Forthcoming events in this series


Fri, 24 May 2024
16:00
L1

North meets South

Alexandru Pascadi and Tim LaRock
Abstract

There will be free pizza provided for all attendees directly after the event just outside L1, so please do come along!

 

North Wing
Speaker: Alexandru Pascadi 
Title: Points on modular hyperbolas and sums of Kloosterman sums
Abstract: Given a positive integer c, how many integer points (x, y) with xy = 1 (mod c) can we find in a small box? The dual of this problem concerns bounding certain exponential sums, which show up in methods from the spectral theory of automorphic forms. We'll explore how a simple combinatorial trick of Cilleruelo-Garaev leads to good bounds for these sums; following recent work of the speaker, this ultimately has consequences about multiple problems in analytic number theory (such as counting primes in arithmetic progressions to large moduli, and studying the greatest prime factors of quadratic polynomials).

 

South Wing
Speaker: Tim LaRock
Title: Encapsulation Structure and Dynamics in Hypergraphs
Abstract: Within the field of Network Science, hypergraphs are a powerful modelling framework used to represent systems where interactions may involve an arbitrary number of agents, rather than exactly two agents at a time as in traditional network models. As part of a recent push to understand the structure of these group interactions, in this talk we will explore the extent to which smaller hyperedges are subsets of larger hyperedges in real-world and synthetic hypergraphs, a property that we call encapsulation. Building on the concept of line graphs, we develop measures to quantify the relations existing between hyperedges of different sizes and, as a byproduct, the compatibility of the data with a simplicial complex representation–whose encapsulation would be maximum. Finally, we will turn to the impact of the observed structural patterns on diffusive dynamics, focusing on a variant of threshold models, called encapsulation dynamics, and demonstrate that non-random patterns can accelerate spreading through the system.

 

Fri, 10 May 2024
16:00
L1

Talks on Talks

Abstract

What makes a good talk? This year, graduate students and postdocs will give a series talks on how to give talks! There may even be a small prize for the audience’s favourite.

If you’d like to have a go at informing, entertaining, or just have an axe to grind about a particularly bad talk you had to sit through, we’d love to hear from you (you can email Ric Wade or ask any of the organizers).
 

Fri, 03 May 2024
16:00
L1

Maths meets Stats

Mattia Magnabosco (Maths) and Rebecca Lewis (Stats)
Abstract

Speaker: Mattia Magnabosco (Newton Fellow, Maths)
Title: Synthetic Ricci curvature bounds in sub-Riemannian manifolds
Abstract: In Riemannian manifolds, a uniform bound on the Ricci curvature tensor allows to control the volume growth along the geodesic flow. Building upon this observation, Lott, Sturm and Villani introduced a synthetic notion of curvature-dimension bounds in the non-smooth setting of metric measure spaces. This condition, called CD(K,N), is formulated in terms of the optimal transport interpolation of measures and consists in a convexity property of the Rényi entropy functionals along Wasserstein geodesics. The CD(K,N) condition represents a lower Ricci curvature bound by K and an upper bound on the dimension by N, and it is coherent with the smooth setting, as in a Riemannian manifold it is equivalent to a lower bound on the Ricci curvature tensor. However, the same relation between curvature and CD(K,N) condition does not hold for sub-Riemannian (and sub-Finsler) manifolds. 

 

Speaker: Rebecca Lewis (Florence Nightingale Bicentenary Fellow, Stats)
Title: High-dimensional statistics
Abstract: Due to the increasing ease with which we collect and store information, modern data sets have grown in size. Whilst these datasets have the potential to yield new insights in a variety of areas, extracting useful information from them can be difficult. In this talk, we will discuss these challenges.

