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These seminars (unless otherwise stated) will take place on Thursdays at 2pm-3pm on an almost weekly basis.
Talks are being given by 2nd and 3rd year Mathematics PhD students for PhD students.
16 January 2025 - 2pm in Drayton House, Room B20
Speaker: Aporva Vashney
TITLE: should machines learn algebraic geometry
Abstract:
I’m going to discuss some ongoing work (in collaboration with Sara Veneziale, Alice Petrov, Abhiram Natarajan and Maosheng Yang) looking at applying machine learning techniques to a problem in algebraic geometry, where integer matrices representing algebraic shapes are classified into two classes denoted “terminal” and “non-terminal”. It was shown (by Coates-Kasprzyk-Veneziale) that neural networks can learn this classification to 95% accuracy, and can classify the data much faster than any known existing algorithm.
Importantly, the input data has a lot of symmetries, e.g. permuting the columns of the matrix doesn’t change its class. I’ll discuss various ideas we had to exploit this fact and improve the architecture of the network. I will completely ignore algebraic geometry in the talk and also mostly black box the neural network side of things, so the talk should be accessible for a wide range of backgrounds.
23 January 2025 - 2pm in 25 Gordon Street, Room 416
Speaker: Elvar Atlason
TITLE: morse theory
Abstract:
Morse Theory is a useful tool for understanding the topology of a manifold by slicing it up along an axis, thus forming a tomogram of the manifold. We will discuss some basic elements of Morse theory, with examples, and see how these lead to rich infinite-dimensional generalisations.
30 January 2025 - 2pm in 25 Gordon Street, Room 416
Speaker: Ella Williams
TITLE: Graph colourings and finding monochromatic patterns
Abstract:
We discuss what it means for a graph to be coloured and whether it is possible to find certain structures within them, before building up to our primary focus: a conjecture of Erdős and Gyárfás from 1995. This conjecture revolves around finding collections of monochromatic paths in coloured graphs. In joint work with Leo Versteegen and Alexey Pokrovskiy, we prove this to be true for all sufficiently large graphs. No prior knowledge of graphs or colourings is needed!
06 February 2025 - 2pm in 25 Gordon Street, Room 416
Speaker: Matias Moreno Bustamente
TITLE: on absence of embedded eigenvalues and stability of bgk waves
Abstract:
We consider space-periodic and inhomogeneous steady states of the one-dimensional electrostatic Vlasov-Poisson system, known as the Bernstein-Greene-Kruskal (BGK) waves. We prove that there exists a large class of the fixed background ion densities and spatial periods, so that the corresponding linearised operator around the associated BGK-equilibria has no embedded eigenvalues inside the essential spectrum. As a consequence we conclude a nonquantitative version of Landau damping around a subclass of such equilibria with monotone dependence on particle energy.
13 February 2025 - 2pm in Drayton House, Room B06
Speaker: Mahdi Hagshenas
TITLE: The effect of expansion and dispersion on waves in cosmological spacetimes
Abstract:
The standard cosmological models describing a homogeneous and isotropic universe in general relativity are represented by the FLRW spacetimes. A step toward understanding the dynamics of the Einstein equation near the FLRW spacetimes is to study the scalar wave equation on the FLRW spacetime and derive robust quantitative estimates.
In this talk, after a brief introduction, we consider the wave equation on cosmological FLRW spacetimes with the expansion rate in the decelerated regime. We then present upcoming work that develops robust techniques, including energy boundedness and the Morawetz estimate, by utilizing the expansion properties of the metric and the dispersive characteristics of waves. Finally, we explain how these estimates lead to a new proof of the decay of waves in the FLRW spacetimes.
20 February 2025
NO SEMINAR
27 February 2025 - 2pm on Maths room 416
Speaker: Clara Neather
TITLE: Understanding pattern formation during diatom morphogenesis using a polymer model
Abstract:
Diatoms are a type of microscopic algae that produce about 20% of the oxygen that we breathe. They have beautiful and intricate patterns in their silica shells, which vary widely across the many diatom species. One theory is that these patterns arise from the phase separation of polyamines, which clump together therefore creating a skeleton for the silica to form around. The variation between species could happen because of changes in the lengths and charges of the polyamines causing the polyamines to phase separate into different patterns. To explore this, I am working on a model in which polyamines are represented by chains of charged particles undergoing Brownian motion. I've also been looking at relating the shape of diatoms to their phylogenetic tree which I will talk a bit about if there is time!
06 March 2025 - 2pm in 230 Daryll Forde Seminar Room, Taviton Street
Speaker: Spencer Bullent
TITLE: Weyl Law of the Steklov Problem on Piecewise Smooth Domains
Abstract:
The spectrum of elliptic operators on a smooth domain encodes geometric information. One way of seeing this effect is via the asymptotics of the counting function, whose form is known as the Weyl law. Less is known about what happens in the case of geometric singularities, but it is an area of active research. This talk will cover the Weyl law of the Dirichlet to Nuemann map, both historical results for smooth domains, and recent results for piecewise smooth domains.
13 March 2025
NO SEMINAR
20 March 2025
NO SEMINAR
27 March 2025
NO SEMINAR