Postgraduate Seminar SeriesThe aim of this seminar series is to give postgraduate students (grads) an opportunity to share their interests with their peers. The series is coordinated by grads for grads. We welcome expressions of interest both in being a speaker for a seminar and in contributing to coordinating the series. If you have any comments on how we can make the most of the series, then we are all ears! How and where? How each seminar is run is up to the speaker on the day, e.g. 'whiteboard talk/talk with slides followed by Q&A'. It is also up to the speaker whether the seminar is held in person and/or via Zoom. Zoom: If you are thinking of attending a seminar via Zoom, please email the contact to confirm the details. Contact: Linus (email@example.com), Malcolm (firstname.lastname@example.org), Rafael (email@example.com), Virginia (firstname.lastname@example.org)
|(Welcoming expressions of interest in speaking.)|
Calendar of talks
|Monday 17 May 2021||4.10pm-5pm||CO350||
Speaker: Linus Richter
Title: On Homological Algebra, Group Extensions, and Descriptive Set Theory
Abstract: One way of thinking about group extensions is via short exact sequences in the category of groups. I will outline, using simplicial homology, how algebraic topology associates algebraic objects as topological invariants. Using cohomology and descriptive set theory, I will then briefly explain how the class of group extensions whose bonding morphisms are Borel is trivial in certain circumstances. This extends results by Kanovei and Reeken (2000).
|Monday 16 November 2020||3.10pm-4pm||CO431||
Speaker: Linus Richter
Title: When the search for proofs turns futile
Abstract: It came as a shock when in 1931 Kurt Gödel proved that mathematics is not complete. We can find mathematical statements that are "independent"; they can neither be proven nor refuted. Surprisingly, while the original independent "Gödel sentence" is a somewhat contrived construction, meaningful mathematical questions can be independent, too.
For example, a problem long confounded set theorists: is there a subset of the real numbers that is larger than the set of integers yet smaller than the real numbers themselves?
The assertion that such intermediate sets do not exist is called the "Continuum Hypothesis" (CH), and many set out to prove CH. In 1963, Paul Cohen showed that those attempts had been futile -- he proved that CH is independent. Cohen did so by inventing the versatile method of "forcing", which has since been used to yield many more independence proofs.
I will introduce some mathematical logic, the notion of independence, and why we care about all this. Using set theory, I will then outline how forcing yields a proof of the independence of CH.
|Monday 2 November 2020||3.10pm-4pm||CO431||
Speaker: Rafael Pereira Lima
Title: KMS states on groupoid C*-algebras
Abstract: The theory of C*-algebras started in the study of quantum mechanics. Since then, the subject has evolved and now it interacts with several areas of mathematics. Many important examples in the theory can be described as groupoid C*-algebras. In this talk, we will introduce these concepts and see a theorem due to Neshveyev, which gives a formula for the KMS states on groupoid C*-algebras. This theorem is an example of how topological properties of the groupoid help us understand C*-algebras in more detail.
|Monday 12 October 2020||3.10pm-4pm||CO431||
Speaker: Josh Baines
Title: The Painlevé-Gullstrand Form of Various Spacetimes
Abstract: Every spacetime is defined by its metric, the mathematical object which further defines the spacetime curvature. From the relativity principle, we have the freedom to choose which coordinate system to write our metric in. Some coordinate systems, however, are better than others. In this talk, we begin with a brief introduction into general relativity, Einstein's masterpiece theory of gravity. We then discuss some physically interesting spacetimes and the coordinate systems that the metrics of these spacetimes can be expressed in. More specifically, we discuss the existence of the rather useful Painlevé-Gullstrand coordinate system in these spacetimes. Using this useful coordinate system then allows us to conduct further analysis of these spacetimes, which we discuss.
|Monday 28 September 2020||3.10pm-4pm||CO431||
Speaker: Meenu Mariya Jose
Title: Recognising Principal Transversal Matroids
Abstract: Lattice path matroids are a well-behaved subclass of transversal matroids - they are closed under minors and duality and can easily be understood geometrically. Principal transversal matroids are another subclass of transversal matroids that is closed under duality but not minors. We investigated the intersection of these classes and found that a polynomial time algorithm can determine when a lattice path matroid is also principal. This is quite the contrast to the fact that it requires a tedious process to prove that a transversal matroid is principal. No prior knowledge of matroids is assumed.
|Monday 31 August 2020||3.10pm-4pm||Zoom||
Speaker: Michal Salter-Duke
Title: Tangles in networks and their application to describing communities
Abstract: Communities in networks are structurally or functionally distinct subgraphs. They can be disjoint or overlapping, depending upon definition; there are several definitions of communities, and many algorithms to identify them. We present a new definition based on the graph-theoretic concept of tangles, and investigate how well it identifies subgraphs that represent cohesive parts of the network, using two protein-protein interaction networks. This requires the development of an algorithm for finding tangles in graphs. We compare our results with standard methods from the literature based on metrics that use metadata to establish communities. Our results show that tangles provide a different view of communities that complements other methods, although they are computationally expensive to identify.
|Monday 10 August 2020||3.10pm-4pm||CO431||
Speaker: Liam Jolliffe
Title: FI modules and their submodules
Abstract: The theory of FI modules was introduced by Church, Ellenburg and Farb in 2014. These modules occur in many different places in the wild, but our interest in them is to gain some insight into the representation theory of the symmetric group. In this talk we will briefly revisit the representation theory of the symmetric group, before defining FI modules and seeing some examples. We will conclude by looking at some families of submodules of representable FI modules and describing some future work.
|Monday 27 July 2020||3.10pm-4pm||CO431 and Zoom||
Speaker: Malcolm Jones
Title: An algebraic model in public health: the groupoid of bubbles
Abstract: Groupoids are a generalisation of groups that arose in the early 20th century in work on quadratic forms by H. Brandt. Since their inception groupoids have provided a fruitful framework in a variety of fields, including fundamental work by J. Renault in operator algebras in the 80s. Groupoids have even appeared in epidemiology as recently as 2014 as models of cognitive processes in biology. In this talk, we will review the elementary theory of groupoids, and we will discuss a widely applicable groupoid model of interactions in populations.
|Monday 29 June 2020||3pm-3.50pm||CO431 and Zoom||
Speaker: Jordan Mitchell Barrett
Title: Ramsey theory of semigroups
Abstract: Many fundamental results in Ramsey theory concern the structure of certain semigroups (sets with an associative binary operation). These include the Hales–Jewett theorem, the Graham–Rothschild theorem, Gowers' FINₖ theorem, and Hindman's theorem. In this talk, we will discuss and aim to understand these fundamental results. Time permitting, we will see a common generalisation of many of these theorems to the setting of arbitrary layered semigroups, as introduced by Farah, Hindman and McLeod, and further generalised in ongoing work of Barrett and Lupini.
Follow the link to see the talk: https://www.youtube.com/watch?v=FuFWwWeeu-Q