Fri, 26 Apr 2024
15:30
Large Lecture Theatre, Department of Statistics, University of Oxford

Inaugural Green Lecture: Tackling the hidden costs of computational science: GREENER principles for environmentally sustainable research

Dr Loïc Lannelongue, Heart and Lung Research Institute, University of Cambridge and the Cambridge-Baker Systems Genomics Initiative
(Department of Statistics, University of Oxford)
Further Information

PLEASE REGISTER FOR THE EVENT HERE: https://www.stats.ox.ac.uk/events/inaugural-green-lecture-dr-loic-lanne…

Dr Loïc Lannelongue is a Research Associate in Biomedical Data Science in the Heart and Lung Research Institute at the University of Cambridge, UK, and the Cambridge-Baker Systems Genomics Initiative. He leads the Green Algorithms project, an initiative promoting more environmentally sustainable computational science. His research interests also include radiogenomics, i.e. combining medical imaging and genetic information with machine learning to better understand and treat cardiovascular diseases. He obtained an MSc from ENSAE, the French National School of Statistics, and an MSc in Statistical Science from the University of Oxford, before doing his PhD in Health Data Science at the University of Cambridge. He is a Software Sustainability Institute Fellow, a Post-doctoral Associate at Jesus College, Cambridge, and an Associate Fellow of the Higher Education Academy.

Abstract

From genetic studies and astrophysics simulations to statistical modelling and AI, scientific computing has enabled amazing discoveries and there is no doubt it will continue to do so. However, the corresponding environmental impact is a growing concern in light of the urgency of the climate crisis, so what can we all do about it? Tackling this issue and making it easier for scientists to engage with sustainable computing is what motivated the Green Algorithms project. Through the prism of the GREENER principles for environmentally sustainable science, we will discuss what we learned along the way, how to estimate the impact of our work and what levers scientists and institutions have to make their research more sustainable. We will also debate what hurdles exist and what is still needed moving forward.

 

Fri, 08 Mar 2024
16:00
L1

Maths meets Stats

James Taylor (Mathematical Institute) and Anthony Webster (Department of Statistics)
Abstract

Speaker: James Taylor
Title: D-Modules and p-adic Representations

Abstract: The representation theory of finite groups is a beautiful and well-understood subject. However, when one considers more complicated groups things become more interesting, and to classify their representations is often a much harder problem. In this talk, I will introduce the classical theory, the particular groups I am interested in, and explain how one might hope to understand their representations through the use of D-modules - the algebraic incarnation of differential equations.

 

Speaker: Anthony Webster
Title: An Introduction to Epidemiology and Causal Inference

Abstract: This talk will introduce epidemiology and causal inference from the perspective of a statistician and former theoretical physicist. Despite their studies being underpinned by deep and often complex mathematics, epidemiologists are generally more concerned by seemingly mundane information about the relationships between potential risk factors and disease. Because of this, I will argue that a good epidemiologist with minimal statistical knowledge, will often do better than a highly trained statistician. I will also argue that causal assumptions are a necessary part of epidemiology, should be made more explicitly, and allow a much wider range of causal inferences to be explored. In the process, I will introduce ideas from epidemiology and causal inference such as Mendelian Randomisation and the "do calculus", methodological approaches that will increasingly underpin data-driven population research.  

Fri, 01 Mar 2024
16:00
L1

Departmental Colloquium: The role of depth in neural networks: function space geometry and learnability

Professor Rebecca Willett (University of Chicago)
Further Information

Rebecca Willett is a Professor of Statistics and Computer Science & the Faculty Director of AI at the Data Science Institute, with a courtesy appointment at the Toyota Technological Institute at Chicago. Her research is focused on machine learning foundations, scientific machine learning, and signal processing. She is the Deputy Director for Research at the NSF-Simons Foundation National Institute for Theory and Mathematics in Biology and a member of the Executive Committee for the NSF Institute for the Foundations of Data Science. She is the Faculty Director of the Eric and Wendy Schmidt AI in Science Postdoctoral Fellowship and helps direct the Air Force Research Lab University Center of Excellence on Machine Learning

Abstract

Neural network architectures play a key role in determining which functions are fit to training data and the resulting generalization properties of learned predictors. For instance, imagine training an overparameterized neural network to interpolate a set of training samples using weight decay; the network architecture will influence which interpolating function is learned. 

