Liquid Crystals
Speaker: Prof. Apala Majumdar, FRSE, FIMA, Department of Mathematics, University of Manchester, UK
Host: Prof. Neela Nataraj
Title: The Mathematics of Liquid Crystals - Theory and Applications
Time, day and date: 12:00:00 PM – 1:00:00 PM, Friday, January 23
Venue: Ramanujan Hall
Abstract: This mini-course will comprise four lectures on the mathematics of liquid crystals and modelling of liquid crystal applications. Liquid crystals are complex materials that combine fluidity with the ordering of solids and consequently, have fascinating physical, mechanical and rheological properties. Liquid crystals are best known as the working material of choice for the multi-billion dollar display industry. We will give a non-technical introduction to liquid crystals - their history, physics and applications, followed by an overview of the main mathematical theories for liquid crystals. We will conclude the lecture course with examples of mathematical modelling of real-life liquid crystal systems.

Commutative Algebra Seminar
Speaker: Prof J. K. Verma
Host: Tony J P
Title: Lipman's conjecture about adjoints of ideals in regular local rings
Time, day and date: 12:00:00 PM – 1:00:00 PM, Friday, January 23
Venue: Room 215
Abstract: Joseph Lipman introduced adjoints of ideals in regular local rings in 1994 for improving the Briancon-Skoda theorem for integral closure of ideals.
He conjectured that for any ideals I in a regular local ring of dimension $d$ $adj(I^{n+1})= I adj(I^n)$ for all $n\geq s(I)-1$ where $s(I)$ is the dimension of the closed fibre when Spec R is blown at the closed set $V(I).$
There is also the conjecture about subadditivity: adj(IJ)\subset ad(I) adj(J)$ for all ideals in regular local rings. Both these conjectures are open. Howald, Cutkosky-Lipman and Takagi Watanabe proved these in some cases using convex geometry and certain vanishing theorems for sheaf cohomology modules.
I will present a new solution to these conjectures for complete ideals in regular local rings of dimension two, using Zariski's theory of complete ideals, a formula of Hoskin-Deligne and mixed multiplicities of ideals.