Although tensor products and their symmetrisation have appeared in mathematical literature since at least the mid-nineteenth century, they rarely appear in the function-theoretic operator theory literature. In this talk, I will introduce the symmetric and antisymmetric tensor products from an operator theoretic point of view. I will present results concerning some of the most fundamental operator-theoretic questions in this area, such as finding the norm and spectrum of the symmetric tensor products of operators. I will then work through some examples of symmetric tensor products of familiar operators, such as the unilateral shift, the adjoint of the shift, and diagonal operators.

Wreath-like product groups were introduced recently and used to construct the first positive examples of rigidity conjectures of Connes and Jones. In this talk, I will review those examples, as well as discuss some ideas to construct examples with other rigidity phenomena by modifying the wreath-like product construction.

This is a continuation of https://www.maths.ox.ac.uk/node/61240

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

Introductory talk Maths 2023.pdf

Leadership and Innovation Presentation.pdf

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.