Preparations are underway for the fourth MIGSAA annual student Colloquium in ICMS, 15 South College Street, Edinburgh EH8 9AA.
13.30: Registration and Coffee in the Chapterhouse
14.00: Melanie Rupflin, Newhaven Lecture Theatre
15.00: Sara Merino-Aceituno, Newhaven Lecture Theatre
16.00: Coffee Break, Chapterhouse
16.30: Enno Lenzmann, Newhaven Lecture Theatre
17.30: Wine Reception & Poster Session, Chapterhouse
Melanie Rupflin (University of Oxford)
Title: Geometric Flows and Minimal Surfaces
Abstract: The classical Plateau problems has been one of the most influential problems in the development of modern analysis. Posed initially by Lagrange, it asks whether a closed curve in Euclidean space always spans a surface with minimal possible area, a question that was answered positively by Douglas and Rado around 1930. In this talk I want to consider some aspects of the classical Plateau Problem and its generalisations and discuss furthermore how one can "flow" to such minimal surfaces by following a suitably defined gradient flow of the Dirichlet energy, i.e. of the integral of gradient squared.
Sara Merino-Aceituno (Imperial College London)
Title: Deriving Continuum Equations from Particle Models using Kinetic Theory: Applications to Biology
Abstract: From the interactions between many particles, individuals or agents, large-scale structures may arise that are at much larger scale than the individuals' sizes. Linking the particle dynamics with these macroscopic structures is key in many fields of Physics, Biology and Sociology. Kinetic theory provides the mathematical framework to build the rigorous bridge between the microscopic and macroscopic descriptions.
Enno Lenzmann (Universität Basel)
Title: Nonlocality, Criticality, and Complete Integrability
Abstract: This talk is an introduction to the recent analysis of nonlocal problems in PDE and geometry. As a guiding example, we will discuss the half-wave maps equation. This is a newly found nonlocal evolution equation with various intriguing properties including Möbius symmetries, infinitely many conservation laws, minimal surfaces, and solitons. In my talk, I will try to highlight some central aspects of the analysis of this evolution equation. The material is based on joint work with Patrick Gérard (Paris-Sud) and Armin Schikorra (Pittsburgh).