Tue, 07 Mar 2017

13:00 - 14:00
N3.12

Sequences

TBA
Fri, 07 Apr 2017

12:00 - 13:00
L6

Nonlinear stability of relativistic vortex sheets in two spatial dimensions

Tao Wang
(University of Brescia)
Abstract

We study vortex sheets for the relativistic Euler equations in three-dimensional Minkowski spacetime. The problem is a nonlinear hyperbolic problem with a characteristic free boundary. The so-called Lopatinskii condition holds only in a weak sense, which yields losses of derivatives. A necessary condition for the weak stability is obtained by analyzing roots of the Lopatinskii determinant associated to the linearized problem. Under such stability condition,  we prove short-time existence and nonlinear stability of relativistic vortex sheets by the Nash-Moser iterative scheme.

Fri, 07 Apr 2017

11:00 - 12:00
L6

On the weakly nonlinear Kelvin-Helmholtz instability of current-vortex sheets

Paolo Secchi
(University of Brescia)
Abstract

We consider the free boundary problem for 2D current-vortex sheets in ideal incompressible magneto-hydrodynamics near the transition point between the linearized stability and instability. In order to study the dynamics of the discontinuity near the onset of the instability, Hunter and Thoo have introduced an asymptotic quadratically nonlinear integro-differential equation for the amplitude of small perturbations of the planar discontinuity. 
In this talk we present our results about the well-posedness of the problem in the sense of Hadamard, under a suitable stability condition, that is the 
local-in-time existence in Sobolev spaces and uniqueness of smooth solutions to the Cauchy problem, and the strong continuous dependence on the data in the same topology.
Joint works with: Alessandro Morando and Paola Trebeschi.
 

Cancer is a complex and resilient set of diseases and the search for a cure requires a multi-strategic approach. Oxford Mathematicians Lucy Hutchinson, Eamonn Gaffney, Philip Maini and Helen Byrne and Jonathan Wagg and Alex Phipps from Roche have addressed this challenge by focusing on the mathematical modelling of blood vessel growth in cancer tumours.

Thu, 09 Mar 2017

16:00 - 17:00
L2

(COW seminar) Gopakumar-Vafa invariants via vanishing cycles

Davesh Maulik
(MIT)
Abstract

Given a Calabi-Yau threefold X, one can count curves on X using various approaches, for example using stable maps or ideal sheaves; for any curve class on X, this produces an infinite sequence of invariants, indexed by extra discrete data (e.g. by the domain genus of a stable map).  Conjecturally, however, this sequence is determined by only a finite number of integer invariants, known as Gopakumar-Vafa invariants.  In this talk, I will propose a direct definition of these invariants via sheaves of vanishing cycles, building on earlier approaches of Kiem-Li and Hosono-Saito-Takahashi.  Conjecturally, these should agree with the invariants as defined by stable maps.  I will also explain how to prove the conjectural correspondence for irreducible curves on local surfaces.  This is joint work with Yukinobu Toda.

Thu, 09 Mar 2017

14:30 - 15:30
L4

(COW seminar) Strange duality on abelian surfaces

Barbara Bolognese
Abstract

With the purpose of examining some relevant geometric properties of the moduli space of sheaves over an algebraic surface, Le Potier conjectured some unexpected duality between the complete linear series of certain natural divisors, called Theta divisors, on the moduli space. Such conjecture is widely known as Strange Duality conjecture. After having motivated the problem by looking at certain instances of quantization in physics, we will work in the setting of surfaces. We will then sketch the proof in the case of abelian surfaces, giving an idea of the techniques that are used. In particular, we will show how the theory of discrete Heisenberg groups and fiber wise Fourier-Mukai transforms, which might be applied to other cases of interest, enter the picture. This is joint work with Alina Marian, Dragos Opera and Kota Yoshioka.

New methods for localising radiation treatment of tumours depend on estimating the spatial distribution of oxygen in the tissue. Oxford Mathematicians hope to improve such estimates by predicting tumour oxygen distributions and radiotherapy response using high resolution images of real blood vessel networks.

Thu, 11 May 2017

17:00 - 18:15
L1

The Sound of Symmetry and the Symmetry of Sound - Marcus du Sautoy

Marcus du Sautoy
(University of Oxford)
Abstract

Symmetry has played a critical role both for composers and in the creation of musical instruments. From Bach’s Goldberg Variations to Schoenberg’s Twelve-tone rows, composers have exploited symmetry to create variations on a theme. But symmetry is also embedded in the very way instruments make sound. The lecture will culminate in a reconstruction of nineteenth-century scientist Ernst Chladni's exhibition that famously toured the courts of Europe to reveal extraordinary symmetrical shapes in the vibrations of a metal plate.

The lecture will be preceded by a demonstration of the Chladni plates with the audience encouraged to participate. Each of the 16 plates will have their own dials to explore the changing input and can accommodate 16 players at a time. Participants will be able to explore how these shapes might fit together into interesting tessellations of the plane. The ultimate idea is to create an aural dynamic version of the walls in the Alhambra.

The lecture will start at 5pm, but the demonstration will be available from 2.30pm.

Please email @email to register

 

 

 

Tue, 02 May 2017
14:00
L3

Nonconvex geometry of low-rank optimizations

Gongguo Tang
(Colorado School of Mines)
Abstract

The past few years have seen a surge of interest in nonconvex reformulations of convex optimizations using nonlinear reparameterizations of the optimization variables. Compared with the convex formulations, the nonconvex ones typically involve many fewer variables, allowing them to scale to scenarios with millions of variables. However, one pays the price of solving nonconvex optimizations to global optimality, which is generally believed to be impossible. In this talk, I will characterize the nonconvex geometries of several low-rank matrix optimizations. In particular, I will argue that under reasonable assumptions, each critical point of the nonconvex problems either corresponds to the global optimum of the original convex optimizations, or is a strict saddle point where the Hessian matrix has a negative eigenvalue. Such a geometric structure ensures that many local search algorithms can converge to the global optimum with random initializations. Our analysis is based on studying how the convex geometries are transformed under nonlinear parameterizations.

Systemic risk, loosely defined, describes the risk that large parts of the financial system will collapse, leading to potentially far-reaching consequences both within and beyond the financial system. Such risks can materialize following shocks to relatively small parts of the financial system and then spread through various contagion channels. Assessing the systemic risk a bank poses to the system has thus become a central part of regulating its capital requirements.

Subscribe to