Commutative Algebra Talk
Speaker: Dr. Shrikant Shekhar
Host: Ananthnarayan Hariharan
Title: Rationality of the Poincaré Series and the Tor-Vanishing property of local rings
Time, day and date: 4:00:00 PM – 5:00:00 PM, Monday, June 15
Venue: Online (https://meet.google.com/ptp-hivy-csz)
Abstract: Attached (https://drive.google.com/drive/folders/1SlhC3HhNTTBJxX2b1Sbvkbck7EKwLUyJ)

Real Algebra Seminar
Speaker: Amrutha Ruddarranu
Host: Manoj Kumar Keshari
Title: A basic theory of power series
Time, day and date: 10:00:00 AM – 11:15:00 AM, Tuesday, June 16
Venue: Ramanujan Hall
Abstract: -

Real Algebra Seminar
Speaker: Niladri Sekhar Patara
Host: Manoj Kumar Keshari
Title: Geometry of linear matrix inequality
Time, day and date: 11:30:00 AM - 12:45:00 PM, Tuesday, June 16
Venue: Ramanujan Hall
Abstract: -

Algebraic groups seminar
Speaker: Ankita Parashar, IIT Bombay
Host: Shripad Garge
Title: Review of Digne-Michel II
Time, day and date: 4:00:00 PM - 6:00:00 PM, Wednesday, June 17
Venue: Room No .105
Abstract: We continue the review of Digne-Michel's book on the representations of finite groups of Lie type. This lecture focuses on the third chapter of the book.

Real Algebra Seminar
Speaker: Amrutha Ruddarranu
Host: Manoj Kumar Keshari
Title: A basic theory of power series
Time, day and date: 10:00:00 AM – 11:15:00 AM, Thursday, June 18
Venue: Ramanujan Hall
Abstract: -

Topology Seminar
Speaker: Aparajita Karmakar, IIT Bombay
Host: Rekha Santhanam
Title: Self-duality in the Burnside category - from spans to spectra
Time, day and date: 11:30:00 AM – 12:30:00 PM, Thursday, June 18
Venue: Room 215
Abstract: The Burnside category is a central object in equivariant homotopy and cohomology theories which encodes the structures of Mackey functors. Classically it is defined using spans of finite G-sets, a description that depends on the finiteness of G. Self-duality of the Burnside category is nearly transparent in its simplicity, but it is an algebraic artifact of a much deeper topological phenomenon. Each orbit has an equivariant suspension spectrum, and there is an equivalent definition of the Burnside category with morphisms given by stable equivariant morphisms. This definition is more general in the sense that it does not depend on the finiteness of the group. The stable orbit spectra satisfy an equivariant self-duality that induces the self duality of the Burnside category itself.

Real Algebra Seminar
Speaker: Niladri Sekhar Patara
Host: Manoj Kumar Keshari
Title: Geometry of linear matrix inequality
Time, day and date: 11:30:00 AM - 12:45:00 PM, Thursday, June 18
Venue: Ramanujan Hall
Abstract: -

Presynopsis Seminar
Speaker: Aamir Yousuf, IIT Bombay-Monash
Host:    Neela Nataraj
Title: New Discretizations for Coupled Multiphysics Models in Slender Geometries
Time, day and date: 11:30:00 AM - 1:00:00 PM, Friday, June 19
Venue: Ramanujan Hall (https://monash.zoom.us/j/87664111088?pwd=6wjE91IGhsBVrOf2UOicTMpapwoP5F.1)
Abstract: (https://drive.google.com/file/d/1xxllARz58CvuHm2go7oJ6RNz0FTT8SBL/view)

This talk addresses the numerical analysis of fourth-order partial differential equations (PDEs) arising in the modeling of thin and very thin elastic structures and coupled thermo-mechanical systems. Classical conforming finite elements for fourth-order problems, such as the Argyris element, require $C^1$-continuity across element boundaries, imposing significant implementation complexity and higher regularity demands on the solution. To overcome these difficulties, we employ nonstandard finite element methods, namely, the Morley, discontinuous Galerkin (dG), and $C^0$ interior penalty (C0IP) finite elements, which relax these continuity requirements while maintaining optimal approximation properties.

Three interconnected problem classes will be addressed in the talk. For the \textit{biharmonic wave equation}, we analyze explicit Leapfrog and implicit Newmark time-stepping schemes, establishing that explicit schemes suffer from a significantly more restrictive Courant--Friedrichs--Lewy (CFL) condition than classical second-order wave problems, and derive optimal error estimates via a modified Ritz projection on $H^2_0(\Omega)$. For the \textit{coupled thermoelastic diffusion and thermo-poroelastic systems}, a fourth-order hyperbolic equation for plate deflection is coupled with second-order parabolic equations for temperature and chemical potential (or pore pressure). A compatible combination of the Newmark and Crank--Nicolson schemes for the hyperbolic and parabolic components, respectively, yields quasi-optimal spatial convergence and quadratic temporal convergence.  For the \textit{dynamic von K\'{a}rm\'{a}n equations} governing geometrically nonlinear large deflections of very thin plates, the nonlinear coupling causes the classical Newmark scheme to lose unconditional stability. We resolve this through an energy-conserving discrete reformulation, establishing unconditional stability, existence and uniqueness of discrete solutions, and optimal a priori error estimates in the energy norm across all three nonstandard finite element frameworks. All theoretical findings are validated through numerical experiments.

Algebraic groups seminar
Speaker: Shripad M Garge, IIT Bombay
Title: Schur Weyl duality V
Time, day and date: 4:00:00 PM - 6:00:00 PM, Friday, June 19
Venue: Room No .105
Abstract: We complete our discussion on the Schur Weyl duality.