Forthcoming events in this series
Job applications involve a lot of work and can be overwhelming. Join us for a workshop and Q+A session focused on breaking down academic applications: we’ll talk about approaching reference letter writers, writing research statements, and discussing what makes a great CV and covering letter.
How do you make the most of graduate supervisions? Whether you are a first year graduate wanting to learn about how to manage meetings with your supervisor, or a later year DPhil student, postdoc or faculty member willing to share their experiences and give advice, please come along to this informal discussion led by DPhil students for the first Fridays@4 session of the term. You can also continue the conversation and learn more about graduate student life at Oxford at Happy Hour afterwards.
George Lusztig is the Abdun-Nur Professor of Mathematics. He joined the MIT mathematics faculty in 1978 following a professorship appointment at the University of Warwick, 1974-77. He was appointed Norbert Wiener Professor at MIT 1999-2009.
Lusztig graduated from the University of Bucharest in 1968, and received both the M.A. and Ph.D. from Princeton University in 1971 under the direction of Michael Atiyah and William Browder. Professor Lusztig works on geometric representation theory and algebraic groups. He has received numerous research distinctions, including the Berwick Prize of the London Mathematical Society (1977), the AMS Cole Prize in Algebra (1985), and the Brouwer Medal of the Dutch Mathematical Society (1999), and the AMS Leroy P. Steele Prize for Lifetime Achievement (2008), "for entirely reshaping representation theory, and in the process changing much of mathematics."
Professor Lusztig is a Fellow of the Royal Society (1983), Fellow of the American Academy of Arts & Sciences (1991), and Member of the National Academy of Sciences (1992). He was the recipient of the Shaw Prize (2014) and the Wolf Prize (2022).
North Wing talk: Dr Thomas Karam
Title: Ranges control degree ranks of multivariate polynomials on finite prime fields.
Abstract: Let $p$ be a prime. It has been known since work of Green and Tao (2007) that if a polynomial $P:\mathbb{F}_p^n \mapsto \mathbb{F}_p$ with degree $2 \le d \le p-1$ is not approximately equidistributed, then it can be expressed as a function of a bounded number of polynomials each with degree at most $d-1$. Since then, this result has been refined in several directions. We will explain how this kind of statement may be used to deduce an analogue where both the assumption and the conclusion are strengthened: if for some $1 \le t < d$ the image $P(\mathbb{F}_p^n)$ does not contain the image of a non-constant one-variable polynomial with degree at most $t$, then we can obtain a decomposition of $P$ in terms of a bounded number of polynomials each with degree at most $\lfloor d/(t+1) \rfloor$. We will also discuss the case where we replace the image $P(\mathbb{F}_p^n)$ by for instance $P(\{0,1\}^n)$ in the assumption.
South Wing talk: Dr Hamid Rahkooy
Title: Toric Varieties in Biochemical Reaction Networks
Abstract: Toric varieties are interesting objects for algebraic geometers as they have many properties. On the other hand, toric varieties appear in many applications. In particular, dynamics of many biochemical reactions lead to toric varieties. In this talk we discuss how to test toricity algorithmically, using computational algebra methods, e.g., Gröbner bases and quantifier elimination. We show experiments on real world models of reaction networks and observe that many biochemical reactions have toric steady states. We discuss complexity bounds and how to improve computations in certain cases.
Come to this session to learn how to get started in consultancy from Dawn Gordon at Oxford University Innovation (OUI). After an introduction to what consultancy is, we'll explore case studies of consultancy work performed by mathematicians and statisticians within the university. This session will also include practical advice on how you can explore consultancy opportunities alongside your research work, from finding potential clients to the support that OUI can offer.
To tie in with mental health awareness week, in this session we'll give a brief overview of the mental health support available through the department and university, followed by a panel discussion on how we can look after our mental health as in an academic setting. We're pleased that several of our department Mental Health First Aiders will be panellists - come along for hints and tips on maintaining good mental health and supporting your colleagues and friends.
For week 4's @email session we welcome the SIAM-IMA student chapter, running their annual Three Minute Thesis competition.
The Three Minute Thesis competition challenges graduate students to present their research in a clear and engaging manner within a strict time limit of three minutes. Each presenter will be allowed to use only one static slide to support their presentation, and the panel of esteemed judges (details TBC) will evaluate the presentations based on criteria such as clarity, pacing, engagement, enthusiasm, and impact. Each presenter will receive a free mug and there is £250 in cash prizes for the winners. If you're a graduate student, sign up here (https://oxfordsiam.com/3mt) by Friday of week 3 to take part! And if not, come along to support your DPhil friends and colleagues, and to learn about the exciting maths being done by our research students.
