Analysis Seminar
Speaker: Dr. Mayuresh Londhe, Sabanci University, Istanbul
Host: Prachi Mahajan
Title: Equi distribution of zeros of polynomials with integer coefficients
Time, day and date: 4:00:00 PM – 5:00:00 PM, Friday, January 02
Venue: Room 114
Abstract: In this talk, we discuss an equi distribution result for the zeros of certain polynomials with integer coefficients. In particular, this gives an equidistribution result for the Galois conjugates of algebraic units, in the spirit of Bilu's work. As an application, we give a solution to the Schur-Siegel-Smyth trace problem. This talk is based on a joint work with Norm Levenberg.

Partial Differential Equations Seminar
Speaker: Sanchit Chaturvedi, New York University
Host: Harsha Hutridurga
Title: Global problems in kinetic theory
Time, day and date: 4:00:00 PM – 5:00:00 PM, Wednesday, January 07
Venue: Ramanujan Hall
Abstract: In this talk I will discuss the problem of global existence and stability of special solutions to kinetic collisional equations that model the dynamics of gas particles. In the first half of the talk I will consider the problem of stability of global Maxwellians for the Landau equations (and Vlasov--Poisson--Landau for the charged case) on a torus and how collisions cause the global Maxwellians to be stable. In the second half I will focus on global problems on the whole space and discuss how the problem of stability is way richer in this case due to the complex interaction of entropic dissipation (due to collisions) and dispersion

Coagulation-fragmentation equations
Speaker: Ram Gopal Jaiswal, IIT Bombay
Host: Harsh Hutridurga
Title: A first course on the Coagulation-Fragmentation equations.
Time, day and date: 11:00:00 AM – 12:30:00 PM, Thursday, January 08
Venue: Ramanujan Hall
Abstract: This series of lectures focuses on the existence and uniqueness of weak solutions to the continuous coagulation equation under suitable assumptions on the coagulation kernel. We study separately the regimes in which solutions conserve total mass and those in which mass conservation may fail in finite time due to a phenomenon known as gelation. We then incorporate fragmentation processes, treating linear and nonlinear (collision-induced) fragmentation separately, and establish the corresponding existence and uniqueness results. Moreover, we prove the existence of mass-conserving stationary (equilibrium) solutions to coagulation equations with linear fragmentation under appropriate assumptions on the coagulation and fragmentation kernels

Talk
Speaker: Utsab Sarkar, IIT Bombay
Host: Mayukh Mukherjee
Title: Stability in Critical Variational Problems
Time, day and date: 5:00:00 PM – 6:00:00 PM, Thursday, January 08
Venue: Online (meet.google.com/gzx-igvq-thu)
Abstract: In the first part (joint work with Souptik Chakraborty), we study quantitative stability for the fractional Hardy–Sobolev inequality and prove a sharp Bianchi-Egnell-type stability estimate showing that near-equality implies proximity to the manifold of minimizers. We then analyze the associated Euler-Lagrange equation, establishing a qualitative Struwe decomposition for near-solutions via Palais-Smale analysis, and showing that finite bubbling is the only obstruction to compactness in all dimensions. Finally, in the low-dimensional range (2s<N<6s-2t), we develop a sharp quantitative multi-bubble theory in which the Euler-Lagrange deficit controls linearly the distance to the multi-bubble manifold and weak interactions between distinct bubbles.
In the second part (joint work with Mayukh Mukherjee), we discuss Dirichlet Gagliardo Nirenberg inequalities on compact manifolds with boundary. We identify the sharp Euclidean and half-space thresholds, establish quantitative stability via transfer from the model geometries, and describe the compactness–bubbling dichotomy at the threshold in terms of boundary geometry.

Time-Harmonic Maxwell's equations
Speaker: Kshitij Sinha, IIT Bombay
Host: Harsha Hutridurga
Title: Time-Harmonic Maxwell's equations - Regularity theory and related topics
Time, day and date: 11:00:00 AM – 12:00:00 PM, Monday, January 12
Venue: Ramanujan Hall
Abstract: In the first seminar of this series, we propose to introduce the time-harmonic Maxwell's equations. Few necessary ingredients to the rigorous study of these equations such as the Friedrich's inequality, the Helmholtz decomposition for L2 vector fields will be discussed. In this talk, we also plan to prove a conditional well-posedness results for these equations.

Stefan Problem Seminar
Speaker: Neeraj Rawat, IIT Bombay
Host: Harsha Hutridurga
Title: Stefan problem - A free boundary value problem
Time, day and date: 11:00:00 AM – 12:30:00 PM, Tuesday, January 13
Venue: Ramanujan Hall
Abstract: In the first Lecture of this series, we will prove the existence and uniqueness of classical solution to the one-phase stefan problem in dimension one.Throughout this series of lectures, we will mainly follow the work of Avner Friedmann.