In this talk, I will describe new insights into the role of network depth in machine learning using the notion of representation costs – i.e., how much it “costs” for a neural network to represent some function f. Understanding representation costs helps reveal the role of network depth in machine learning. First, we will see that there is a family of functions that can be learned with depth-3 networks when the number of samples is polynomial in the input dimension d, but which cannot be learned with depth-2 networks unless the number of samples is exponential in d. Furthermore, no functions can easily be learned with depth-2 networks while being difficult to learn with depth-3 networks. 

Together, these results mean deeper networks have an unambiguous advantage over shallower networks in terms of sample complexity. Second, I will show that adding linear layers to a ReLU network yields a representation cost that favors functions with latent low-dimension structure, such as single- and multi-index models. Together, these results highlight the role of network depth from a function space perspective and yield new tools for understanding neural network generalization. 

Fri, 23 Feb 2024
16:00
L1

Demystifying careers for mathematicians in the Civil Service

Sarah Livermore (Department for Business and Trade)
Abstract

Sarah Livermore has worked in the Civil Service for over 10 years, using the maths skills gained in her physics degrees (MPhys, DPhil) whilst studying at Oxford. In this session she’ll discuss some of the roles available to people with a STEM background in the Civil Service, a ‘day in the life’ of a civil servant, typical career paths and how to apply.

Fri, 16 Feb 2024
16:00
L1

Conferences and networking

Naomi Andrew, Jane Coons, Antonio Esposito, Romain Ruzziconi
(Mathematical Institute (University of Oxford))
Abstract

Conferences and networking are important parts of academic life, particularly early in your academic career.  But how do you make the most out of conferences?  And what are the does and don'ts of networking?  Learn about the answers to these questions and more in this panel discussion by postdocs from across the Mathematical Institute.

Fri, 09 Feb 2024
16:00
L1

Creating Impact for Maths Research via Consulting, Licensing and Spinouts

Dawn Gordon, Amelia Griffiths and Paul Gass
(Oxford University Innovation)
Abstract

Oxford University Innovation, the University’s commercialisation team, will explain the support they can give to Maths researchers who want to generate commercial impact from their work and expertise. In addition to an overview of consulting, this talk will explain how mathematical techniques and software can be protected and commercialised.

Fri, 02 Feb 2024
16:00
L1

Graduate Jobs in finance and the recruitment process

Keith Macksoud, Executive Director at Options Group
(Options Group)
Abstract

Join us for a session with Keith Macksoud, Executive Director at global recruitment consultant Options Group in London and who previously has > 20 years’ experience in Prime Brokerage Sales at Morgan Stanley, Citi, and Deutsche Bank.  Keith will discuss the recruitment process for financial institutions, and how to increase your chances of a successful application. 

Keith will detail his finance background in Prime Brokerage and provide students with an exclusive look behind the scenes of executive search and strategic consulting firm Options Group. We will look at what Options Group does, how executive search firms work and the Firm’s 30-year track record of placing individuals at many of the industries’ largest and most successful global investment banks, investment managers and other financial services-related organisations. 

About Options Group

Options Group is a leading global executive search and strategic consulting firm specializing in financial services including capital markets, global markets, alternative investments, hedge funds, and private banking/wealth management.

https://www.optionsgroup.com/

Fri, 26 Jan 2024
16:00
L1

North meets South

Dr Cedric Pilatte (North Wing) and Dr Boris Shustin (South Wing)
Abstract

Speaker: Cedric Pilatte 
Title: Convolution of integer sets: a galaxy of (mostly) open problems

Abstract: Let S be a set of integers. Define f_k(n) to be the number of representations of n as the sum of k elements from S. Behind this simple definition lie fascinating conjectures that are very easy to state but seem unattackable. For example, a famous conjecture of Erdős and Turán predicts that if f_2 is bounded then it has infinitely many zeroes. This talk is designed as an accessible overview of these questions. 
 
Speaker: Boris Shustin

Title: Manifold-Free Riemannian Optimization

Abstract: Optimization problems constrained to a smooth manifold can be solved via the framework of Riemannian optimization. To that end, a geometrical description of the constraining manifold, e.g., tangent spaces, retractions, and cost function gradients, is required. In this talk, we present a novel approach that allows performing approximate Riemannian optimization based on a manifold learning technique, in cases where only a noiseless sample set of the cost function and the manifold’s intrinsic dimension are available.

