Fri, 20 Nov 2009

16:30 - 17:00
DH 1st floor SR

Modelling Overland Flow and Soil Erosion: Sediment Transportation

Jason Zhong
(University of Oxford)
Abstract

Hairsine-Rose (HR) model is the only multi sediment size soil erosion

model. The HR model is modifed by considering the effects of sediment bedload and

bed elevation. A two step composite Liska-Wendroff scheme (LwLf4) which

designed for solving the Shallow Water Equations is employed for solving the

modifed Hairsine-Rose model. The numerical approximations of LwLf4 are

compared with an independent MOL solution to test its validation. They

are also compared against a steady state analytical solution and experiment

data. Buffer strip is an effective way to reduce sediment transportation for

certain region. Modifed HR model is employed for solving a particular buffer

strip problem. The numerical approximations of buffer strip are compared

with some experiment data which shows good matches.

Wed, 28 Oct 2009
11:30
ChCh, Tom Gate, Room 2

When good groups go bad

Owen Cotton-Barratt
(University of Oxford)
Abstract

Much of group theory is concerned with whether one property entails another. When such a question is answered in the negative it is often via a pathological example. We will examine the Rips construction, an important tool for producing such pathologies, and touch upon a recent refinement of the construction and some applications. In the course of this we will introduce and consider the profinite topology on a group, various separability conditions, and decidability questions in groups.

Wed, 18 Nov 2009
11:30
ChCh, Tom Gate, Room 2

The Major Problems in Group Representation Theory

David Craven
(University of Oxford)
Abstract

The representation theory of groups is surrounded by deep and difficult conjectures. In this talk we will take a tour of (some of) these problems, including Alperin's weight conjecture, Broué's conjecture, and Puig's finiteness conjecture.

Fri, 23 Oct 2009

16:30 - 17:00
DH 1st floor SR

Dislocation dynamics and instability

Yichao Zhu
(University of Oxford)
Abstract

Dislocation channel-veins and Persist Slip Band (PSB) structures are characteristic configurations in material science. To find out the formation of these structures, the law of motion of a single dislocation should be first examined. Analogous to the local expansion in electromagnetism, the self induced stress is obtained. Then combining the empirical observations, we give a smooth mobility law of a single dislocation. The stability analysis is carried our asymptotically based on the methodology in superconducting vortices. Then numerical results are presented to validate linear stability analysis. Finally, based on the evidence given by the linear stability analysis, numerical experiments on the non-linear evolution are carried out.

Tue, 03 Nov 2009

14:00 - 15:00
Gibson 1st Floor SR

An alternative approach to regularity for the Navier-Stokes equations in critical spaces

Gabriel Koch
(University of Oxford)
Abstract

We present an alternative viewpoint on recent studies of regularity of solutions to the Navier-Stokes equations in critical spaces. In particular, we prove that mild solutions which remain bounded in the

space $\dot H^{1/2}$ do not become singular in finite time, a result which was proved in a more general setting by L. Escauriaza, G. Seregin and V. Sverak using a different approach. We use the method of "concentration-compactness" + "rigidity theorem" which was recently developed by C. Kenig and F. Merle to treat critical dispersive equations. To the authors' knowledge, this is the first instance in which this method has been applied to a parabolic equation. This is joint work with Carlos Kenig.

Thu, 19 Nov 2009

12:30 - 13:30
Gibson 1st Floor SR

Regularity near the axis for axially symmetric stationary electro-vaccum space-times

Luc Nguyen
(University of Oxford)
Abstract

According to the Ernst-Geroch reduction, in an axially symmetric stationary electrovac spacetime, the Einstein-Maxwell equations reduce to a harmonic map problem with singular boundary data. I will discuss the “regularity” of the reduced harmonic maps near the boundary and its implication on the regularity of the corresponding spacetimes.

Wed, 04 Nov 2009

11:30 - 12:30
ChCh, Tom Gate, Room 2

The Quest for $\mathbb{F}_\mathrm{un}$

Tobias Barthel
(University of Oxford)
Abstract

We will present different ideas leading to and evolving around geometry over the field with one element. After a brief summary of the so-called numbers-functions correspondence we will discuss some aspects of Weil's proof of the Riemann hypothesis for function fields. We will see then how lambda geometry can be thought of as a model for geometry over $\mathbb{F}_\mathrm{un}$ and what some familiar objects should look like there. If time permits, we will

explain a link with stable homotopy theory.

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