# Warwick Women in Maths

##### Wednesday 10th March 2021

This afternoon-only online event aims to celebrate the achievements of female and non-binary mathematicians. Alongside this, we aim to inspire female and non-binary undergraduates to pursue a PhD in maths or related subjects.

There will be presentations on a wide range of topics covering different areas of pure and applied maths. We will conclude the event with an informal Q&A session with current PhD students.

Join us on MS Teams on Wednesday 10th March to find out more about what research in maths looks like, where a career in maths can take you, and to gain an insight into the personal experiences of a variety of mathematicians.

## Event details

• Wednesday 10th March 1.20pm onwards
• The event will be held online. Please use this link to join the MS team for the event
• Alternatively, please email the organisers to be sent a link to the event

The event is open to anyone regardless of gender or background. Feel free to drop in to as many talks as you like. We look forward to seeing you there!

## Schedule

Please note that there will be a 5 minute Q&A and handover between each talk.

1.20 - 1.30 : Welcome and introduction!

1.30 - 1.45 : Adela Gherga - Computing elliptic curves over $$\mathbb{Q}$$

1.50 - 2.05 : Ellie Archer - Random fractal trees

2.10 - 2.25 : Sophie Meakin - Mathematical modelling and forecasting during the COVID-19 pandemic

2.30 - 2.45 : Coffee break

2.45 - 3.10 : Josephine Evans - Entropy and collective motion

3.15 - 3.40 : Susana Gomes - From linear control theory to nonlinear dynamics: controlling thin film flows

3.45 - 4.00 : Coffee break

4.00 - 4.45 : Carolina Araujo - Algebraic geometry - research and trajectory

4.45 - 5.30 : Panel discussion and Q&A with current PhD students

## Keynote speaker

#### Carolina Araujo

Carolina is a Brazilian mathematician working in the field of complex algebraic geometry. She obtained her Ph.D in mathematics from Princeton University in 2004, and has been a researcher at IMPA (Institute for Pure and Applied Mathematics, Rio de Janeiro, Brazil) since 2006. She was appointed Simons Associate at ICTP from 2015 to 2020, was an invited speaker at the ICM 2018 in Rio de Janeiro, and was awarded the Ramanujan Prize in 2020. She is vice-chair of the Committee for Women in Mathematics of the International Mathematical Union, and coordinated the organization of the first World Meeting for Women in Mathematics - (WM)² - in 2018. She is also the mother of 5 year old Iago.

##### Algebraic geometry - research and trajectory

Algebraic geometry is one of the oldest and most active fields of mathematics. It studies geometric objects that are defined by polynomial equations. In this talk, I will give a brief introduction to algebraic geometry, highlighting some major recent developments and guiding problems in the field. I will also discuss my trajectory as a scientist, and some projects to promote gender equity and diversity in mathematics that I have been involved with.

## Speakers

Adela is an EPSRC Postdoctoral Fellow in the Department of Mathematics at the University of Warwick. Adela's research focuses on problems in computational and algebraic number theory, with a particular focus on elliptic curves and Diophantine equations. Adela completed a PhD in Mathematics at the University of British Columbia in Vancouver, Canada in 2019. Outside of work, Adela enjoys coding, climbing, and playing the violin poorly.

##### Computing elliptic curves over $$\mathbb{Q}$$

Let $$S = \{p_1, \dots, p_v\}$$ be a set of prime numbers. Consider the set of all elliptic curves over $$\mathbb{Q}$$ having good reduction outside $$S$$ and bounded conductor $$N$$. Currently, using modular forms, all such curves have been determined for $$N \leq 500000$$, the bulk of this work being attributed to Cremona. Early attempts to tabulate all such curves often relied on reducing the problem to one of solving a number of certain integral binary forms called Thue-Mahler equations. These are Diophantine equations of degree at least $$3$$ of the form

$F(x,y) = c_0x^n + c_1x^{n-1}y + \cdots + c_{n-1}xy^{n-1} + c_ny^n = cp_1^{z_1}\cdots p_v^{z_v},$

where the values $$x, y$$, and $$z_1, \dots, z_v$$ are unknown. A theorem of Bennett-Rechnitzer shows that the problem of computing all elliptic curves over $$\mathbb{Q}$$ of conductor $$N$$ reduces to solving a number of Thue-Mahler equations. To resolve all such equations, there exists a practical method of Tzanakis-de Weger using bounds for linear forms in $$p$$-adic logarithms and various reduction techniques. In this talk, we describe our refined implementation of this method and discuss the key steps used in our algorithm.

