Numerical Analysis seminar
Speaker: Lara Theallier (Humboldt-Universitat zu Berlin)
Host: Neela Nataraj
Title: Lower energy bounds in the Landau-de Gennes model for nematic liquid crystals
Time, day and date: 2:30:00 PM, Monday, March 17
Venue: Ramanujan Hall
Abstract: The mathematics and simulation of new materials is one of the challenges in semilinear partial differential equations with a surprisingly complicated energy landscape. Pierre-Gilles de Gennes received the Nobel Prize in physics in 1991 for methods developed for studying order phenomena in simple systems that can be generalized to more complex forms of matter, in particular to liquid crystals and polymers. The Landau-de Gennes minimization problem in the focus of the presentation is a very simplified model in nematic liquid crystals. It is a semi-linear energy minimization problem of the Ginzburg-Landau-type for superconductors. The presentation introduces some mathematics and focuses on the discretization by the nonconforming enhanced Crouzeix-Raviart finite element method. After some global weak convergence results, the discretization is utilized for the computation of guaranteed lower energy bounds. Numerical results show convergence and comparisons also for a conforming variant.

Commutative Algebra seminar
Speaker: Samarendra Sahoo (IIT Bombay)
Host: Tony Puthenpurakal
Title: The Auslander-Reiten Conjecture
Time, day and date: 4:00:00 PM, Tuesday, March 18
Venue: Ramanujan Hall
Abstract: The Auslander-Reiten conjecture, proposed in 1975, states that if Ext^i(M,M)=Ext^i(M,R)=0 for all i≥1, then the finitely generated module M over a commutative ring R with unity must be projective. Although the conjecture remains unresolved, several partial results have been established. Notably, it holds true when R is a complete intersection (CI) or a Cohen-Macaulay (CM) normal ring. In this lecture series, we will explore the work of D. Ghosh and R. Takahashi, who identified a specific class of modules that satisfy the conjecture.