Maths Colloquium 2018-19
The School Colloquia are given by eminent speakers and present an overview of important topics of general interest in the mathematical sciences.
These invited lectures are intended to be accessible to all graduate students and academics in the department. MMath and MSc students may also benefit from these presentations.
The talks normally take place on Wednesdays, 15:10-16:10, in lecture room M/0.40 on the ground floor of the School, unless advised differently. All are welcome to attend.
6 March 2019
Professor Kathryn Hess (Lausanne)
Topology meets neuroscience
I will present an overview of the wide variety of applications of topology to neuroscience that my group has worked on over the past few years, including classification of neuron morphologies and structural and functional connectomics and network plasticity. This work has been carried out in collaboration with the Blue Brain Project at the EPFL.
12 December 2018
Professor Barbara Niethammer (Bonn)
Smoluchowski's classical coagulation model
In 1916 Smoluchowski derived a mean-field model for mass aggregation in order to develop a mathematical theory for coagulation processes. Since Smoluchowski's groundbreaking work his model has been used in a diverse range of applications such as aerosol physics, polymerization, population dynamics, or astrophysics. After reviewing some basic properties of the model I will address the fundamental question of dynamic scaling, that is whether solutions develop a universal self-similar form for large times. This issue is only understood for some exactly solvable cases, while in the general case most questions are still completely open. I will give an overview of the main results in the past decades and explain why we believe that in general the scaling hypothesis is not true.
14 November 2018
Professor Vladimir Dotsenko (Trinity College Dublin)
Old and new aspects of the Poincaré-Birkhoff-Witt theorem
The Poincaré-Birkhoff-Witt theorem on universal enveloping algebras of Lie algebras is one of the fundamental results in many areas of mathematics: from differential geometry and representation theory to homological algebra and deformation quantisation. I shall give a short overview of that result and some of its proofs that emerged in about 120 years since Poincaré published a paper about it, and outline a new proof which perhaps captures its category-theoretic essence in the best way possible. The talk is partly based on a joint work with Pedro Tamaroff.
27 September 2018
Dr Peter Hintz (MIT)
Stability of black holes
More than a hundred years ago, Schwarzschild first wrote down the mathematical description of a black hole; on a technical level, black holes are certain types of solutions of Einstein's equations of general relativity. While they have since become part of popular culture, many fundamental questions about them remain unanswered: for example, it is not yet known mathematically if they are stable! I will explain what that means and outline a recent proof of full nonlinear stability (obtained in joint work with A. Vasy) in the case that the cosmological constant is positive, a condition consistent with current cosmological models of the universe. The talk is intended as a non-technical introduction to the subject, with a focus on the central role played by modern microlocal and spectral theoretical techniques.
- Download a list of colloquium talks from 2017/18 academic year.
- Download a list of colloquium talks from 2016/17 academic year.
- Download a list of colloquium talks from 2015/16 academic year.
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