Postgraduate Seminars Spring 2024

These seminars (unless otherwise stated) will take place on Tuesdays at 12pm-1pm on an almost weekly basis.

11 January 2024 in 25 Gordon Street - Room 416 - 2pm-3pm

Speaker: Enric Sole-Farre
Supervisor: Dr L Foscolo

TITLE: cohomogeneity one - from pdes to groups and odes

One of the main problems in differential geometry is solving PDEs involving different geometric quantities. Solutions to most of these PDEs are hard to come by, and one is often forced to reduce to very symmetric scenarios to find examples of solutions. I will first revise some instances of the case with maximal symmetry: homogeneous space; before moving to the cohomogeneity one case. The driving PDE examples will be the Einstein equation and the exceptional holonomy conditions.

18 January 2024 - No seminar


30 January 2024 in 25 Gordon Street - Room 416 - 2pm-3pm

Speaker: Maartje Wisse

TITLE: khovanov homology and embedded surfaces

Khovanov Homology is a categorical tool developed in the early 2000s which provides a generalisation of the Jones polynomial for knots (and links). This talk will cover Khovanov's construction and why it is an invariant. It will then focus on why functoriality makes it an ideal candidate for distinguishing embedded surfaces bounded by knots. The talk will be at an accessible level, with lots of pretty pictures!

6 February 2024 in 25 Gordon Street - Room 416 & On Zoom - 2pm-3pm

Speaker: Aporva Varshney

TITLE: What is the vibe of a derived category?

While Britain was plunged into the depths of Beatlemania, mathematicians in France were plunged into the depths of derived categories. We will seek to understand the vibes of derived categories, which are at the heart of modern day algebraic geometry. Instead of slogging through painful definitions I'll try to give an idea of what sorts of problems people like to work on and why they're important. I'll also hopefully make some vague allusions to string theory and explain why we sometimes have to listen to The Physicists. The only prerequisites will be basic linear algebra, and being okay with handwaving a lot of details.

Zoom link: https://ucl.zoom.us/j/91821165877
Meeting ID: 918 2116 5877


20 February 2024 in 25 Gordon Street - Room 416 & On Zoom - 2pm-3pm

Speaker: Devi Prasad Panigrahi

TITLE: Motility induced pattern formation in chemically communicating active matter

Biological cells are known to communicate with one another using chemical signals, through a process known as Quorum Sensing (QS). In several microorganisms, it has been seen that QS can regulate the motility of a cell, and the intra-cellular chemical machinery driving this has also been identified. However, it is still not clear how this intra-cellular regulation of motility which occurs at the individual cellular scale, can lead to large-scale pattern formation, at length scales which are orders of magnitude larger than the cell. In this talk, I will be presenting a minimalistic agent-based model which can capture some of the essential features of this process, and I will also compare this with a continuum description.

Zoom link: https://ucl.zoom.us/j/91538407334


27 February 2024 in 25 Gordon Street - Room 416 & On Zoom - 2pm-3pm

Speaker: Margaret-Ann Withington (Queen Mary University)

TITLE: viscosity bounds in liquids with different structure and bonding types

Recently, it was realised that liquid viscosity has a lower bound which is nearly constant for all liquids and is governed by fundamental physical constants. This was supported by experimental data in noble and molecular liquids. Here, we perform large-scale molecular dynamics simulations to ascertain this bound in two other important liquid types: the ionic molten salt system LiF and metallic Pb. We find that these ionic and metallic systems similarly have lower viscosity bounds corresponding to the minimum of kinematic viscosity of about 10−7 m2s. We show that this agrees with experimental data in other systems with different structures and bonding types, including noble, molecular, metallic and covalent liquids. This expands the universality of viscosity bounds into the main system types known.

Zoom link: https://ucl.zoom.us/j/5814881880 ; Meeting ID: 581 488 1880


5 March 2024 in 25 Gordon Street - Room 416 & On Zoom - 2pm-3pm

Speaker: Srinath Kailasa

TITLE: implementing modern fast multipole methods

N-Body problems arise naturally across science and engineering. Consider for example the electrostatic interaction of a set of N charged particles, or the gravitational interaction of N massive objects. Naively computed, simulating these interactions is intractable, as the problem is of O(N^2) complexity. In this talk I give a summary of powerful hierarchical methods that can, for certain classes of problems, reduce the complexity to O(N) or O(N ln N) with a bounded complexity. Indeed, the applicability of such methods is broadened by the formulation of a PDE as an integral equation, which leads to systems that correspond to N body problems. The integral equation formulation of PDEs opens up a wide variety of phenomena for computer simulation, from the electrostatics of virus molecules, to applications of electromagnetic scattering. I give an overview of recent software and algorithmic advances for the high performance simulation of such problems designed for the latest compute architectures.

Zoom link: https://ucl.zoom.us/j/92382946975

12 March 2024 - No Seminar


19 March 2024 in 25 Gordon Street - Room 416 & On Zoom - 2pm-3pm

Speaker: Samuel Harris

TITLE: electrocuting flowers and freezing penguins

Note: no animals or plants were harmed in the making of this talk.

Many natural phenomena can be well represented by simple, two-dimensional models and solved using simple, fast and accurate numerical methods. Two such problems will be explored in this talk. First, we investigate the electrostatic interaction between flowers and pollinators. It was recently discovered that bees and spiders can detect natural electrical fields. The question is whether flowers, which charge in the presence of such fields, use this to become more detectable to pollinators. We develop an extension of the AAA-least squares algorithm for solving such two-domain electrostatics problems, an extension which appears to be new in the literature. It is found that the electrical signals produced by the plant can reveal information to the pollinator about the flower shape, available pollen and the presence of other nearby arthropods. Second, we examine penguins huddling in a cold wind. The huddle evolves due to three effects: heat lost to the wind, heat generated by the penguins and the conservation of huddle size. The exterior governing equations for the wind and temperature are conformally invariant, motivating the use of a conformal mapping method in simulating the huddle propagation. The interior Poisson equation is not conformally invariant, so the interior temperature is instead found using the one-domain AAA-least squares algorithm. The results show that, irrespective of the starting shape, penguin huddles evolve into an egg-like steady shape dependent on the wind strength, parameterised by the Péclet number Pe, and a parameter β measuring the strength of the interior heat generation by the penguins. The numerical methods outlined in this talk are applicable to many other natural (free boundary) problems in fluid mechanics and mathematical biology.

Zoom link: https://ucl.zoom.us/j/96251197474


26 March 2024 in 25 Gordon Street - Room 416 & On Zoom - 2pm-3pm

Speaker: Yuxuan Wang

TITLE: a cost optimization problem in carbon management

Topics on climate changing have received high attention from all quarters in the recent decades, as it is one of the greatest threats to human civilization. The key point is about carbon management. Governments have taken many kinds of actions in recent decades, such as fiscal or pricing policies, regulatory policies, and direct public investment. Our work focuses on exploring the lowest economic cost to reach the goal of limiting global warming in a proper range. Different from some research in the past, we assume that the path of carbon emission develops as a stochastic process and solve the problem by stochastic optimal control. By building two stochastic processes for carbon emissions and invested funding, the problem is formulated into a stochastic target problem. It is also considered in quantile hedging case, which could help economize the cost a lot. We prove the dynamic programming principle(DPP) for our model, and then  provide the dynamic programming equation in both common and viscosity case.

Zoom link: https://ucl.zoom.us/j/95417079773