Triangle Seminars
Tuesday, 22 Oct 2013
Exact representations of Susceptible-Infectious-Removed (SIR) epidemic dynamics on networks
Kieran Sharkey
(Liverpool)
Abstract:
The majority of epidemic models fall into two categories: 1) deterministic models represented by differential equations and 2) stochastic models which can be evaluated by simulation. In this presentation I will discuss the precise connection between these models. Until recently, exact correspondence was only established in situations exhibiting large degrees of symmetry or for infinite populations.
I will consider SIR dynamics on finite static contact networks. I will give an overview of two provably exact deterministic representations of the underlying stochastic model for tree-like networks. These are the message passing description of Karrer and Newman and my pair-based moment closure representation. I will discuss the relationship between the two representations and the relative merits of both.
The majority of epidemic models fall into two categories: 1) deterministic models represented by differential equations and 2) stochastic models which can be evaluated by simulation. In this presentation I will discuss the precise connection between these models. Until recently, exact correspondence was only established in situations exhibiting large degrees of symmetry or for infinite populations.
I will consider SIR dynamics on finite static contact networks. I will give an overview of two provably exact deterministic representations of the underlying stochastic model for tree-like networks. These are the message passing description of Karrer and Newman and my pair-based moment closure representation. I will discuss the relationship between the two representations and the relative merits of both.
Posted by: KCL
Wednesday, 23 Oct 2013
Conformal Bootstrap, the 3d Ising Model, and the Epsilon-expansion
📍 London
Slava Rychkov
(CERN and ENS and Univ.Paris 6)
Abstract:
A classic problem in field theory is to compute the critical exponents of the second-order phase transitions in 3d, for example for the Ising model universality class. Traditionally, this problem has been approached via RG-based techniques, such as the Wilson-Fisher epsilon-expansion. Here I will discuss another method to extract the critical exponents, and more, by using conformal field theory.
A classic problem in field theory is to compute the critical exponents of the second-order phase transitions in 3d, for example for the Ising model universality class. Traditionally, this problem has been approached via RG-based techniques, such as the Wilson-Fisher epsilon-expansion. Here I will discuss another method to extract the critical exponents, and more, by using conformal field theory.
Posted by: KCL
Resurgence in QFT: the Principal Chiral Model
Daniele Dorigoni
(DAMTP, Cambridge)
Abstract:
I will review the concept of Borel transform and resurgence behavior for the perturbative expansion of generic physical observables presenting particular examples coming from quantum mechanics and supersymmetric localized QFT.
I will then discuss more in details the physical role of non-perturbative saddle points of path integrals in theories without instantons, using the example of the asymptotically free two-dimensional principal chiral model (PCM). Standard topological arguments based on homotopy considerations suggest no role for non-perturbative saddles in such theories. However, resurgence theory, unifying perturbative and non-perturbative physics, predicts the existence of several types of non-perturbative saddles associated with features of the large-order structure of perturbation theory. These points are illustrated in the PCM, where we found new non-perturbative fractionalized saddle point field configurations, and give a quantum interpretation of previously discovered `uniton’ unstable classical solutions.
I will review the concept of Borel transform and resurgence behavior for the perturbative expansion of generic physical observables presenting particular examples coming from quantum mechanics and supersymmetric localized QFT.
I will then discuss more in details the physical role of non-perturbative saddle points of path integrals in theories without instantons, using the example of the asymptotically free two-dimensional principal chiral model (PCM). Standard topological arguments based on homotopy considerations suggest no role for non-perturbative saddles in such theories. However, resurgence theory, unifying perturbative and non-perturbative physics, predicts the existence of several types of non-perturbative saddles associated with features of the large-order structure of perturbation theory. These points are illustrated in the PCM, where we found new non-perturbative fractionalized saddle point field configurations, and give a quantum interpretation of previously discovered `uniton’ unstable classical solutions.
Posted by: IC
Thursday, 24 Oct 2013
Four point correlation functions and 5-point amplitudes
Paul Heslop
(Durham University)
Abstract:
Abstract:
There has been much progress in understanding the four-point
correlator of Stress Energy multiplets in N=4 SYM recently. I will
discuss recent progress in evaluating high loop Feynman integrals
using leading singularities, asymptotics and the symbol. This is used
to evaluate the three-loop four-point correlation function from its
integrand. Then I will show how the full (parity even and odd) 5-point
amplitude can be found from the same four-point correlator integrand.
Abstract:
There has been much progress in understanding the four-point
correlator of Stress Energy multiplets in N=4 SYM recently. I will
discuss recent progress in evaluating high loop Feynman integrals
using leading singularities, asymptotics and the symbol. This is used
to evaluate the three-loop four-point correlation function from its
integrand. Then I will show how the full (parity even and odd) 5-point
amplitude can be found from the same four-point correlator integrand.
Posted by: QMW
Friday, 25 Oct 2013
Instantons on Special Geometries
Maike Tormählen
(Hannover and City U.)
Abstract:
Instantons in higher-dimensional gauge theories appear, for example, in the context of string compactification. The instanton condition on the compact part of spacetime ensures supersymmetry preservation. My aim is to better understand instantons on special holonomy manifolds. I introduce higher-dimensional instantons and show how the instanton condition can be rewritten as a set of differential equations and algebraic conditions. These equations can be solved under certain simplifying assumptions. The algebraic conditions can be interpreted as relations of a certain quiver gauge theory. I describe the construction of these quivers and show that the instanton conditions match the quiver relations.
Instantons in higher-dimensional gauge theories appear, for example, in the context of string compactification. The instanton condition on the compact part of spacetime ensures supersymmetry preservation. My aim is to better understand instantons on special holonomy manifolds. I introduce higher-dimensional instantons and show how the instanton condition can be rewritten as a set of differential equations and algebraic conditions. These equations can be solved under certain simplifying assumptions. The algebraic conditions can be interpreted as relations of a certain quiver gauge theory. I describe the construction of these quivers and show that the instanton conditions match the quiver relations.
Posted by: IC