## Research Seminars in the School of Mathematical Sciences

The School of Mathematical Sciences host regular research seminars delivered by internal and external researchers on topics across mathematical sciences. Seminars take place on the Kevin Street campus and are open to all.

## Seminar 05/12/13: Social contact network models for combatting airborne infectious diseases

Social contact network models for combatting airborne infectious diseases

Sean McGarraghy

Quinn & Smurfit Schools of Business, UCD

Thursday 5 December 2013

1pm, Room KA3-011, DIT Kevin Street

Abstract:

Standard "compartment" models of infectious disease transmission divide the population into compartments such as Susceptible, Exposed, Infected and Recovered (in the SEIR model) and model the dynamics of movement among the compartments by differential equations. However, they do not take into account the way disease actually spreads, through contacts between Exposed/Infected people and others. More recent approaches, e.g., (Moore & Newman, 2000; Meyers et al, 2005) have looked at social contact networks to model disease transmission and epidemics, with infection spreading along edges (physical contacts) in the social network. Once the network parameters have been chosen, simulations can be run to study the progress of the disease in the network and the efficacy of control or prevention approaches such as targeted vaccinations, and so make recommendations to decision makers on the best use of resources. In this talk we describe the use of social contact networks to study the airborne infectious disease measles in Tanzania, where it is still a major problem. Census and other data are used to better initialise the network with realistic contact information and network structure, and simulations are run both with and without interventions. This leads to recommendations for targeted interventions. This is joint work with Herieth Rwezaura.

## Seminar 17/10/13: Characterizing the list of eigenvalues of a matrix with nonnegative real entries

Characterizing the list of eigenvalues of a matrix with nonnegative real entries

Professor Thomas Laffey

UCD

Thursday 17 October 2013

1pm, Room KA3-011, DIT Kevin Street

## Seminar 26/09/13: Nonlinear Stationary Phase

Nonlinear Stationary Phase

Spyros Kamvissis

Thursday 26 September 2013

1pm, Room KA3-011, DIT Kevin Street

Abstract:

We consider the stability of the stationary and the periodic Toda lattice under a "short range" perturbation. It is an old result that in the first case the perturbed lattice asymptotically reduces to a finite system of solitons. In the periodic case, however it approaches a modulated lattice (plus a finite system of solitons) that we describe explicitly. Our method relies on the equivalence of the inverse spectral problem to a matrix Riemann-Hilbert factorisation problem: in the first case it is defined in the complex sphere while in the periodic case it is defined in a hyperelliptic curve. We prove our result by applying (and generalising) the so-called nonlinear stationary phase method for Riemann-Hilbert problems.

## Seminar 10/10/13: Schroedinger operators with Wigner-von Neumann potentials: pseudogaps in the continuous spectrum

Schroedinger operators with Wigner-von Neumann potentials: pseudogaps in the continuous spectrum

Sergey Simonov

Dublin Institute of Technology

Thursday 10 October 2013

1pm, Room KA3-011, DIT Kevin Street

Abstract:

In the first part of the talk we will recall the most basic notions related to the spectral theory of half-line Schroedinger operators. Then we will discuss phenomena of vanishing of the spectral density and presence of eigenvalues embedded into continuous spectrum.

## Seminar 18/04/13: Direct and inverse spectral problems for 2-dimensional Hamiltonian systems

Direct and inverse spectral problems for 2-dimensional Hamiltonian systems

Harald Woracek

Vienna University of Technology

Thursday 18 April 2013

1pm, Room KA3-011, DIT Kevin Street

### More Articles...

- Seminar 11/04/13: Analyticity of rotational travelling water waves
- Seminar 19/02/13: Classifying the long-run behaviour of globally stable differential equations subject to random perturbations
- Seminar 05/02/13: Dressing method in soliton theory
- Seminar 29/11/12: Eigenfunction expansions associated with the one-dimensional Schroedinger equation