Short Course
Speaker: Prof. Jerome Droniou, University of Montpellier
Host: Parthanil Roy
Title: Introduction to a polytopal complex: the Discrete De Rham method
Time, day and date: 9:30:00 AM – 11:00:00 AM, Thursday, January 15
Venue: Ramanujan Hall (https://us06web.zoom.us/j/6950684207?pwd=VkNmYzFBd0c0QWx3azhJODJ0QUp1Zz09&omn=85848985788 ID: 695 068 4207 Passcode: 802747)
Abstract: I will start by explaining what the de Rham complex is and, through examples, why it is important for the theoretical analysis of certain partial differential equations involving gradient, curl or divergence operators.
I will then present the Discrete De Rham (DDR) method, an arbitrary-order discretisation of the de Rham complex that is applicable on generic polyhedral meshes. We will see that the construction of the method is entirely based on mimicking integration-by-parts properties (for the gradient, the curl and the divergence), and is hierarchical: we construct the space and discrete operators starting from the edges, then going on the faces, then on the elements.
I will highlight the main properties of the DDR method, which allows for convergence analysis of schemes built on it. A particular focus will be on the notion of "adjoint consistency" which arises due to the non-conformity of the method. I will detail such a convergence analysis on the example of the Stokes equations in curl-curl formulation.

Coagulation-Fragmentation equations
Speaker: Ram Gopal Jaiswal, IIT Bombay
Host: Harsha Hutridurga
Title: A first course on the Coagulation-Fragmentation equations.
Time, day and date: 11:00:00 AM – 12:30:00 PM, Thursday, January 15
Venue: Ramanujan Hall
Abstract: This series of lectures focuses on the existence and uniqueness of weak solutions to the continuous coagulation equation under suitable assumptions on the coagulation kernel. We study separately the regimes in which solutions conserve total mass and those in which mass conservation may fail in finite time due to a phenomenon known as gelation. We then incorporate fragmentation processes, treating linear and nonlinear (collision-induced) fragmentation separately, and establish the corresponding existence and uniqueness results. Moreover, we prove the existence of mass-conserving stationary (equilibrium) solutions to coagulation equations with linear fragmentation under appropriate assumptions on the coagulation and fragmentation kernels.

Short Course
Speaker: Prof. Jerome Droniou, University of Montpellier
Host: Parthanil Roy
Title: Introduction to a polytopal complex: the Discrete De Rham method
Time, day and date: 4:00:00PAM – 05:30:00PAM, Thursday, January 15
Venue: Ramanujan Hall (https://us06web.zoom.us/j/6950684207?pwd=VkNmYzFBd0c0QWx3azhJODJ0QUp1Zz09&omn=85848985788 ID: 695 068 4207 Passcode: 802747)
Abstract: I will start by explaining what the de Rham complex is and, through examples, why it is important for the theoretical analysis of certain partial differential equations involving gradient, curl or divergence operators.
I will then present the Discrete De Rham (DDR) method, an arbitrary-order discretisation of the de Rham complex that is applicable on generic polyhedral meshes. We will see that the construction of the method is entirely based on mimicking integration-by-parts properties (for the gradient, the curl and the divergence), and is hierarchical: we construct the space and discrete operators starting from the edges, then going on the faces, then on the elements.
I will highlight the main properties of the DDR method, which allows for convergence analysis of schemes built on it. A particular focus will be on the notion of "adjoint consistency" which arises due to the non-conformity of the method. I will detail such a convergence analysis on the example of the Stokes equations in curl-curl formulation.

Maxwell's equations
Speaker: Kshitij Sinha, IIT Bombay
Host: Harsha Hutridurga
Title: Time-Harmonic Maxwell's equations - Regularity theory and related topics
Time, day and date: 11:15:00 AM – 12:30:00 PM, Monday, January 19
Venue: Ramanujan Hall
Abstract: -

Thesis Defence
Speaker: Sakshi, IIT Bombay
Host: Sudhir R. Ghorpade
Title: Structure and Symmetries of Affine Cartesian Codes and Constructions of Convolutional Codes
Time, day and date: 2:30:00 PM - 3:30:00 PM, Monday, January 19
Venue: Ramanujan Hall
Abstract: We give a presentation of the PhD thesis which focuses mainly on two topics in algebraic coding theory, namely affine Cartesian codes and convolutional codes. For affine Cartesian codes, we investigate the minimum weight codewords and automorphism groups. For convolutional codes, we develop new constructions of Maximum Distance Profile (MDP).

