The Mathematical Horizons Mini-Symposium, organized by the Qatar Mathematics Research Forum (QMRF), brings together leading researchers to discuss recent advances in several areas of Mathematics. Through a series of invited talks, the event explores exciting topics like mathematical models of sustainability, physics-informed neural networks, wrinkling and geometric mechanics.

Schedule

• 12:30–1:00 p.m.
  Lunch and Informal Networking
• 1:00–2:00 p.m.
  Talk 1: Henrik Shahgholian: Exploring the Sustainability Landscape: A Mathematical Perspective
  
• 2:00–3:00 p.m.
  Talk 2: Rafayel Barkhudaryan: Physics-Informed Neural Networks for  Fully Nonlinear PDE’s
• 3:00–3:30 p.m.
  Coffee Break
• 3:30–4:30 p.m.
  Talk 3: Francesco Dal Corso: Bifurcations and wrinkling instabilities (and restabilization) in ultra-thin parallelogram-shaped hyperelastic membranes 

RSVP to attend

Talk 1: Henrik Shahgholian: Exploring the Sustainability Landscape: A Mathematical Perspective

About the speaker: Full Professor of Mathematics at KTH Royal Institute of Technology (Sweden), widely recognized for his extensive contributions to the field of Partial Differential Equations (PDEs), specifically focusing on free boundary problems. He has over 140 publications, including 2 books and he frequently collaborates with other distinguished mathematicians, such as Luis Caffarelli and Alessio Figalli, on advanced elliptic equations and free boundary regularity.

Abstract: In this talk, I will share my personal journey in exploring sustainability through a mathematical lens. My goal is to show teachers and students why we must bring the conversation about our planet into our classrooms and academic meetings. We will focus on raising awareness of how even the most basic mathematical concepts can help us make sense of large-scale environmental challenges.This presentation is designed at the simplest level possible, avoiding complex formulas to focus on core ideas. We will look at how math acts like a map, helping us track how energy and resources move through our world. By using simple math models, we can learn how to design systems that last and discover better ways to care for our environment.The talk provides an overview of existing discussions on sustainability rather than stating final results or proposing fixed solutions. Please do not see this as a talk to attend passively; instead, I invite you to engage with your own suggestions,

Talk 2: Rafayel Barkhudaryan: Physics-Informed Neural Networks for Fully Nonlinear PDE’s

About the speaker: Dr. Rafayel Barkhudaryan, Vice-Rector for Scientific Affairs at Yerevan State University, is an expert in numerical analysis, scientific computing, and PDE methods. With leadership roles at major mathematical institutions and international research experience, his work combines theoretical rigor and computational insight.  

Abstract: Physics-Informed Neural Networks (PINNs) provide a mesh-free framework for solving partial differential equations by embedding the equations into the training process. This talk focuses on fully nonlinear PDEs, with particular emphasis on convergence. We discuss theoretical and numerical aspects of convergence, key challenges arising from nonlinearity, and illustrate results on representative examples.”

Talk 3: Francesco Dal Corso: Bifurcations and wrinkling instabilities (and restabilization) in ultra-thin parallelogram-shaped hyperelastic membranes 

About the speaker: Dr. Francesco Dal Corso at the University of Trento conducts research on the mechanics of solids and structural instability, including elastic localization, strain gradient effects, and geometric mechanics. His contributions connect mathematical modeling with experimental and theoretical insights into wrinkling and structural phenomena.  

Abstract: Wrinkling is a commonly observed out-of-plane instability in membrane structures due to their extremely low bending-to-stretching stiffness ratio. It has been extensively investigated for symmetric membrane geometries and boundary conditions that induce planar non-uniform stress states by preventing the lateral contraction at the edges, and is also known to potentially display self-restabilization. This presentation outlines a recent investigation into an initially flat, parallelogram-shaped hyperelastic membrane, focusing on the influence of the inclination angle defining  the membrane shape as a deviation from the rectangular geometry. It is shown that wrinkling can occur either centrally or at the two opposite obtuse-angled corners—even for small inclination angles—during stretching with unconstrained lateral contraction, a condition under which the flat configuration for the rectangular counterpart remains always stable.

Three distinct evolutions of the wrinkling pattern are numerically identified, all ultimately leading to corner localized wrinkles. This final state may arise (i) directly, without a prior bifurcation, or after the appearance of central wrinkling that either (ii) restabilizes or (iii) separates and migrates toward the corners. A closed-form expression for the critical wrinkling condition is derived by combining a perturbation approach with an energy based method in the framework of linear elasticity. This provides an accurate estimate of the onset and pattern of central wrinkling. The present findings reveal new pathways in wrinkling pattern evolution and introduce a novel approach to unconventional boundary value problems, with potential applications ranging from lightweight structural systems to flexible electronics