Speakers

Dr. Mario Falciatore (University of Galway, Ireland)

Tuesday 10^th June at 2pm in ADB1020

Title: Zeta Functions: from Arithmetic to Analysis

Abstract: Zeta functions appear in many areas of Mathematics, including Number Theory, Geometry and Mathematical Physics. The most famous example is the Riemann zeta function, which was originally defined as a simple infinite series yet is deeply connected to the distribution of prime numbers due to the remarkable arithmetic information it encodes. In this talk, we will explore what zeta functions are, why they are interesting and how they arise naturally in Mathematics. We will examine how they transform arithmetic properties into analytic entities and explore the surprising connections this perspective establishes between various branches of Mathematics.

For this talk no prior knowledge of Complex Analysis or Number Theory will be assumed — just curiosity!

Dr. Francesca Ballatore (Laboratoire J. A. Dieudonn´e, Universit´e Cˆote d’Azur, Nice, France)

Wednesday 11^th June at 2pm in ADB1020

Title: Modelling brain tumour progression and cerebral ventricle deformation through a patient-specific mechanical framework

Abstract: Brain tumours pose significant medical challenges due to their unpredictable location and varying degrees of malignancy. Malignant brain tumours, in particular, are known for their aggressive behaviour, presenting obstacles to effective treatment. The growth of a brain tumour can result in a mass effect, causing compression and displacement of surrounding healthy brain tissue. This can lead to changes in ventricle volume, resulting in increased intracranial pressure and potentially severe neurological complications [1]. Additionally, adjacent healthy areas may also be compressed, further compromising their normal function and contributing to the overall impact of the tumour. The current standard of care for brain tumours involves surgical resection as the primary treatment, followed by radiation therapy and chemotherapy, whenever feasible [2]. In this study, we propose a multiphase mechanical model for brain tumour growth that quantifies deformations and solid stresses caused by the expanding tumour mass. Our model considers the influence of brain fibres on the tumour’s anisotropic growth patterns, accounting for the irregular and heterogeneous nature of brain tumours. To construct realistic three-dimensional brain geometries and capture the shape of the ventricles, we incorporate patient-specific MRI and DTI data. By investigating the intricate interactions between brain tumours and the surrounding brain tissue, our model yields valuable insights into the extent of ventricular compression caused by tumour growth. Additionally, it elucidates the tumour’s impact on adjacent healthy brain areas. The numerical results obtained using the software FEniCS show the model’s effectiveness in capturing the complex dynamics of brain tumour growth and its mechanical impact on surrounding brain tissue. This work contributes to advancing our understanding of tumour progression and has the potential to guide the development of targeted therapies tailored to individual patients.

References:

[1] A. Ahmed, M. U. UlHaq, Z. Mustansar, A. Shaukat, and L. Margetts, How growing tu-

mour impacts intracranial pressure and deformation mechanics of brain. Royal Society

Open Science (2021), pp. 210165.

[2] R. Stupp et al., Radiotherapy plus Concomitant and Adjuvant Temozolomide for

Glioblastoma. New England Journal of Medicine (2005), pp. 987–996.