Book Reading
Speaker: Prof. Chandrashekhar Khare, Dept of Maths, UCLA
Host: S. Krishnan
Title: Chasing a Conjecture
Time, day and date: 3:30:00 PM – 5:00:00 PM, Monday, January 19
Venue: Ramanujan Hall
Abstract: The speaker, Chandrashekhar Khare is a Professor at the Dept of Maths, UCLA and recently authored a book "Chasing a Conjecture" on which he will speak. Excerpts from the book will be read. The event is a public lecture on a Conjecture in Number Theory but does not expect mathematical maturity from the audience.

Pre-synopsis Seminar
Speaker: Chayan Karmakar, IIT Bombay
Host: Ravi Raghunathan
Title: Character Values at Special Elements in Complex Classical Groups
Time, day and date: 4:00:00 PM – 5:00:00 PM, Monday, January 19
Venue: Room 215
Abstract: -

Stefan Problem
Speaker: Neeraj Rawat, IIT Bombay
Host: Harsha Hutridurga
Title: Stefan problem - A free boundary problem
Time, day and date: 11:15:00 AM – 12:30:00 PM, Tuesday, January 20
Venue: Ramanujan Hall
Abstract: -

Coagulation-Fragmentation equations
Speaker: Ram Gopal Jaiswal, IIT Bombay
Host: Harsha Hutridurga
Title: A first course on the Coagulation-Fragmentation equations.
Time, day and date: 9:30:00 AM – 11:00:00 AM, Wednesday, January 21
Venue: Ramanujan Hall
Abstract: -

Talk
Speaker: Mohmedmunavvar Mubarak Bapu, IIT Kanpur
Host: Debanjana Mitra
Title: Controllability results for two systems of nonlinear partial differential equations
Time, day and date: 2:30:00 PM – 3:30:00 PM, Wednesday, January 21
Venue: Online
Link: https://us06web.zoom.us/j/87110001554?pwd=8Hys9A00FlTb9gmOd1ZfALkwAE120T.1
(Meeting ID: 871 1000 1554 Passcode: 464604)
Abstract: In this talk, we study controllability results for two nonlinear partial differential equation systems. The first one is the Grey–Scott reaction–diffusion system, and the second one is a fourth-order pseudo-parabolic equation with a source term.
For both systems, we first study the null controllability of the corresponding linearized problems. In the case of the Gray–Scott system, the equation is linearized around a positive trajectory. Using Carleman inequalities, we obtain an observability inequality, whichleads to the null controllability of the linearized system. The nonlinear controllability result is then obtained by applying Kakutani’s fixed-point theorem, giving local controllability to a trajectory.
For the pseudo-parabolic equation, we first rewrite the fourth-order equation as a coupled parabolic-elliptic system of second order. We then show that null controllability of the parabolic part is equivalent to null controllability of the original pseudo-parabolic equation. Using Carleman estimates, we obtain the null controllability result for the linear parabolic equation. Finally, the controllability of the nonlinear system is obtained by using the source term method together with the Banach fixed-point theorem.

Mathematics Colloquium
Speaker: Prof. Joachim Rosenthal, University of Zurich, Switzerland
Host: Sudhir R. Ghorpade
Title: The Standardization Process to Post-Quantum Cryptography
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, January 21
Venue: Ramanujan Hall
Abstract: Public key cryptography has been at the center of modern cryptography. It is not only used for the exchange of secret keys but also for the authentication of entities on the Internet, for digital signatures and for the construction of digital currencies.
Until a few years ago most public key systems were based on the hardness of factoring integers or on the hardness of the discrete logarithm problem in an elliptic curve.
With the realization that a quantum computer would make many practically used public key cryptographic systems obsolete it became an important research topic to design public key systems which are expected to be secure even if a powerful quantum computer would exist.
This new area of research is called post-quantum cryptography and there has been in the last couple of years a lot of efforts to come up with new standards to be used in everyday applications.
The lecture will overview the currently used systems and the current ongoing standardization process. We will also explain the underlying mathematical problems.

Commutative Algebra seminar
Speaker: Tony Puthenpurakal, IIT Bombay
Title: Modular invariant theory and Steenrod operators
Time, day and date: 3:00:00 PM - 4:00:00 PM, Thursday, January 2
Venue: Ramanujan Hall
Abstract: We study modular invariant theory. We investigate applications of Steenrod operators on i

Algebraic groups seminar
Speaker: Dipendra Prasad, IIT Bombay
Host: Shripad Garge
Title: Finite Groups of Lie Type
Time, day and date: 4:00:00 PM – 5:00:00 PM, Thursday, January 22
Venue: Room 215
Abstract: General introduction to the whole subject as well as to the seminar series. The seminar will be based on the book "Representations of finite groups of Lie type" by Digne and Michel, 2nd edition (2020).

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.

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.