Past Colloquia

1 December 2017
16:00
Abstract

The theory of metric measure spaces with Ricci curvature from below is growing very quickly, both in the "Riemannian" class RCD and the general  CD one. I will review some of the most recent results, by illustrating the key identification results and technical tools (at the level of calculus in metric measure spaces) underlying these results.
 

10 November 2017
16:00
Professor Paul Riley, Professor Eleanor Stride
Abstract

The fourth QBIOX Colloquium will take place in the Mathematical Institute on Friday 10th November (5th week) and feature talks from Professor Paul Riley (Department of Pathology, Anatomy and Genetics / BHF Oxbridge Centre for Regenerative Medicine, https://www.dpag.ox.ac.uk/research/riley-group) and Professor Eleanor Stride (Institute of Biomedical Engineering, http://www.ibme.ox.ac.uk/research/non-invasive-therapy-drug-delivery/peo...).

1600-1645 - Paul Riley, "Enroute to mending broken hearts".
1645-1730 - Eleanor Stride, "Reducing tissue hypoxia for cancer therapy".
1730-1800 - Networking and refreshments.

We very much hope to see you there. As ever, tickets are not necessary, but registering to attend will help us with numbers for catering.
Please see the following link for further details and a link to register.
https://www.eventbrite.co.uk/e/qbiox-colloquium-michelmas-term-2017-tick...

Abstracts
Paul Riley - "En route to mending broken hearts".
We adopt the paradigm of understanding how the heart develops during pregnancy as a first principal to inform on adult heart repair and regeneration. Our target for cell-based repair is the epicardium and epicardium-derived cells (EPDCs) which line the outside of the forming heart and contribute vascular endothelial and smooth muscle cells to the coronary vasculature, interstitial fibroblasts and cardiomyocytes. The epicardium can also act as a source of signals to condition the growth of the underlying embryonic heart muscle. In the adult heart, whilst the epicardium is retained, it is effectively quiescent. We have sought to extrapolate the developmental potential of the epicardium to the adult heart following injury by stimulating dormant epicardial cells to give rise to new muscle and vasculature. In parallel, we seek to modulate the local environment into which the new cells emerge: a cytotoxic mixture of inflammation and fibrosis which prevents cell engraftment and integration with survived heart tissue. To this end we manipulate the lymphatic vessels in the heart given that, elsewhere in the body, the lymphatics survey the immune system and modulate inflammation at peripheral injury sites. We recently described the development of the cardiac lymphatic vasculature and revealed in the adult heart that they undergo increased vessel sprouting (lymphangiogenesis) in response to injury, to improve function, remodelling and fibrosis. We are currently investigating whether increased lymphangiogenesis functions to clear immune cells and constrain the reparative response for optimal healing. 

Eleanor Stride - "Reducing tissue hypoxia for cancer therapy"
Hypoxia, i.e. a reduction in dissolved oxygen concentration below physiologically normal levels, has been identified as playing a critical role in the progression of many types of disease and as a key determinant of the success of cancer treatment. It poses a particular challenge for treatments such as radiotherapy, photodynamic and sonodynamic therapy which rely on the production of reactive oxygen species. Strategies for treating hypoxia have included the development of hypoxia-selective drugs as well as methods for directly increasing blood oxygenation, e.g. hyperbaric oxygen therapy, pure oxygen or carbogen breathing, ozone therapy, hydrogen peroxide injections and administration of suspensions of oxygen carrier liquids. To date, however, these approaches have delivered limited success either due to lack of proven efficacy and/or unwanted side effects. Gas microbubbles, stabilised by a biocompatible shell have been used as ultrasound contrast agents for several decades and have also been widely investigated as a means of promoting drug delivery. This talk will present our recent research on the use of micro and nanobubbles to deliver both drug molecules and oxygen simultaneously to a tumour to facilitate treatment.

20 October 2017
16:00
Robert Calderbank
Abstract

Coding theory revolves around the question of what can be accomplished with only memory and redundancy. When we ask what enables the things that transmit and store information, we discover codes at work, connecting the world of geometry to the world of algorithms.

This talk will focus on those connections that link the real world of Euclidean geometry to the world of binary geometry that we associate with Hamming.

20 October 2017
14:30
Peter Sarnak
Abstract

A cubic polynomial equation in four or more variables tends to have many integer solutions, while one in two variables has a limited number of such solutions. There is a body of work establishing results along these lines. On the other hand very little is known in the critical case of three variables. For special such cubics, which we call Markoff surfaces, a theory can be developed. We will review some of the tools used to deal with these and related problems.