Liliana Borcea is the Peter Field Collegiate Professor of Mathematics at the University of Michigan. Her research interests are in scientific computing and applied mathematics, including the scattering and transport of electromagnetic waves.
Title: When data driven reduced order modelling meets full waveform inversion
Abstract:
This talk is concerned with the following inverse problem for the wave equation: Determine the variable wave speed from data gathered by a collection of sensors, which emit probing signals and measure the generated backscattered waves. Inverse backscattering is an interdisciplinary field driven by applications in geophysical exploration, radar imaging, non-destructive evaluation of materials, etc. There are two types of methods:
(1) Qualitative (imaging) methods, which address the simpler problem of locating reflective structures in a known host medium.
(2) Quantitative methods, also known as velocity estimation.
Typically, velocity estimation is formulated as a PDE constrained optimization, where the data are fit in the least squares sense by the wave computed at the search wave speed. The increase in computing power has lead to growing interest in this approach, but there is a fundamental impediment, which manifests especially for high frequency data: The objective function is not convex and has numerous local minima even in the absence of noise.
The main goal of the talk is to introduce a novel approach to velocity estimation, based on a reduced order model (ROM) of the wave operator. The ROM is called data driven because it is obtained from the measurements made at the sensors. The mapping between these measurements and the ROM is nonlinear, and yet the ROM can be computed efficiently using methods from numerical linear algebra. More importantly, the ROM can be used to define a better objective function for velocity estimation, so that gradient based optimization can succeed even for a poor initial guess.
The Lecture will be followed by a Drinks Reception in the ground floor social area. To help with catering arrangements, please book your place here https://forms.office.com/e/Nw3qSZtzCs.
Lenka Zdeborová is a Professor of Physics and Computer Science at École Polytechnique Fédérale de Lausanne, where she leads the Statistical Physics of Computation Laboratory. She received a PhD in physics from University Paris-Sud and Charles University in Prague in 2008. She spent two years in the Los Alamos National Laboratory as the Director's Postdoctoral Fellow. Between 2010 and 2020, she was a researcher at CNRS, working in the Institute of Theoretical Physics in CEA Saclay, France. In 2014, she was awarded the CNRS bronze medal; in 2016 Philippe Meyer prize in theoretical physics and an ERC Starting Grant; in 2018, the Irène Joliot-Curie prize; in 2021, the Gibbs lectureship of AMS and the Neuron Fund award. Lenka's expertise is in applications of concepts from statistical physics, such as advanced mean field methods, the replica method and related message-passing algorithms, to problems in machine learning, signal processing, inference and optimization. She enjoys erasing the boundaries between theoretical physics, mathematics and computer science.
The affinity between statistical physics and machine learning has a long history. Theoretical physics often proceeds in terms of solvable synthetic models; I will describe the related line of work on solvable models of simple feed-forward neural networks. I will then discuss how this approach allows us to analyze uncertainty quantification in neural networks, a topic that gained urgency in the dawn of widely deployed artificial intelligence. I will conclude with what I perceive as important specific open questions in the field.
Join us for our first Fridays@4 session of Trinity about different academic routes people take post-PhD, with a particular focus on fellowships and grants. We’ll hear from Jason Lotay about his experiences on both sides of the application process, as well as hear about the experiences of ECRs in the South Wing, North Wing, and Statistics. Towards the end of the hour we’ll have a Q+A session with the whole panel, where you can ask any questions you have around this topic!
Dr. Keven Roy from RMS Moody's Analytics (who are currently hiring!) will share his experience of transitioning from academia to industry, discussing his fascinating work in modelling climate change and how his mathematical background has helped him succeed in industry. After the approximately 20-minute talk, we'll hold a Q&A session to discuss the importance of considering industry in your job search. Aimed primarily at PhD students and postdocs, this session will explore options beyond academia that can provide a fulfilling career (as well as good work-life balance, and financial compensation!).
Join us for a thought-provoking discussion at Fridays@4 to expand your career horizons and help you make informed decisions about your future. There will be lots of time for Q&A in this session, but if you have questions for Keven you can also send them in advance to Jess Crawshaw (session organiser) - @email.
