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In her recent work, Mina Aganagic proposed novel perspectives on computing knot homologies associated with any simple Lie algebra. One of her proposals relies on counting intersection points between Lagrangians in Landau-Ginsburg models on symmetric powers of Riemann surfaces. In my talk, I am going to present a concrete algebraic algorithm for finding such intersection points, turning the proposal into an actual calculational tool. I am going to illustrate the construction on the example of the sl_2 invariant for the Hopf link. I am also going to comment on the extension of the story to homological invariants associated to gl(m|n) super Lie algebras, solving this long-standing problem. The talk is based on our work in progress with Mina Aganagic and Elise LePage.

5d Superconformal Field Theories (SCFTs) are intrinsically strongly-coupled UV fixed points, whose realization hinges on string theoretic methods: they can be constructed by compactifying M-theory on local Calabi-Yau threefold singularities or alternatively from the world-volume of 5-brane-webs in type IIB string theory. There is a correspondence between 5-brane-webs and toric Calabi-Yau threefolds, however this breaks down when multiple 5-branes are allowed to end on a single 7-brane. In this talk, we extend this connection and provide a geometric realization of brane configurations including 7-branes. Along the way, we also review techniques developed in the past few years to describe the Higgs branch of these 5d SCFTs, including magnetic quivers and Hasse diagram for symplectic singularities. 

I will present results from arXiv:2202.13924, where we studied the difference between integrable and chaotic motion in quantum theory as manifested by the complexity of the corresponding evolution operators. The notion of complexity of interest to us will be Nielsen’s complexity applied to the time-dependent evolution operator of the quantum systems. I will review Nielsen’s complexity, discuss the difficulties associated with this definition and introduce a simplified approach which appears to retain non-trivial information about the integrable properties of the dynamical systems.

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.

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

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.

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.

While scattering problems are posed on unbounded domains, volumetric discretizations typically require truncating the domain at a finite distance, closing the system with some sort of boundary condition.  These conditions typically suffer from some deficiency, such as perturbing the boundary value problem to be solved or changing the character of the operator so that the discrete system is difficult to solve with iterative methods.

We introduce a new technique for the Helmholtz problem, based on using the Green formula representation of the solution at the artificial boundary.  Finite element discretization of the resulting system gives optimal convergence estimates.  The resulting algebraic system can be solved effectively with a matrix-free GMRES implementation, preconditioned with the local part of the operator.  Extensions to the Morse-Ingard problem, a coupled system of pressure/temperature equations arising in modeling trace gas sensors, will also be given.

A 2d SCFT given as a non-linear sigma model of a Ricci-flat Kahler target 

space is not a rational CFT in general; only special points in the moduli 

space of the target-space metric, the 2d SCFTs are rational. 

Gukov-Vafa's paper in 2002 hinted at a possibility that such special points 

may be characterized by the property "complex multiplication" of the target space, 

which has its origin in number theory. We revisit the idea, refine the Conjecture, 

and prove it in the case the target space is T^4. 
 

This presentation is based on arXiv:2205.10299 and 2212.13028 .