Fri, 19 Jan 2024
16:00
L1

Mathematical Societies and Organisations

Chris Breward, Sam Cohen, Rebecca Crossley, Dawid Kielak and Ulrike Tillmann
(Mathematical Institute)
Abstract
Mathematical societies and organisations run exciting academic activities and provide important funding opportunities. This session will include presentations on the London Mathematical Society (by LMS Rep Dawid Kielak), the Institute of Mathematics and its Applications (by Chris Breward), the Society for Industrial and Applied Mathematics (by Sam Cohen and Becky Crossley) and the Isaac Newton Institute (by its Director, Ulrike Tillmann).
 
The event will be followed by free pizza.
Fri, 01 Dec 2023
16:00
L1

Departmental Colloquium: Ana Caraiani

Ana Caraiani
Abstract

Title: Elliptic curves and modularity

Abstract: The goal of this talk is to give you a glimpse of the Langlands program, a central topic at the intersection of algebraic number theory, algebraic geometry and representation theory. I will focus on a celebrated instance of the Langlands correspondence, namely the modularity of elliptic curves. In the first part of the talk, I will give an explicit example, discuss the different meanings of modularity for rational elliptic curves, and mention applications. In the second part of the talk, I will discuss what is known about the modularity of elliptic curves over more general number fields.

Fri, 24 Nov 2023
16:00
L1

Maths meets Stats

Dr Ximena Laura Fernandez (Mathematical Institute) and Dr Brett Kolesnik (Department of Statistics)
Abstract

Speaker: Ximena Laura Fernandez
Title: Let it Be(tti): Topological Fingerprints for Audio Identification

Abstract: Ever wondered how music recognition apps like Shazam work or why they sometimes fail? Can Algebraic Topology improve current audio identification algorithms? In this talk, I will discuss recent collaborative work with Spotify, where we extract low-dimensional homological features from audio signals for efficient song identification despite continuous obfuscations. Our approach significantly improves accuracy and reliability in matching audio content under topological distortions, including pitch and tempo shifts, compared to Shazam.

Talk based on the work: https://arxiv.org/pdf/2309.03516.pdf
 

Speaker: Brett Kolesnik
Title: Coxeter Tournaments

Abstract: We will present ongoing joint work with three Oxford PhD students: Matthew Buckland (Stats), Rivka Mitchell (Math/Stats) and Tomasz Przybyłowski (Math). We met last year as part of the course SC9 Probability on Graphs and Lattices. Connections with geometry (the permutahedron and generalizations), combinatorics (tournaments and signed graphs), statistics (paired comparisons and sampling) and probability (coupling and rapid mixing) will be discussed.

Fri, 17 Nov 2023
16:00
L1

Careers outside academia

V-Nova and Dr Anne Wolfes (Careers Service)
Abstract

What opportunities are available outside of academia? What skills beyond strong academic background are companies looking for to be successful in transitioning to industry? Come along and hear from video technology company V-Nova and Dr Anne Wolfes from the Careers Service to get some invaluable advice on careers outside academia.

Logo

Fri, 10 Nov 2023
16:00
L1

North meets South

Dr Lasse Grimmelt (North Wing) and Dr Yang Liu (South Wing)
Abstract

Speaker: Lasse Grimmelt (North Wing)
Title: Modular forms and the twin prime conjecture

Abstract: Modular forms are one of the most fruitful areas in modern number theory. They play a central part in Wiles proof of Fermat's last theorem and in Langland's far reaching vision. Curiously, some of our best approximations to the twin-prime conjecture are also powered by them. In the existing literature this connection is highly technical and difficult to approach. In work in progress on this types of questions, my coauthor and I found a different perspective based on a quite simple idea. In this way we get an easy explanation and good intuition why such a connection should exists. I will explain this in this talk.

