## 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 11/10/12: Indefinite spectral problems and the HELP inequality

Indefinite spectral problems and the HELP inequality

Alex Kostenko

Vienna University

Thursday 11 October 2012

1pm, Room KA3-011, DIT Kevin Street

Abstract:

We study two problems. The first one is the similarity problem for indefinite Sturm--Liouville spectral problems. The second object is the so-called HELP inequality, a version of the classical Hardy-Littlewood inequality proposed by W.N. Everitt in 1971. Both problems are well understood when the corresponding Sturm-Liouville differential expression is regular. Our main main objective is to give criteria for both the validity of the HELP inequality and the similarity to a self-adjoint operator in the singular case. Namely, we establish new criteria formulated in terms of the behavior of the corresponding Weyl-Titchmarsh m-functions at zero and at infinity. As a biproduct of this result we show that both problems are closely connected. Next we characterize the behavior of m-functions in terms of coefficients and then these results enable us to reformulate the obtained criteria in terms of coefficients. Finally, we apply these results for the study of the two-way diffusion equation, also known as the time-independent Fokker-Plank equation.

## Seminar 04/10/12: Seminar Elliptic variational problems with non-local operators

Elliptic variational problems with non-local operators

Carlos Argaez

Dublin Institute of Technology

Thursday 4 October 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 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 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.