Chair: Ian Hewitt (Associate HoD (People))
Panel:
James Sparks (Head of Department)
Helen Byrne (winner of MPLS Outstanding Supervisor Awards for 2022)
Ali Goodall (Head of Faculty Services and HR)
Matija Tapuskovic (EPSRC Postdoctoral Research Fellow and JRF at Corpus Christi)
Scientific discussions with colleagues, at conferences and seminars, during supervisions and collaborations, are a crucial part of our research process. How can we ensure our academic discussions are fruitful, respectful, and a positive experience for everyone involved? What factors and power dynamics can impact our conversations? How can we make sure everyone’s voice is heard and respected? This panel discussion will probe these questions and encourage us all to reflect on how we approach our academic discussions.
Speaker: Dr Aleksander Horawa (North Wing)
Title: Bitcoin, elliptic curves, and this building
Abstract:
We will discuss two motivations to work on Algebraic Number Theory: applications to cryptography, and fame and fortune. For the first, we will explain how Bitcoin and other companies use Elliptic Curves to digitally sign messages. For the latter, we will introduce two famous problems in Number Theory: Fermat's Last Theorem, worth a name on this building, and the Birch Swinnerton--Dyer conjecture, worth $1,000,000 according to some people in this building (Clay Mathematics Institute).
Speaker: Dr Jemima Tabeart (South Wing)
Title: Numerical linear algebra for weather forecasting
Abstract:
The quality of a weather forecast is strongly determined by the accuracy of the initial condition. Data assimilation methods allow us to combine prior forecast information with new measurements in order to obtain the best estimate of the true initial condition. However, many of these approaches require the solution an enormous least-squares problem. In this talk I will discuss some mathematical and computational challenges associated with data assimilation for numerical weather prediction, and show how structure-exploiting numerical linear algebra approaches can lead to theoretical and computational improvements.
This session will introduce the opportunities for entrepreneurship and generating commercial impact available to researchers and students across MPLS. Representatives from the Maths Institute and across the university will discuss training and resources to help you begin enterprising and develop your ideas. We will hear from Paul Gass and Dawn Gordon about the support that can be provided by Oxford University Innovation, discussing commercialisation of research findings, consultancy, utilising your expertise and the protection and licensing of Intellectual Property.
Please see below slides from the talk:
20230217 Short Seminar - Maths Fri@4_FINAL- Dept (1)_0.pdf
Title: “Mathematical models of curiosity”
Prof. Bassett is the J. Peter Skirkanich Professor at the University of Pennsylvania, with appointments in the Departments of Bioengineering, Electrical & Systems Engineering, Physics & Astronomy, Neurology, and Psychiatry. They are also an external professor of the Santa Fe Institute. Bassett is most well-known for blending neural and systems engineering to identify fundamental mechanisms of cognition and disease in human brain networks.
What is curiosity? Is it an emotion? A behavior? A cognitive process? Curiosity seems to be an abstract concept—like love, perhaps, or justice—far from the realm of those bits of nature that mathematics can possibly address. However, contrary to intuition, it turns out that the leading theories of curiosity are surprisingly amenable to formalization in the mathematics of network science. In this talk, I will unpack some of those theories, and show how they can be formalized in the mathematics of networks. Then, I will describe relevant data from human behavior and linguistic corpora, and ask which theories that data supports. Throughout, I will make a case for the position that individual and collective curiosity are both network building processes, providing a connective counterpoint to the common acquisitional account of curiosity in humans.
Title: “Causal learning from observational data”
Please register in advance using the online form: https://www.stats.ox.ac.uk/events/florence-nightingale-lecture-2023
Marloes Henriette Maathuis is a Dutch statistician known for her work on causal inference using graphical models, particularly in high-dimensional data from applications in biology and epidemiology. She is a professor of statistics at ETH Zurich in Switzerland.
I will discuss a line of work on estimating causal effects from observational data. In the first part of the talk, I will discuss identification and estimation of causal effects when the underlying causal graph is known, using adjustment. In the second part, I will discuss what one can do when the causal graph is unknown. Throughout, examples will be used to illustrate the concepts and no background in causality is assumed.
In this session, we will hold a panel discussion on how to best give an academic talk. Among other topics, we will focus on techniques for engaging your audience, for determining the level and technical details of the talk, and for giving both blackboard and slide presentations. The discussion will begin with a directed panel discussion before opening up to questions from the audience.
