Wed, July 10, 2019
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8:00am [3:00pm] Anisa Chorwadwala : IISER Pune Description: Mathematics Colloquium Talk 1. Speaker: Anisa Chorwadwala. Affiliation: IISER Pune. Date and Time: Wednesday 10 July, 3:00 pm - 4:00 pm. Venue: Room 216, Department of Mathematics. Title: A Glimpse of Shape Optimization Problems. Abstract: The following questions arise quite naturally from what we see around us. Why are soap bubbles that float in air approximately spherical? Why does a herd of reindeer form a round shape when attacked by wolves? Of all geometric objects having a certain property, which ones have the greatest area or volume; and of all objects having a certain property, which ones have the least perimeter or surface area? These problems have been stimulating much mathematical thought. Mathematicians have been trying to answer such questions and this has led to a branch of mathematical analysis known as “shape optimisation problems”. A typical shape optimisation problem is, as the name suggests, to find a shape which is optimal in the sense that it minimises a certain cost functional while satisfying given constraints. Isoperimetric problems form a special class of shape optimisation problems. A typical isoperimetric problem is to enclose a given area with a shortest possible curve. In many cases, the functional being minimised depends on solution/s of a given partial differential equation defined on a variable domain. The plan is to give a glimpse of a few shape optimization problems we have worked on. [4:30pm] Apala Majumdar : University of Bath. Description: Mathematics Colloquium Talk 2. Speaker: Apala Majumdar. Affiliation: University of Bath. Date and Time: Wednesday 10 July, 4:30 pm - 5:30 pm. Venue: Room 216, Department of Mathematics. Title: Solution Landscapes in the Landau-de Gennes Theory for Nematic Liquid Crystals. Abstract: Nematic liquid crystals are quintessential examples of soft matter, intermediate in character between solids and liquids, with long-range orientational order. We model spatio-temporal pattern formation for nematic liquid crystals on two-dimensional polygonal geometries, which are relevant for applications. We work within the powerful continuum Landau-de Gennes theory for nematic liquid crystals. We illustrate the complex solution landscapes on square domains as a function of the square size, temperature and boundary conditions, reporting a novel Well Order Reconstruction Solution on nnao-scale geometries. We discuss generalizations to arbitrary 2D polygons, using symmetry-based and variational techniques to study stable patterns in distinguished asymptotic limits. We conclude by reviewing recent work on stabilization of interior vortices by magneto-nematic coupling in ferronematics, which leads to new possibilities for magneto-mechanical effects in nematic-based materials. This is joint work with researchers in Peking University, Shanghai Jiao Tong, IIT Delhi, IIT Bombay, Illinois Technological University and University of Verona.