Special Colloquium
Speaker: Apala Majumdar, University of Manchester
Host: Neela Nataraj
Title: Continuum Theories for Liquid Crystals and their Applications
Time, day and date: 12:00:00 PM – 1:00:00 PM, Thursday, November 06
Venue: Ramanujan Hall
Abstract: Liquid crystals are classical examples of partially ordered materials that combine fluidity with the directionality and ordering of solids. Liquid crystals are anisotropic materials, with direction-dependent physical, optical and rheological properties, making them the working material of choice for a range of opto-electronic devices, e.g., liquid crystal displays, photonics, sensors, photovoltaics etc. In this talk, we review the mathematical theories for two canonical liquid crystal phases: nematic and smectic liquid crystals. Nematic liquid crystals are complex liquids with orientational ordering or special material directions whereas smectic liquid crystals can be regarded as layered liquid crystals, i.e., orientationally ordered layers of liquid crystal molecules with the layers stacked on top of each other. We focus on Landau-de Gennes type theories for these phases and describe the essential mathematical frameworks - the liquid crystal order parameters, the free energies, the governing systems of partial differential equations and their solution landscapes. We then discuss the applications of these theories to a prototype liquid crystal device - the planar bistable nematic device. We conclude with some recent work on inverse problems in the Landau-de Gennes theory for nematic liquid crystals, i.e., how to reconstruct material properties from relevant experimental measurements using Bayesian methods? All collaborations will be acknowledged throughout the talk.

Student Seminar
Speaker: Suraj Mishra, IIT Bombay
Host: Suman Kumar Sahoo
Title: Rooted Tree Modules
Time, day and date: 5:30:00 PM – 6:30:00 PM, Thursday, November 06
Venue: Class 215
Abstract: In this talk we will discuss a particular type of module over path algebra of a locally bound Quiver, called a rooted tree module and a combinatorial criterion for checking the indecomposability of the rooted tree module. If time permits, we can also talk about the direct sum decomposition of a decomposable rooted tree module into indecomposable summands.

Analysis seminar
Speaker: Prof. S. Thangavelu
Host: Sanjoy Pusti
Title: On Hardy's inequality for fractional powers of the sublaplacian
Time, day and date: 4:00:00 PM – 5:15:00 PM, Friday, November 07
Venue: Ramanujan Hall
Abstract: In these lectures we plan to give an introduction to Hardy's inequality for fractional powers of the sublaplacian on the Heisenberg group. We will recall the case of the standard Laplacian on $ \R^n $ and give a proof of Hardy's inequality for $ (-Delta)^s $ using extension problem and trace Hardy inequality. We will then develop necessary background for studying the modified extension problem for the sublaplacian, establish an analogue of trace Hardy inequality and deduce Hardy's inequality.

Student Seminar
Speaker: Om Milind Joglekar, IIT Bombay
Host: Suman Kumar Sahoo
Title: Classification of Moore graphs
Time, day and date: 5:30:00 PM – 6:30:00 PM, Friday, November 07
Venue: Room 215
Abstract: Moore graphs are the “perfect” examples in the degree–diameter problem — regular graphs that exactly meet the Moore bound for given degree k and diameter d. They’re extremely rare, and understanding when they can exist turns out to be a surprisingly rigid question. In this talk I’ll look at Moore graphs in general diameter and show how strong algebraic constraints narrow down the possibilities. Specializing to diameter 2, this leads to the famous condition that k can only be 3, 5, 7 or 57. *The asterisk in the title is because the k=57 case is still an unsolved problem. All in all, we know every Moore graph that exists except possibly the one corresponding to k=57.