Fri, 10 Jun 2022

13:30 - 17:00
Lecture Theatre 5

### Groups and Geometry in the South East

(Mathematical Institute)
Further Information

### Property (T) and random quotients of hyperbolic groups

#### 1:30

Calum Ashcroft (Cambridge)

In his original manuscript on hyperbolic groups, Gromov asked whether random quotients of non-elementary hyperbolic groups have Property (T). This question was later refined by Ollivier, and then answered in the case of random quotients of free groups by Zuk (and Kotowski--Kotowski).

In this talk we answer the Gromov--Ollivier question in the affirmative. We will discuss random quotients and some of their properties, in particular with relation to Property (T).

### Connections between hyperbolic geometry and median geometry

#### 2:45

Cornelia Drutu (Oxford)

In this talk I shall explain how groups endowed with various forms of hyperbolic geometry, from lattices in rank one simple groups to acylindrically hyperbolic groups, present various degrees of compatibility with the median geometry. This is joint work with Indira Chatterji, and with John Mackay.

### Division, group rings, and negative curvature

#### 4:00

Grigori Avramidi (Bonn)

In 1997 Delzant observed that fundamental groups of hyperbolic manifolds with large injectivity radius have nicely behaved group rings. In particular, these rings have no zero divisors and only the trivial units. In this talk I will explain how to extend this observation to show such rings have a division algorithm (generalizing the division algorithm for group rings of free groups discovered by Cohn) and that these group rings havefreedom theorems’’ showing that all of their ideals that are generated by few elements are free, where the specific value of `few’ depends on the injectivity radius of the manifold (which can be viewed as generalizations from subgroups to ideals of some freedom theorems of Delzant and Gromov). This has geometric consequences to the homotopy classification of 2-complexes with surface fundamental groups and to complexity of cell structures on hyperbolic manifolds.

Thu, 09 Jun 2022

12:00 - 13:00
L1

### The ever-growing blob of fluid

Graham.Benham@maths.ox.ac.uk
(Mathematical Institute)
Abstract

Consider the injection of a fluid onto an impermeable surface for an infinite length of time... Does the injected fluid reach a finite height, or does it keep on growing forever? The classical theory of gravity currents suggests that the height remains finite, causing the radius to grow outwards like the square root of time. When the fluid resides within a porous medium, the same is thought to be true. However, recently I used some small scale experiments and numerical simulations, spanning 12 orders of magnitude in dimensionless time, to demonstrate that the height actually grows very slowly, at a rate ~t^(1/7)*(log(t))^(1/2). This strange behaviour can be explained by analysing the flow in a narrow "inner region" close to the source, in which there are significant vertical velocities and non-hydrostatic pressures. Analytical scalings are derived which match closely with both numerics and experiments, suggesting that the blob of fluid is in fact ever-growing, and therefore becomes unbounded with time.

Fri, 18 Feb 2022

14:00 - 17:00
L2

### Centre for Topological Data Analysis Group Meeting

Various Speakers
(Mathematical Institute)
Fri, 21 Jan 2022

15:00 - 16:00
L6

### A Multivariate CLT for Dissociated Sums with Applications to Random Complexes

(Mathematical Institute)
Abstract

Acyclic partial matchings on simplicial complexes play an important role in topological data analysis by facilitating efficient computation of (persistent) homology groups. Here we describe probabilistic properties of critical simplex counts for such matchings on clique complexes of Bernoulli random graphs. In order to accomplish this goal, we generalise the notion of a dissociated sum to a multivariate setting and prove an abstract multivariate central limit theorem using Stein's method. As a consequence of this general result, we are able to extract central limit theorems not only for critical simplex counts, but also for generalised U-statistics (and hence for clique counts in Bernoulli random graphs) as well as simplex counts in the link of a fixed simplex in a random clique complex.

Fri, 03 Dec 2021

16:00 - 17:00
L1

### North Meets South

Candida Bowtell and Joshua Bull
(Mathematical Institute)
Abstract

This session will take place live in L1 and online. A Teams link will be shared 30 minutes before the session begins.