#### Ellie Archer

Ellie finished her PhD at Warwick in 2020 and is now a postdoc at Tel Aviv University. Ellie's research focuses on random walks and random graphs, especially those with fractal properties.

##### Random fractal trees

Random trees are classical objects in probability theory and turn out to be excellent models for a range of physical phenomena. In certain settings, they also have fractal properties. In this talk I will introduce my favourite random fractal tree, the Brownian CRT, and describe some of its key properties, including a cool stick-breaking construction and links to other models.

#### Sophie Meakin

Sophie is currently a Research Fellow in real-time modelling of infectious disease outbreaks at the London School of Hygiene & Tropical Medicine where she contributing to short-term forecasts of COVID-19 in the UK and the US. Before this, Sophie completed her PhD at the University of Warwick. Her research interests are in the application of mathematical modelling to support decision-making and preparedness during outbreaks and she has also worked for the World Health Organisation as part of the 2018-2020 North-Kivu Ebola outbreak response.

##### Mathematical modelling and forecasting during the COVID-19 pandemic

Mathematical modelling, including short-term forecasting of COVID-19 cases, hospital admissions and deaths, has played a key role in informing the management of the COVID-19 pandemic globally. In this talk I will describe some of the methods we use for making and evaluating forecasts during the pandemic, with a particular focus on COVID-19 hospital activity in England and COVID-19 deaths in the United States of America.

#### Josephine Evans

Josephine grew up in London and then the Brecon Beacons in south Wales. Both her undergraduate and PhD were in Cambridge. Despite the fact that Josephine works in more and more applied areas she did a PhD in the pure mathematics department. Josephine's PhD was in kinetic theory of gasses and applying tools from the intersection of PDE analysis and stochastic analysis to long time behaviour problems in kinetic theory. Her PhD supervisor was Clement Mouhot, who comes from a very a strong French tradition in applied analysis. After her PhD, Josephine spent almost two years as a post-doc in Universite Paris Dauphine under the supervision of Jean Dolbeault. Josephine joined Warwick as a Warwick Zeeman Lecturer (which is a fixed term assistant professor position) in July.

##### Entropy and collective motion

I will talk about what entropy is from a mathematical point of view. I will also discuss the background of my field, kinetic theory, which is about the modelling of collective motion (or gas particles, birds, bacteria, opinions). I will discuss how entropy first entered kinetic theory with the work of Boltzmann and a bit about the modern challenges in understanding how entropy behaves in various systems.

#### Susana Gomes

Susana is an applied mathematician, and a Warwick Zeeman Lecturer in the Mathematics Institute. She is originally from Portugal, where she obtained her Undergraduate and MSc degrees in the University of Coimbra, after which she moved to the UK for a PhD degree at Imperial College London. She joined Warwick in 2018, after two short postdoctoral positions at Imperial.

##### From linear control theory to nonlinear dynamics: controlling thin film flows

The flow of a thin film down an inclined plane is a canonical setup in fluid mechanics, with technological applications such as manufacturing LCD screens or microchips. Mathematically, it provides a very rich framework for modelling, analysis and control. In this talk, I will summarise a hierarchy of models, obtained from the Navier-Stokes equations using asymptotic analysis techniques, usually consisting of fourth order nonlinear partial differential equations describing the evolution of the interfaces of these flows. Depending on the application, we would like to robustly and efficiently manipulate these flows so that their interface has a prescribed shape (e.g. a flat interface for a smooth coating of a screen or a wavy shape to guarantee efficient cooling of microchips). I will propose a linear feedback control methodology, developed at the lower levels of this hierarchy, which stabilises any desired interfacial shape, and will investigate their robustness across the hierarchy of models, and into real-life situations, exemplified by direct numerical simulations of the Navier-Stokes equations.

## Q&A Session

We will be joined for the Q&A by the following students: Alice (MASDOC), Francesca (OxWaSP), Ana (OxWaSP), and Emma (MathSys).

## Piscopia

The Piscopia Initiative was founded in October 2019 by PhD students at the University of Edinburgh, in order to tackle the participation crisis of women and non-binary students in maths research across the UK.

We offer both UK-wide and university-specific events at 11 local Piscopia committees, aimed at undergraduate and MSc students in maths and related disciplines, who self-identify as female or non-binary.

Our 4-stage plan is to:

• Raise awareness for PhD options
• Highlight women and non-binary role models
• Provide attendees with a support network and platform within the UK-wide Piscopia community
• Leave a legacy that will have a positive impact on maths research in the UK