridge)
Abstract
Milnor's prime decomposition theorem states that every oriented 3-manifold M is diffeomorphic can be written as a connected sum of "prime" manifolds in an essentially unique way: M == P_1 # ... # P_n # (S^1 x S^2)^{#g}. This reduces many questions about 3-manifolds to the prime case, but when studying 3-manifolds in families this reduction is not so straightforward. For example, a diffeomorphism of M need not respect the decomposition into prime factors.
I will explain recent joint work with Boyd and Bregman, in which we use a homotopical version of the prime decomposition theorem to describe the classifying space BDiff(M) (the "moduli space" of M) in terms of moduli spaces of the P_i. More precisely, we establish a "prime decomposition fibre sequence" that describes the moduli space in terms of BDiff(P_1 u ... u P_n) and a space of handle-attachments that is amenable to computations. To illustrate this, I will discuss our calculation of the rational cohomology ring of BDiff((S^1 x S^2)#(S^1 x S^2)).
Tue, 26 May 2026
15:00
15:00
L6
Groethendieck pairs from iterated Dehn filling
Francesco Fournier-Facio
(Cambridge)
Abstract
A Groethendieck pair consists of a finitely generated residually finite group G, with a finitely generated subgroup N such that the inclusion N -> G induces an isomorphism of profinite completions. I will present a new method to produce Groethendieck pairs with peculiar properties, using iterated group theoretic Dehn filling on hyperbolic virtually special groups. Such pairs witness the profinite non-invariance of quasimorphisms, stable commutator length, and actions on hyperbolic spaces and finite-dimensional CAT(0) cube complexes.
Thu, 07 May 2026
14:00 -
15:00
Lecture Room 3
Private estimation in stochastic block models
Prof Po-Ling Loh
(Cambridge)
Abstract
Professor Po-Ling Loh will talk about; 'Private estimation in stochastic block models'
We study the problem of private estimation for stochastic block models, where the observation comes in the form of an undirected graph, and the goal is to partition the nodes into unknown, underlying communities. We consider a notion of differential privacy known as node differential privacy, meaning that two graphs are treated as neighbors if one can be transformed into the other by changing the edges connected to exactly one node. The goal is to develop algorithms with optimal misclassification error rates, subject to a certain level of differential privacy.
We present several algorithms based on private eigenvector extraction, private low-rank matrix estimation, and private SDP optimization. A key contribution of our work is a method for converting a procedure which is differentially private and has low statistical error on degree-bounded graphs to one that is differentially private on arbitrary graph inputs, while maintaining good accuracy (with high probability) on typical inputs. This is achieved by considering a certain smooth version of a map from the space of all undirected graphs to the space of bounded-degree graphs, which can be appropriately leveraged for privacy. We discuss the relative advantages of the algorithms we introduce and also provide some lower-bounds for the performance of any private community estimation algorithm.
This is joint work with Laurentiu Marchis, Ethan D'souza, and Tomas Flidr.
Fri, 20 Feb 2026
16:00
16:00
L1
Where do you draw the (dividing) line?
Julia Wolf
(Cambridge)
Abstract
A longstanding classification programme in model theory aims to determine when a mathematical structure exhibits tame, structurally simple—as opposed to wild, intractable—behaviour. A key role is played by so-called dividing lines, i.e. properties of logical formulas (or theories) that separate these regimes. In this talk, we demonstrate how the lens of combinatorics has allowed us to gain new insight into higher-order dividing lines, drawing on examples in graphs and groups. We also explain how this perspective has led to advances in higher-order Fourier analysis and statistical learning.
This talk intends to be accessible to beginning graduate students in all areas of mathematics.
Wed, 05 Nov 2025
16:00 -
17:00
L6
Improving acylindrical actions on trees
Will Cohen
(Cambridge)
Abstract
Loosely speaking, an action of a group on a tree is acylindrical if long enough paths must have small stabilisers. Groups admitting such actions form a natural subclass of acylindrically hyperbolic groups, and interesting an feature of acylindrical actions on trees is that many interesting properties are inherited from their vertex stabilisers. In order to make use of this, it is important to have some degree of control over these stabilisers. For example, can we ask for these stabilisers to be finitely generated, or even malnormal (or finite-height)? Even stronger, if our group is hyperbolic, can we ask for the stabilisers to be quasiconvex?
In this talk, I will introduce acylindrical actions and some stronger and related concepts, and discuss a method known as the Dunwoody—Sageev resolution that we can use to move between these concepts and provide positive answers to the above questions in some cases.
Tue, 10 Mar 2026
15:00
15:00
L6
Automaticity of generalised triangle groups and relationship with l^2 homology
Ana Isakovic
(Cambridge)
Abstract
In 1984 Cannon showed that cocompact discrete hyperbolic groups have finitely many cone types. In this talk, I will demonstrate how this result can be extended to non-positively curved k-fold triangle groups. I will further show how this implies that such groups have an automatic structure and how we can use this information to construct top dimensional l^2 cycles.