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

Real Algebra Seminar
Speaker: Niladri Sekhar Patra, IIT Bombay
Host: Manoj Kumar Keshari
Title: Netzer and Plaumann - Geometry of linear matrix inequality.
Time, day and date: 11:30:00 AM – 12:45:00 PM, Wednesday, June 10 
Venue: Ramanujan Hall
Abstract: - 

Algebraic groups seminar
Speaker: Ankita Parashar, IIT Bombay, Mumbai
Host: Shripad Garge
Title: Review of Digne-Michel
Time, day and date: 4:00:00 PM - 6:00:00 PM, Wednesday, June 10
Venue: Room No .105
Abstract: We restart our seminar on "Representations of finite groups of Lie type" with this review.

Real Algebra Seminar
Speaker: Amrutha Ruddarranu
Host: Manoj Kumar Keshari
Title: Ruiz – A basic theory of power series ring.
Time, day and date: 10:00:00 AM – 11:15:00 AM, Friday, June 12
Venue: Ramanujan Hall
Abstract: -

Real Algebra Seminar
Speaker: Niladri Sekhar Patra, IIT Bombay
Host: Manoj Kumar Keshari
Title: Netzer and Plaumann - Geometry of linear matrix inequality.
Time, day and date: 11:30:00 AM – 12:45:00 PM, Friday, June 12
Venue: Ramanujan Hall
Abstract: - 

Algebraic groups seminar
Speaker: Shripad M Garge, IIT Bombay, Mumbai
Title: Schur Weyl duality V
Time, day and date: 4:00:00 PM - 6:00:00 PM, Friday, June 12
Venue: Room No .105
Abstract: We complete our discussion on the Schur-Weyl duality

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.

Topology Seminar
Speaker: Bittu Singh, IIT Bombay
Host: Rekha Santhanam
Title: Applications of Rational Homotopy Theory
Time, day and date: 11:30:00 AM – 12:30:00 PM, Thursday, June 25
Venue: Room 215
Abstract: In my previous two talks, we discussed how Bousfield and Gugenheim reformulated Sullivan's rational homotopy theory within the framework of model categories and established a Quillen equivalence between suitable rational spaces and commutative differential graded algebras over Q.

In this talk, we begin with some applications of rational homotopy theory. First, we will see how rational homotopy theory provides a simple explanation for why the non-torsion part of the homotopy groups of spheres is concentrated in certain degrees, a result originally proved by Serre. We will then discuss another major application of rational homotopy theory, namely the solution of the closed geodesic problem due to Vigué-Poirrier and Sullivan, which relates the algebraic structure of the rational cohomology ring of a manifold to the existence of infinitely many closed geodesics.

Lectures on Digne-Michel
Speaker: Chayan
Host: Shripad M. Garge
Title: Digne-Michel
Time, day and date: 4:00:00 PM – 5:00:00 PM, Thursday, June 24
Venue: Room 105
Abstract: -

Postdoc extension talk
Speaker: Sucharita Biswas, IIT Bombay
Host: S Krishnan
Title: Classification of Wilf Equivalence and Shape Wilf Equivalence classes for POPs and Short Pattern Sets
Time, day and date: 10:30:00 AM - 11:30:00 AM, Monday, June 29
Venue: Ramanujan Hall
Abstract: Permutation pattern avoidance is a central topic in enumerative combinatorics. In this talk, I will discuss Wilf equivalence and shape Wilf equivalence for permutation patterns, with a particular focus on partially ordered patterns (POPs) and short pattern sets. Partially ordered patterns generalize the classical notion of permutation patterns by allowing certain entries of a pattern to be incomparable. I will present a complete Wilf equivalence classification of POPs of sizes $3$, $4$, and $5$ whose connected components are chains, thereby confirming a conjecture of Dimitrov posed during the problem session of the British Combinatorial Conference 2024 (BCC30). I will also describe recent results on shape Wilf equivalence for families of claw-shaped POPs. In particular, we prove that several such families are shape Wilf equivalent and obtain enumerative formulas for the corresponding avoidance classes.
Turning to short pattern sets, I will present a complete classification of shape Wilf equivalence classes for triples of patterns of length $3$. This work extends to a complete classification of quadruples and quintuples of patterns of length $3$, obtained in subsequent joint work. If time permits, I will conclude with a brief discussion of pattern avoidance in matchings, highlighting its rich connections with shape Wilf equivalence and related bijective phenomena.

Topology seminar
Speaker: Bittu Singh, IIT Bombay
Host: Rekha Santhanam
Title: Applications of Rational Homotopy Theory
Time, day and date: 4:00:00 PM – 4:40:00 PM, Monday, June 29
Venue: Room 215
Abstract: We now have all the tools from rational homotopy theory to algebraically model free loop spaces, which is key to its rational cohomology ring.
We continue the talk by presenting the solution to the closed geodesic problem due to Vigué-Poirrier and Sullivan. This solution relates the algebraic structure of the rational cohomology ring of a manifold to the existence of infinitely many closed geodesics.

Topology seminar
Speaker: Sudharshan Gurjar, IIT Bombay
Host: Rekha Santhanam
Title: Eilenberg MacLane and Moore spaces in algebraic geometry.
Time, day and date: 4:40:00 PM – 5:20:00 PM, Monday, June 29
Venue: Room 215
Abstract: I will make some comments about Eilenberg MacLane and Moore spaces in the setting of complex manifolds/complex algebraic geometry, with special focus on complex surfaces.