Past Seminars

26 November 2021
16:00
Mareli Grady (Outreach Events Coordinator) and Vicky Neale (Whitehead Lecturer)
Abstract

This session will take place live in L1 only and not online on Teams. 

Are you interested in sharing your love of Maths with the next generation of mathematicians, but you don’t know where to start? In this session we will discuss some basic principles and top tips for creating a workshop for students aged 14–16, and get you started on developing your own. There will also be the opportunity to work on this further afterwards and potentially deliver your session as part of the Oxfordshire Maths Masterclasses (for local school students) in Hilary Term. Bring along your favourite bit of maths and a willingness to have a go.

 

26 November 2021
16:00
Justin Kaidi

Further Information: 

It is also possible to join online via TEAMS.

Abstract

In this talk I will review the “holomorphic modular bootstrap,” i.e. the classification of rational conformal field theories via an analysis of the modular differential equations satisfied by their characters. By making use of the representation theory of PSL(2, Zn), we describe a method to classify allowed central charges and weights (c, hi) for theories with any number of characters d. This allows us to avoid various bottlenecks encountered previously in the literature, and leads to a classification of consistent characters up to d = 5 whose modular differential equations are uniquely fixed in terms of (c, hi). In the process, we identify the full set of constraints on the allowed values of the Wronskian index for fixed d ≤ 5.

The join button will be published on the right (Above the view all button) 30 minutes before the seminar starts (login required).

  • String Theory Journal Club
26 November 2021
15:00
Abstract

In this talk, I'll present inequalities bounding the number of critical cells in a filtered cell complex on the one hand, and the entries of the Betti tables of the multi-parameter persistence modules of such filtrations on the other hand. Using the Mayer-Vietoris spectral sequence we first obtain strong and weak Morse inequalities involving the above quantities, and then we improve the weak inequalities achieving a sharp lower bound for the number of critical cells. Furthermore, we prove a sharp upper bound for the minimal number of critical cells, expressed again in terms of the entries of Betti tables. This is joint work with Andrea Guidolin (KTH, Stockholm). The full paper is posted online as arxiv:2108.11427.

The join button will be published on the right (Above the view all button) 30 minutes before the seminar starts (login required).

  • Applied Topology Seminar
26 November 2021
14:00
Liam Jolliffe
Abstract

The Specht modules are of fundamental importance to the representation theory of the symmetric group, and their 0th cohomology is understood through entirely combinatorial methods due to Gordon James. Over fields of odd characteristic, Hemmer proposed a similar combinatorial approach to calculating their 1st degree cohomology, or extensions by the trivial module. This combinatorial approach motivates the definition of universal $p$-ary designs, which we shall classify. We then explore the consequences of this classification to problem of determining extensions of Specht modules. In particular, we classify all extensions of Specht modules indexed by two-part partitions by the trivial module and shall see some far-reaching conditions on when the first cohomology of a Specht module is trivial.

  • Junior Algebra and Representation Theory Seminar
26 November 2021
14:00
Dr Richard Earl
Abstract

This session is particularly aimed at fourth-year and OMMS students who are completing a dissertation this year. The talk will be given by Dr Richard Earl who chairs Projects Committee. For many of you this will be the first time you have written such an extended piece on mathematics. The talk will include advice on planning a timetable, managing the  workload, presenting mathematics, structuring the dissertation and creating a narrative, providing references and avoiding plagiarism.

26 November 2021
10:00
Darryl Hond

Further Information: 

The challenge they will present is on predicting the performance of artificial neural network (ANN) classifiers and understanding their reliability for predicting data that are not presented in the training set. We encourage all interested party to join us and especially those interested in machine learning and data science.

  • Industrial and Interdisciplinary Workshops
25 November 2021
14:00
Tim Dodwell
Abstract

Uncertainty Quantification through Markov Chain Monte Carlo (MCMC) can be prohibitively expensive for target probability densities with expensive likelihood functions, for instance when the evaluation it involves solving a Partial Differential Equation (PDE), as is the case in a wide range of engineering applications. Multilevel Delayed Acceptance (MLDA) with an Adaptive Error Model (AEM) is a novel approach, which alleviates this problem by exploiting a hierarchy of models, with increasing complexity and cost, and correcting the inexpensive models on-the-fly. The method has been integrated within the open-source probabilistic programming package PyMC3 and is available in the latest development version.

In this talk I will talk about the problems with the Multilevel Markov Chain Monte Carlo (Dodwell et al. 2015). In so we will prove detailed balance for Adaptive Multilevel Delayed Acceptance, as well as showing that multilevel variance reduction can be achieved without bias, not possible in the original MLMCMC framework.

I will talk about our implementation in the latest version of pymc3, and demonstrate how for classical inverse problem benchmarks the AMLDA sampler offers huge computational savings (> factor of 100 fold speed up).

Finally I will talk heuristically about new / future research, in which we seek to develop parallel strategies for this inherently sequential sampler, as well as point to interesting applied application areas in which the method is proving particular effective.

 

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This talk will be in person.

  • Computational Mathematics and Applications Seminar

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