Joint works with Bourgain/Gamburd and with Ghosh
 

9 June 2017
16:00
Caroline Series
Abstract

The cover of the December 2016 AMS Notices shows an eye-like region picked out by blue and red dots and surrounded by green rays. The picture, drawn by Yasushi Yamashita, illustrates Gaven Martin’s search for the smallest volume 3-dimensional hyperbolic orbifold. It represents a family of two generator groups of isometries of hyperbolic 3-space which was recently studied, for quite different reasons, by myself, Yamashita and Ser Peow Tan.

After explaining the coloured dots and their role in Martin’s search, we concentrate on the green rays. These are Keen-Series pleating rays which are used to locate spaces of discrete groups. The theory also suggests why groups represented by the red dots on the rays in the inner part of the eye display some interesting geometry.
 

12 May 2017
16:00
Abstract

Hinke Osinga, University of Auckland
joint work with: Bernd Krauskopf and Stefanie Hittmeyer (University of Auckland)

Dynamical systems of Lorenz type are similar to the famous Lorenz system of just three ordinary differential equations in a well-defined geometric sense. The behaviour of the Lorenz system is organised by a chaotic attractor, known as the butterfly attractor. Under certain conditions, the dynamics is such that a dimension reduction can be applied, which relates the behaviour to that of a one-dimensional non-invertible map. A lot of research has focussed on understanding the dynamics of this one-dimensional map. The study of what this means for the full three-dimensional system has only recently become possible through the use of advanced numerical methods based on the continuation of two-point boundary value problems. Did you know that the chaotic dynamics is organised by a space-filling pancake? We show how similar techniques can help to understand the dynamics of higher-dimensional Lorenz-type systems. Using a similar dimension-reduction technique, a two-dimensional non-invertible map describes the behaviour of five or more ordinary differential equations. Here, a new type of chaotic dynamics is possible, called wild chaos. 


 

 

28 April 2017
16:00
Catharina Stroppel
Abstract

Permutations of finitely many elements are often drawn as permutation diagrams. We take this point of view as a motivation to construct and describe more complicated algebras arising for instance from differential operators, from operators acting on (co)homologies, from invariant theory, or from Hecke algebras. The surprising fact is that these diagrams are elementary and simple to describe, but at the same time describe relations between cobordisms as well as categories of represenetations of p-adic groups. The goal of the talk is to give some glimpses of these phenomena and indicate which role categorification plays here.
 

3 March 2017
16:00
Ana Caraiani
Abstract

The law of quadratic reciprocity and the celebrated connection between modular forms and elliptic curves over Q are both examples of reciprocity laws. Constructing new reciprocity laws is one of the goals of the Langlands program, which is meant to connect number theory with harmonic analysis and representation theory.

In this talk, I will survey some recent progress in establishing new reciprocity laws, relying on the Galois representations attached to torsion classes which occur in the cohomology of arithmetic hyperbolic 3-manifolds. I will outline joint work in progress on better understanding these Galois representations, proving modularity lifting theorems in new settings, and applying this to elliptic curves over imaginary quadratic fields.

10 February 2017
16:00
Abstract

Self-organization is observed in systems driven by the “social engagement” of agents with their local neighbors. Prototypical models are found in opinion dynamics, flocking, self-organization of biological organisms, and rendezvous in mobile networks.

We discuss the emergent behavior of such systems. Two natural questions arise in this context. The underlying issue of the first question is how different rules of engagement influence the formation of clusters, and in particular, the emergence of 'consensus'. Different paradigms of emergence yield different patterns, depending on the propagation of connectivity of the underlying graphs of communication.  The second question involves different descriptions of self-organized dynamics when the number of agents tends to infinity. It lends itself to “social hydrodynamics”, driven by the corresponding tendency to move towards the local means. 

We discuss the global regularity of social hydrodynamics for sub-critical initial configurations.

27 January 2017
16:00
Paul Klemperer
Abstract

Mathematical methods are increasingly being used to design auctions. Paul Klemperer will talk about some of his own experience which includes designing the U.K.'s mobile phone licence auction that raised £22.5 billion, and a new auction that helped the Bank of England in the financial crisis. (The then-Governor, Mervyn King, described it as "a marvellous application of theoretical economics to a practical problem of vital importance".) He will also discuss further development of the latter auction using convex and "tropical" geometric methods.

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