## 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 03/05/12: Soliton interactions of a class of vector nonlinear Schroedinger equations

Soliton interactions of a class of vector nonlinear Schroedinger equations

Vladimir Gerdjikov

Institute for Nuclear Research & Nuclear Energy, Bulgarian Academy of Sciences

Thursday 3 May 2012

1pm, Room KA3-011, DIT Kevin Street

## Seminar 26/04/12: Modelling the renal medulla

Modelling the renal medulla

Alan Hegarty

University of Limerick

Thursday 26 April 2012

1pm, Room KA3-011, DIT Kevin Street

Abstract:

It has been understood for more than 60 years that the kidney concentrates urine using countercurrent exchanges among multiple parallel tubes. The originally hypothesised primary driving force, active salt transport in the ascending limbs of the "loops of Henle", has subsequently been observed to be possible only for the outer medulla, and the driving force within the inner medulla is still not fully understood. I will review the history of models of the urine concentration function of the kidney and present some recent work on transient models.

## Seminar 09/04/12: W.S Gosset or "Student" - the Guinness Brewer in charge of Statistics

W.S Gosset or "Student" - the Guinness Brewer in charge of Statistics

Philip Boland

University College Dublin

Thursday 19 April 2012

1pm, Room KA3-011, DIT Kevin Street

Abstract:

The talk about William Sealy Gosset, a famed statistician from Guinness, will be of a general and historical nature, comprehensible to anyone with an interest in statistics and/or industrial mathematics.

## Seminar 24/04/12: Lane-Emden equation and beyond

Lane-Emden equation and beyond

Marius Ghergu

University College Dublin

Tuesday 24 April 2012

1pm, Room KA3-011, DIT Kevin Street

Abstract:

Lane-Emden equation was introduced in the end of 19th century to account for polytropes in hydrostatic equilibrium as simple model for stars. We present an overview of some recent results regarding a qualitative study of this equation and its associated systems.

## Seminar 29/03/12: Integrable models for shallow water with 'energy dependent' spectral problems

Integrable models for shallow water with 'energy dependent' spectral problems

Tony Lyons

Dublin Institute of Technology

Thursday 29 March 2012

1pm, Room KA3-011, DIT Kevin Street

Abstract:

We study the inverse problem for spectral operators with 'energy depending potentials'. In particular, we study spectral operators with quadratic dependence on the spectral parameter. The corresponding hierarchy of integrable equations includes the Kaup-Boussinesq equation. The talk will briefly review the Riemann-Hilbert problem formulation for this inverse problem. We will then discuss the explicit construction of the one-soliton solution. We also present a brief overview of the multi-soliton solution. Based on work with R. Ivanov.