Thu, 07 Jun 2007

14:00 - 15:00
Comlab

Artificial time integration

Prof Uri Ascher
(University of British Columbia)
Abstract

Many recent algorithmic approaches involve the construction of a differential equation model for computational purposes, typically by introducing an artificial time variable. The actual computational model involves a discretization of the now time-dependent differential system, usually employing forward Euler. The resulting dynamics of such an algorithm is then a discrete dynamics, and it is expected to be ''close enough'' to the dynamics of the continuous system (which is typically easier to analyze) provided that small -- hence many -- time steps, or iterations, are taken. Indeed, recent papers in inverse problems and image processing routinely report results requiring thousands of iterations to converge. This makes one wonder if and how the computational modeling process can be improved to better reflect the actual properties sought.

In this talk we elaborate on several problem instances that illustrate the above observations. Algorithms may often lend themselves to a dual interpretation, in terms of a simply discretized differential equation with artificial time and in terms of a simple optimization algorithm; such a dual interpretation can be advantageous. We show how a broader computational modeling approach may possibly lead to algorithms with improved efficiency.

Wed, 06 Jun 2007
12:00
L3

Constructing Gauge Theory Amplitudes

Ruth Britto
(Amsterdam)
Abstract
 
Gauge theory amplitudes lie at the meeting ground of perturbative QCD and twistor string theory.  The past three years have seen dramatic developments in the analytic computation of amplitudes and their interpretation in twistor space geometry.  I will discuss applications to collider experiments and describe direct, systematic procedures for deriving one-loop amplitudes from tree amplitudes, using new insights regarding unitarity.

 
 
Tue, 05 Jun 2007
17:00
L1

The beginning of the Atlas of self-similar groups

Prof. R. Grigorchuk
(Texas A&M)
Abstract

 

We will speak about the problem of classification of self-similar groups. The

main focus will be on groups generated by three-state  automata over an

alphabet on two letters. Numerous examples will be presented, as well as some

results concerning this class of groups.

 

Mon, 04 Jun 2007
14:15
DH 3rd floor SR

SLE and alpha SLE driven by Levy processes

Dr Qingyang Guan
(Imperial College, London)
Abstract
  Schramm Loewner Evolutions (SLE) are random planar curves (if κ ≤ 4) or growing compact sets generated by a curve (if κ > 4). We consider more general L
Mon, 04 Jun 2007
14:00
DH 2nd floor SR

Discussion Meeting 2

Abstract

There will be three discussion meetings based on aspects of the

programme open to all internal project members. Others interested in

attending should contact Carlos Mora-Corral.

Mon, 04 Jun 2007
12:00
L3

Evaluating gauge-theoretic amplitudes with twistor diagrams

Andrew Hodges
(Oxford)
Abstract
 
Amplitudes in gauge theory at tree-level can be expressed economically in terms of twistor diagrams  (hep-th/0503060, hep-th/0512336). This formalism has recently been used to write down the 8-field scattering amplitudes in a simple form, going beyond the results previously obtained (hep-th/0603101). This talk will give an elementary account of how this is done.
 
Fri, 01 Jun 2007
15:15
L3

Borel Isomorphism Relations

David Marker
(University of Illinois, Chicago)
Abstract

 

Countable Borel equivalence relations arise naturally as orbit equivalence

relations for countable groups. For each countable Borel equivalence relation E

there is an infinitary sentence such that E is equivalent to the isomorphism

relation on countable models of that sentence. For first order theories the

question is open.