Talk
Speaker: Dr. Aniruddha Seal, Department of Mathematics, IISc, Bangalore
Host: Neela Nataraj
Title: Numerical Analysis of Finite Element Methods for Time-Fractional Problems
Time, day and date: 3:15:00 PM – 4:15:00 PM, Wednesday, January 28
Venue: Online (https://us06web.zoom.us/j/6950684207?pwd=VkNmYzFBd0c0QWx3azhJODJ0QUp1Zz09&omn=81584666321 Meeting ID: 695 068 4207 Passcode: 802747)
Abstract: Fractional differential equations arise naturally in models of anomalous diffusion, phase separation, and nonlocal transport phenomena. Their inherent nonlocality poses significant analytical and numerical challenges, particularly in the construction of stable and accurate discretization schemes. Time-fractional models, in particular, are widely used to describe processes with memory effects and nonlocal temporal behavior, and require careful numerical treatment supported by rigorous mathematical analysis. 
In this talk, we present finite element formulations based on C0 interior penalty and weak Galerkin frameworks for time-fractional problems. We discuss the ideas used to establish stability and convergence of the presented schemes, and incorporate numerical experiments that support the theoretical results. The talk highlights how careful mathematical analysis and appropriate discretization strategies lead to reliable and accurate simulation of nonlocal time-dependent problems.

Real Algebraic Geometry and Combinatorial Optimization Seminar
Speaker: Luca Wellmeier, UiT - The Arctic University of Norway
Host: Sudhir R. Ghorpade
Title: Hierarchies in Polynomial Optimization
Time, day and date: 5:15:00 PM - 6:15:00 PM, Wednesday, January 28
Venue: Ramanujan Hall
Abstract: Polynomial optimization provides a unifying framework for problems arising in combinatorics, quantum information, power systems, and robotics, among many more - thereof also many well-known NP-hard problems. This motivates the study of systematic relaxations rather than exact solution methods. The goal of this talk is to give a brief introduction to the Moment-SOS hierarchy, a sequence of semidefinite relaxations rooted in real algebraic geometry. From one viewpoint, polynomial nonnegativity is approximated by membership in the sum-of-squares cone, connecting the theory to classical work on Hilbert's 14th problem and Positivstellensätze. From the dual viewpoint, the same hierarchy arises from truncated moment problems and the reconstruction of measures. This duality yields a theoretically rich class of tractable algorithms for computing tight bounds on polynomial optimization problems, which have been proven useful in many domains.

Monge-Ampere equation
Speaker: Sooraj AP, IIT Bombay
Host: Harsha Hutridurga
Title: On the Monge-Ampere equation
Time, day and date: 11:30:00 AM – 12: 45:00 PM, Thursday, January 29
Venue: Room 215
Abstract: In these lectures, we will study the existence and regularity of the solutions to the Monge-Ampere equation. The pre-requisites from convex analysis will be recalled/introduced as and when necessary, during the lectures. The primary references followed are (1) the Bourbaki lecture by Alessio Figalli, (2) the 2017 book by Figalli and (3) a Bulletin of AMS article by Guido De Philippis and Figalli.

Student APS
Speaker: Pradip Kumar Maity, IIT Bombay
Host: Suman Kumar Sahoo
Title: Determining lower order perturbations from partial Cauchy data
Time, day and date: 2:00:00 PM – 3:00:00 PM, Thursday, January 29
Venue: Ramanujan Hall
Abstract: This is my second aps. In this talk, we will talk about the Calder\'{o}n problem for biharmonic operators with partial boundary data.

Commutative Algebra Seminar
Speaker: Prof. Tony J P, IIT Bombay
Title: Modular invariant theory and Steenrod operators II
Time, day and date: Thursday, January 29
Venue: Ramanujan Hall
Abstract: -

Algebraic groups seminar
Speaker: Dipendra Prasad, IIT Bombay
Host: Shripad Garge
Title: Representations of finite groups of Lie type, an overview, II
Time, day and date: 4:00:00 PM – 5:30:00 PM, Thursday, January 29
Venue: Room 215
Abstract: We continue with the overview of the subject.

Liquid Crystals
Speaker: Prof. Apala Majumdar, FRSE, FIMA, Department of Mathematics, University of Manchester, UK
Host: Parthanil Roy
Title: The Mathematics of Liquid Crystals - Theory and Applications
Time, day and date: 12:00:00 PM – 1:00:00 PM, Friday, January 30
Venue: Ramanujan Hall
Online: https://us06web.zoom.us/j/6950684207?pwd=VkNmYzFBd0c0QWx3azhJODJ0QUp1Zz09&omn=83584890072 (Meeting ID: 695 068 4207 Passcode: 802747)
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.

Liquid Crystals
Speaker: Prof. Apala Majumdar, FRSE, FIMA, Department of Mathematics, University of Manchester, UK
Host: Parthanil Roy
Title: The Mathematics of Liquid Crystals - Theory and Applications
Time, day and date: 2:30:00 PM – 3:30:00 PM, Friday, January 30
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.