Speaker: Yang Liu (South Wing)
Title: Obtaining Pseudo-inverse Solutions With MINRES


Abstract: The celebrated minimum residual method (MINRES) has seen great success and wide-spread use in solving linear least-squared problems involving Hermitian matrices, with further extensions to complex symmetric settings. Unless the system is consistent whereby the right-hand side vector lies in the range of the matrix, MINRES is not guaranteed to obtain the pseudo-inverse solution. We propose a novel and remarkably simple lifting strategy that seamlessly integrates with the final MINRES iteration, enabling us to obtain the minimum norm solution with negligible additional computational costs. We also study our lifting strategy in a diverse range of settings encompassing Hermitian and complex symmetric systems as well as those with semi-definite preconditioners.

 

 

 

Fri, 03 Nov 2023
16:00
L1

Departmental Colloquium (Alicia Dickenstein) - Algebraic geometry tools in systems biology

Alicia Dickenstein
Further Information

Alicia Dickenstein is an Argentine mathematician known for her work on algebraic geometry, particularly toric geometry, tropical geometry, and their applications to biological systems.

Abstract

In recent years, methods and concepts of algebraic geometry, particularly those of real and computational algebraic geometry, have been used in many applied domains. In this talk, aimed at a broad audience, I will review applications to molecular biology. The goal is to analyze standard models in systems biology to predict dynamic behavior in regions of parameter space without the need for simulations. I will also mention some challenges in the field of real algebraic geometry that arise from these applications.

Fri, 27 Oct 2023
16:00
L1

Academic job application workshop

Abstract

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.

Fri, 20 Oct 2023
16:00
L1

Departmental Colloquium (Tamara Kolda) - Generalized Tensor Decomposition: Utility for Data Analysis and Mathematical Challenges

Tamara Kolda
Further Information
Tamara Kolda is an independent mathematical consultant under the auspices of her company MathSci.ai based in California. From 1999-2021, she was a researcher at Sandia National Laboratories in Livermore, California. She specializes in mathematical algorithms and computation methods for tensor decompositions, tensor eigenvalues, graph algorithms, randomized algorithms, machine learning, network science, numerical optimization, and distributed and parallel computing.
Abstract
Tensor decomposition is an unsupervised learning methodology that has applications in a wide variety of domains, including chemometrics, criminology, and neuroscience. We focus on low-rank tensor decomposition using canonical polyadic or CANDECOMP/PARAFAC format. A low-rank tensor decomposition is the minimizer according to some nonlinear program. The usual objective function is the sum of squares error (SSE) comparing the data tensor and the low-rank model tensor. This leads to a nicely-structured problem with subproblems that are linear least squares problems which can be solved efficiently in closed form. However, the SSE metric is not always ideal. Thus, we consider using other objective functions. For instance, KL divergence is an alternative metric is useful for count data and results in a nonnegative factorization. In the context of nonnegative matrix factorization, for instance, KL divergence was popularized by Lee and Seung (1999). We can also consider various objectives such as logistic odds for binary data, beta-divergence for nonnegative data, and so on. We show the benefits of alternative objective functions on real-world data sets. We consider the computational of generalized tensor decomposition based on other objective functions, summarize the work that has been done thus far, and illuminate open problems and challenges. This talk includes joint work with David Hong and Jed Duersch.
Fri, 13 Oct 2023
16:00
L1

You and Your Supervisor

Abstract

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.

Mon, 12 Jun 2023
16:00
L1

Departmental Colloquium

George Lusztig
(Massachusetts Institute of Technology)
Further Information

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).

Fri, 09 Jun 2023
16:00
L2

North meets South

Dr Thomas Karam (North Wing) and Dr Hamid Rahkooy (South Wing)
Abstract

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.

Fri, 02 Jun 2023
16:00
L1

OUI: Consultancy 101

Dawn Gordon, Project Manager
(Oxford University Innovation)
Abstract

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.

Fri, 26 May 2023
16:00
L1

Looking after our mental health in an academic environment

Abstract

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.

Fri, 19 May 2023
16:00
L1

SIAM Student Chapter: 3-minute thesis competition

Abstract

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 partAnd if not, come along to support your DPhil friends and colleagues, and to learn about the exciting maths being done by our research students.