Candida Bowtell

Title: Chess puzzles: from recreational maths to fundamental mathematical structures

Abstract:
Back in 1848, in a German chess magazine, Max Bezzel asked how many ways there are to place 8 queens on a chessboard so that no two queens can attack one another. This question caught the attention of many, including Gauss, and was subsequently generalised. What if we want to place n non-attacking queens on an n by n chessboard? What if we embed the chessboard on the surface of a torus? How many ways are there to do this? It turns out these questions are hard, but mathematically interesting, and many different strategies have been used to attack them. We'll survey some results, old and new, including progress from this year.

Joshua Bull

Title: From Cancer to Covid: topological and spatial descriptions of immune cells in disease

Abstract:
Advances in medical imaging techniques mean that we have increasingly detailed knowledge of the specific cells that are present in different diseases. The locations of certain cells, like immune cells, gives clinicians clues about which treatments might be effective against cancer, or about how the immune system reacts to a Covid infection - but the more detailed this spatial data becomes, the harder it is for medics to analyse or interpret. Instead, we can turn to tools from topological data analysis, mathematical modelling, and spatial statistics to describe and quantify the relationships between different cell types in a wide range of medical images. This talk will demonstrate how mathematics can be used as a tool to advance our understanding of medicine, with a focus on immune cells in both cancer and covid-19.

Fri, 19 Nov 2021

16:00 - 17:00
L1

### Mathematigals

(Mathematical Institute)
Abstract

This session will take place live in L1 and online. A Teams link will be shared 30 minutes before the session begins.

How can we make maths more accessible, promote its many applications, and encourage more women to enter the field? These are the questions we aim to address with Mathematigals.

Caoimhe Rooney and Jessica Williams met in 2015 at the start of their PhDs in mathematics in Oxford, and in 2020, they co-founded Mathematigals. Mathematigals is an online platform producing content to demonstrate fun mathematical curiosities, showcase ways maths can be used in real life, and promote female mathematicians. Mathematigals primarily produces animated videos that present maths in a way that is engaging to the general public.

In this session, Jess and Caoimhe will talk about their initial motivation to begin Mathematigals, demonstrate the process behind their content creation, and describe their future visions for the platform. The session will end with an opportunity for the audience to provide feedback or ideas to help Mathematigals on their journey to encourage future mathematicians.

Fri, 12 Nov 2021

16:00 - 17:00
L1

### North Meets South

Anna Parlak and Gill Grindstaff
(Mathematical Institute)
Abstract

This session will take place live in L1 and online. A Teams link will be shared 30 minutes before the session begins.

Fri, 29 Oct 2021

16:00 - 17:00
L1

Edwina Yeo and Jay Swar
(Mathematical Institute)
Abstract

This session will take place live in L1 and online. A Teams link will be shared 30 minutes before the session begins.

Fri, 22 Oct 2021

16:00 - 17:00
L1

### What does a DPhil in Oxford look like?

Brian Tyrrell, Naya Yerolemou and Alice Kerr
(Mathematical Institute)
Abstract

This session will take place live in L1 and online. A Teams link will be shared 30 minutes before the session begins.

Thu, 14 Jan 2021

10:00 - 12:00
Virtual

### An invitation to matroid theory - Day 3, Lectures 1 & 2

Greg Henselman-Petrusek
(Mathematical Institute)
Further Information

Zoom passcode: Basis

Abstract

Giancarlo Rota once wrote of matroids that "It is as if one were to
condense all trends of present day mathematics onto a single
structure, a feat that anyone would a priori deem impossible, were it
not for the fact that matroids do exist" (Indiscrete Thoughts, 1997).
This makes matroid theory a natural hub through which ideas flow from
one field of mathematics to the next. At the end of our three-day
workshop, participants will understand the most common objects and
constructions in matroid theory to the depth suitable for exploring
many of these interesting connections. We will also pick up some
highly practical matroid tools for working through problems in
persistent homology, (optimal) cycle representatives, and other
objects of interest in TDA.

#### Day 3, Lecture 1

Circuits in persistent homology

#### Day 3, Lecture 2

Exercise: write your own persistent homology algorithm!

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