Title: “Prime numbers: Techniques, results and questions”
The basic question in prime number theory is to try to understand the number of primes in some interesting set of integers. Unfortunately many of the most basic and natural examples are famous open problems which are over 100 years old!
We aim to give an accessible survey of (a selection of) the main results and techniques in prime number theory. In particular we highlight progress on some of these famous problems, as well as a selection of our favourite problems for future progress.
Matthew Buckland
Branching Interval Partition Diffusions
We construct an interval-partition-valued diffusion from a collection of excursions sampled from the excursion measure of a real-valued diffusion, and we use a spectrally positive Lévy process to order both these excursions and their start times. At any point in time, the interval partition generated is the concatenation of intervals where each excursion alive at that point contributes an interval of size given by its value. Previous work by Forman, Pal, Rizzolo and Winkel considers self-similar interval partition diffusions – and the key aim of this work is to generalise these results by dropping the self-similarity condition. The interval partition can be interpreted as an ordered collection of individuals (intervals) alive that have varying characteristics and generate new intervals during their finite lifetimes, and hence can be viewed as a class of Crump-Mode-Jagers-type processes.
Ofir Gorodetsky
Smooth and rough numbers
We all know and love prime numbers, but what about smooth and rough numbers?
We'll define y-smooth numbers -- numbers whose prime factors are all less than y. We'll explain their application in cryptography, specifically to factorization of integers.
We'll shed light on their density, which is modelled using a peculiar differential equation. This equation appears naturally in probability theory.
We'll also explain the dual notion to smooth numbers, that of y-rough numbers: numbers whose prime factors are all bigger than y, and in some sense generalize primes.
We'll explain their importance in sieve theory. Like smooth numbers, their density has interesting properties and will be surveyed.
Your supervisor is the person you will interact with on a scientific level most of all during your studies here. As a result, it is vital that you establish a good working relationship. But how should you do this? In this session we discuss tips and tricks for getting the most out of your supervisions to maximize your success as a researcher. Note that this session will have no faculty in the audience in order to allow people to speak openly about their experiences.
What should we be thinking about when we're making a diagram for a paper? How do we help it to express the right things? Or make it engaging? What kind of colour palette is appropriate? What software should we use? And how do we make this process as painless as possible? Join Joshua Bull and Christoph Dorn for a lively Fridays@4 session on illustrating mathematics, as they share tips, tricks, and their own personal experiences in bringing mathematics to life via illustrations.
Ilia Smilga
Margulis spacetimes and crooked planes
We are interested in the following problem: which groups can act
properly on R^n by affine transformations, or in other terms, can occur
as a symmetry group of a "regular affine tiling"? If we additionally
require that they preserve a Euclidean metric (i.e. act by affine
isometries), then these groups are well-known: they all contain a
finite-index abelian subgroup. If we remove this requirement, a
surprising result due to Margulis is that the free group can act
properly on R^3. I shall explain how to construct such an action.
Charles Parker
Unexpected Behavior in Finite Elements for Linear Elasticity
One of the first problems that finite elements were designed to approximate is the small deformations of a linear elastic body; i.e. the 2D/3D version of Hooke's law for springs from elementary physics. However, for nearly incompressible materials, such as rubber, certain finite elements seemingly lose their approximation power. After briefly reviewing the equations of linear elasticity and the basics of finite element methods, we will spend most of the time looking at a few examples that highlight this unexpected behavior. We conclude with a theoretical result that (mostly) explains these findings.
Academic research can be challenging and can bring with it difficulties in maintaining good mental health. This session will be led by Rebecca Reed, Mental Health First Aid (MHFA) Instructor, Meditation & Yoga Teacher and Personal Development Coach and owner of wellbeing company Siendo. Rebecca will talk about how we can maintain good mental fitness, recognizing good practices to ensure we avoid mental-health difficulties before they begin. We have deliberately set this session to be at the beginning of the academic year in this spirit. We will also talk about maintaining good mental health specifically in the academic community.
Abstract:
Welcome (back) to Fridays@4! To start the new academic year in this session we’ll introduce what Fridays@4 is for our new students and colleagues. This session will be a chance to meet current students and ECRs from across Maths and Stats who will share their hints and tips on conducting successful research in Oxford. There will be lots of time for questions, discussions and generally meeting more people across the two departments – everyone is welcome!